From c27b259c5e79cef2b5589ec42e545bae541f8105 Mon Sep 17 00:00:00 2001
From: Sepand KASHANI <sepand@kashani.ch>
Date: Fri, 15 Sep 2023 09:52:52 +0200
Subject: [PATCH] v1.0.0 docs.

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diff --git a/WARNINGS.log b/WARNINGS.log
index f5145c5a..5023df83 100644
--- a/WARNINGS.log
+++ b/WARNINGS.log
@@ -1,4 +1,64 @@
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/lipschitz.ipynb:286: WARNING: invalid syntax (<unknown>, line 24) in document 'guide/lipschitz'
+/home/sep/Documents/Repositories/pyxu/doc/fair/howto.rst:2: WARNING: Duplicate explicit target name: "catalogue website".
+/home/sep/Documents/Repositories/pyxu/doc/fair/howto.rst:33: WARNING: invalid syntax (<unknown>, line 2) in document 'fair/howto'
+Parsed source in `python` block:
+concatenations: from pyxu.opt.solver import GradientDescent
+block source:   ModuleNotFoundError: No module named 'pyxu.opt.solver.GradientDescent'
+/home/sep/Documents/Repositories/pyxu/doc/fair/plugins/pyxu-eigh.rst:164: ERROR: Content block expected for the "raw" directive; none found.
+/home/sep/Documents/Repositories/pyxu/doc/fair/plugins/pyxu-gradient-descent.rst:164: ERROR: Content block expected for the "raw" directive; none found.
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:129: WARNING: Title underline too short.
+
+Implicit Functionals: The Undercover Agents 🕵️‍♀️
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:129: WARNING: Title underline too short.
+
+Implicit Functionals: The Undercover Agents 🕵️‍♀️
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:27: WARNING: File not found: 'api/operator.interop.html#general'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:27: WARNING: File not found: 'api/abc.html#pyxu.abc.Map.apply'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:27: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffFunc.grad'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:27: WARNING: File not found: 'api/abc.html#pyxu.abc.ProxFunc.prox'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:34: WARNING: File not found: 'api/abc.html#pyxu.abc.Func'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:61: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffFunc'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:76: WARNING: File not found: 'api/operator.interop.html#pyxu.operator.interop.from_torch'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:76: WARNING: File not found: 'api/operator.interop.html#pyxu.operator.interop.from_jax'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:81: WARNING: File not found: 'api/abc.html#pyxu.abc.ProxFunc'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:97: WARNING: File not found: 'api/abc.html#pyxu.abc.ProxFunc.moreau_envelope'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:124: WARNING: File not found: 'api/abc.html#pyxu.abc.ProxDiffFunc'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:124: WARNING: File not found: 'api/abc.html#pyxu.abc.LinFunc'
+/home/sep/Documents/Repositories/pyxu/doc/guide/funcs.ipynb:124: WARNING: File not found: 'api/abc.html#pyxu.abc.QuadraticFunc'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:11: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:17: WARNING: File not found: 'api/operator.interop.html#general'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:17: WARNING: File not found: 'api/abc.html#pyxu.abc.Map.apply'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:17: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp.adjoint'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:17: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffMap.jacobian'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:46: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:55: WARNING: File not found: 'api/abc.html#pyxu.abc.Map.apply'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:66: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp.adjoint'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:100: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:102: WARNING: File not found: 'api/abc.html#pyxu.abc.Map.lipschitz'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:102: WARNING: File not found: 'api/abc.html#pyxu.abc.Map.estimate_lipschitz'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:108: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp.svdvals'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:110: WARNING: File not found: 'api/abc.html#pyxu.abc.SquareOp.trace'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:112: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp.pinv'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:118: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:118: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp.from_array'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:124: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:129: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffMap'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:134: WARNING: File not found: 'api/abc.html#pyxu.abc.Map.apply'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:134: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:136: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffMap.jacobian'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:146: WARNING: File not found: 'api/operator.interop.html#pyxu.operator.interop.from_torch'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:146: WARNING: File not found: 'api/operator.interop.html#pyxu.operator.interop.from_jax'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:148: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffMap'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:153: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp'
+/home/sep/Documents/Repositories/pyxu/doc/guide/fwdops.ipynb:153: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffMap'
+/home/sep/Documents/Repositories/pyxu/doc/guide/hpc.ipynb:219: WARNING: File not found: 'api/runtime.html#pyxu.runtime.Precision'
+/home/sep/Documents/Repositories/pyxu/doc/guide/lipschitz.ipynb:30: WARNING: File not found: 'api/abc.html#pyxu.abc.Map.lipschitz'
+/home/sep/Documents/Repositories/pyxu/doc/guide/lipschitz.ipynb:30: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffMap.diff_lipschitz'
+/home/sep/Documents/Repositories/pyxu/doc/guide/lipschitz.ipynb:40: WARNING: File not found: 'api/abc.html#pyxu.abc.Map.estimate_lipschitz'
+/home/sep/Documents/Repositories/pyxu/doc/guide/lipschitz.ipynb:298: WARNING: File not found: 'api/index.html'
+/home/sep/Documents/Repositories/pyxu/doc/guide/lipschitz.ipynb:298: WARNING: File not found: 'api/abc/arithmetic.html#'
+/home/sep/Documents/Repositories/pyxu/doc/guide/lipschitz.ipynb:286: WARNING: invalid syntax (<unknown>, line 24) in document 'guide/lipschitz'
 Parsed source in `python` block:
 concatenations: # Access Lipschitz constant of an operator 'op'
 lip_const = op.lipschitz
@@ -32,21 +92,95 @@ block source:   >> op1 = difffunc * linop;
                 >> op2.diff_lipschitz == linop.lipschitz * diffmap.diff_lipschitz
                 True
                 ...
-/Users/mmjasime/Documents/Github/pyxu/doc/fair/howto.rst:2: WARNING: Duplicate explicit target name: "catalogue website".
-/Users/mmjasime/Documents/Github/pyxu/doc/fair/howto.rst:33: WARNING: invalid syntax (<unknown>, line 2) in document 'fair/howto'
+/home/sep/Documents/Repositories/pyxu/doc/examples/contributing.ipynb:42: WARNING: invalid syntax (<unknown>, line 5) in document 'examples/contributing'
 Parsed source in `python` block:
-concatenations: import pyxu.opt.solver.GradientDescent
-block source:   ModuleNotFoundError: No module named 'pyxu.opt.solver.GradientDescent'
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:640: ERROR: Unexpected indentation.
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:638: WARNING: Inline interpreted text or phrase reference start-string without end-string.
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:644: WARNING: Block quote ends without a blank line; unexpected unindent.
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:653: WARNING: Inline interpreted text or phrase reference start-string without end-string.
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:655: WARNING: Definition list ends without a blank line; unexpected unindent.
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:765: ERROR: Unexpected indentation.
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:763: WARNING: Inline interpreted text or phrase reference start-string without end-string.
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:768: WARNING: Block quote ends without a blank line; unexpected unindent.
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:109: WARNING: File not found: 'examples/TODO'
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:156: WARNING: expected ':' (<unknown>, line 29) in document 'examples/DifferentialOperators'
+concatenations: try:
+    from pyxu.opt.solver import GradientDescent
+except ImportError as e:
+    print(e)
+block source:   !pip install pyxu-gradient-descent
+/home/sep/Documents/Repositories/pyxu/doc/fair/score.rst:29: WARNING: Bullet list ends without a blank line; unexpected unindent.
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:33: WARNING: File not found: 'api/abc.html#pyxu.abc.Map.apply'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:33: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffMap.jacobian'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:33: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffFunc.grad'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:33: WARNING: File not found: 'api/abc.html#pyxu.abc.ProxFunc.prox'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:33: WARNING: File not found: 'api/abc.html#pyxu.abc.LinOp.adjoint'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:39: WARNING: File not found: 'api/abc/arithmetic.html'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:41: WARNING: File not found: 'api/abc.html#pyxu.abc.arithmetic.Rule'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:42: WARNING: File not found: 'api/abc.html#pyxu.abc.arithmetic.ScaleRule'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:43: WARNING: File not found: 'api/abc.html#pyxu.abc.arithmetic.ArgScaleRule'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:44: WARNING: File not found: 'api/abc.html#pyxu.abc.arithmetic.ArgShiftRule'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:45: WARNING: File not found: 'api/abc.html#pyxu.abc.arithmetic.AddRule'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:46: WARNING: File not found: 'api/abc.html#pyxu.abc.arithmetic.ChainRule'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:47: WARNING: File not found: 'api/abc.html#pyxu.abc.arithmetic.PowerRule'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:48: WARNING: File not found: 'api/abc.html#pyxu.abc.arithmetic.TransposeRule'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:53: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffFunc'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:53: WARNING: File not found: 'api/abc.html#pyxu.abc.DiffMap'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:95: WARNING: File not found: 'api/operator/blocks.html#pyxu.operator.coo_block'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:95: WARNING: File not found: 'api/operator/blocks.html#pyxu.operator.block'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:95: WARNING: File not found: 'api/operator/blocks.html#pyxu.operator.block_diag'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:95: WARNING: File not found: 'api/operator/blocks.html#pyxu.operator.stack'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:95: WARNING: File not found: 'api/operator/blocks.html#pyxu.operator.vstack'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:95: WARNING: File not found: 'api/operator/blocks.html#pyxu.operator.hstack'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:18: WARNING: invalid syntax (<unknown>, line 1) in document 'guide/algebra'
+Parsed source in `python` block:
+block source: >> op1 + op2  # Addition of two operators
+              >> op1 * op2  # Composition of two operators
+              >> op ** 3    # Exponentiation of an operator
+              >> op.argscale(c)  # Dilation by a scalar 'c'
+              >> op.argshift(x)  # Shifting by a vector 'x'
+              >> 4 * op  # Scaling by a scalar
+              >> op.T  # Transposing
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:55: WARNING: invalid syntax (<unknown>, line 1) in document 'guide/algebra'
+Parsed source in `python` block:
+block source: >> h = f * L
+              >> h.grad(x) = L.jacobian(x).adjoint(f.grad(L(x)))
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:64: WARNING: cannot assign to function call here. Maybe you meant '==' instead of '='? (<unknown>, line 1) in document 'guide/algebra'
+Parsed source in `python` block:
+block source: op.apply(arr) = lhs.apply(rhs.apply(arr))
+              op.lipschitz = lhs.lipschitz * rhs.lipschitz
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:71: WARNING: cannot assign to function call here. Maybe you meant '==' instead of '='? (<unknown>, line 1) in document 'guide/algebra'
+Parsed source in `python` block:
+block source: op.prox(arr, tau) = rhs.adjoint(lhs.prox(rhs.apply(arr), tau))
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:77: WARNING: cannot assign to function call here. Maybe you meant '==' instead of '='? (<unknown>, line 1) in document 'guide/algebra'
+Parsed source in `python` block:
+block source: op.jacobian(arr) = lhs.jacobian(rhs.apply(arr)) * rhs.jacobian(arr)
+              op.diff_lipschitz =
+                  linear * linear  => 0
+                  linear * diff    => lhs.lipschitz * rhs.diff_lipschitz
+                  diff   * linear  => lhs.diff_lipschitz * (rhs.lipschitz ** 2)
+                  diff   * diff    => infty
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:88: WARNING: cannot assign to function call here. Maybe you meant '==' instead of '='? (<unknown>, line 1) in document 'guide/algebra'
+Parsed source in `python` block:
+block source: op.grad(arr) = lhs.grad(rhs.apply(arr)) @ rhs.jacobian(arr).asarray()
+/home/sep/Documents/Repositories/pyxu/doc/guide/algebra.ipynb:100: WARNING: invalid syntax (<unknown>, line 1) in document 'guide/algebra'
+Parsed source in `python` block:
+block source: >> coo_block(([A(500,1000), B(1,1000), C(500,500), D(1,3)],  # data
+                 ...      [[0, 1, 0, 2],  # i
+                 ...       [0, 0, 2, 1],  # j
+                          ]),grid_shape=(3, 3))
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:17: WARNING: File not found: 'api/opt.solver.html#pyxu.opt.solver.CG'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:29: WARNING: File not found: 'api/opt.solver.html#pyxu.opt.solver.PGD'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:58: WARNING: File not found: 'api/opt.solver.html#pyxu.opt.solver.CondatVu'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:58: WARNING: File not found: 'api/opt.solver.html#pyxu.opt.solver.PD3O'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:58: WARNING: File not found: 'api/opt.solver.html#pyxu.opt.solver.ADMM'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:58: WARNING: File not found: 'api/opt.solver.html#pyxu.opt.solver.ChambollePock'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:74: WARNING: File not found: 'api/opt.solver.html#pyxu.opt.solver.DouglasRachford'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:76: WARNING: File not found: 'api/opt.solver.html#pyxu.opt.solver.Adam'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:127: WARNING: File not found: 'api/opt.stop.html'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:144: WARNING: File not found: 'api/abc.html#pyxu.abc.Solver'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:144: WARNING: File not found: 'api/abc.html#pyxu.abc.Solver.m_init'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:144: WARNING: File not found: 'api/abc.html#pyxu.abc.Solver.m_step'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:148: WARNING: File not found: 'api/abc.html#pyxu.abc.Solver.fit'
+/home/sep/Documents/Repositories/pyxu/doc/guide/algorithms.ipynb:66: WARNING: invalid syntax (<unknown>, line 1) in document 'guide/algorithms'
+Parsed source in `python` block:
+block source: >> K = vstack([K_1, ..., K_J])
+              >> H = hstack([h_1, ..., h_J])
+/home/sep/Documents/Repositories/pyxu/doc/guide/diff_ops.ipynb:11: WARNING: File not found: 'api/operator/linop.html#derivatives'
+/home/sep/Documents/Repositories/pyxu/doc/guide/diff_ops.ipynb:18: WARNING: File not found: 'api/operator/linop.html#pyxu.operator.PartialDerivative'
+/home/sep/Documents/Repositories/pyxu/doc/guide/diff_ops.ipynb:535: WARNING: File not found: 'api/operator/linop.html#pyxu.operator.Gradient'
+/home/sep/Documents/Repositories/pyxu/doc/guide/diff_ops.ipynb:545: WARNING: File not found: 'api/operator/linop.html#pyxu.operator.Hessian'
+/home/sep/Documents/Repositories/pyxu/doc/guide/diff_ops.ipynb:93: WARNING: expected an indented block after function definition on line 20 (<unknown>, line 29) in document 'guide/diff_ops'
 Parsed source in `python` block:
 concatenations: def D(f):
     """
@@ -76,8 +210,8 @@ block source:   def finite_difference(
                         gpu: bool = False,
                         dtype: typ.Optional[pyct.DType] = None,
                         sampling: typ.Union[pyct.Real, cabc.Sequence[pyct.Real, ...]] = 1,
-                    ) -> pyct.OpT
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:171: WARNING: expected ':' (<unknown>, line 29) in document 'examples/DifferentialOperators'
+                    ) -> pyct.OpT:
+/home/sep/Documents/Repositories/pyxu/doc/guide/diff_ops.ipynb:107: WARNING: expected an indented block after function definition on line 20 (<unknown>, line 29) in document 'guide/diff_ops'
 Parsed source in `python` block:
 concatenations: def D(f):
     """
@@ -107,8 +241,8 @@ block source:   def gaussian_derivative(
                         gpu: bool = False,
                         dtype: typ.Optional[pyct.DType] = None,
                         sampling: typ.Union[pyct.Real, cabc.Sequence[pyct.Real, ...]] = 1,
-                    ) -> pyct.OpT
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:680: WARNING: expected an indented block after function definition on line 139 (<unknown>, line 148) in document 'examples/DifferentialOperators'
+                    ) -> pyct.OpT:
+/home/sep/Documents/Repositories/pyxu/doc/guide/diff_ops.ipynb:579: WARNING: expected an indented block after function definition on line 139 (<unknown>, line 148) in document 'guide/diff_ops'
 Parsed source in `python` block:
 concatenations: def D(f):
     """
@@ -258,7 +392,7 @@ block source:   def Gradient(
                     parallel: bool = False,
                     **diff_kwargs,
                 ) -> pyct.OpT:
-/Users/mmjasime/Documents/Github/pyxu/doc/examples/DifferentialOperators.ipynb:694: WARNING: expected an indented block after function definition on line 139 (<unknown>, line 152) in document 'examples/DifferentialOperators'
+/home/sep/Documents/Repositories/pyxu/doc/guide/diff_ops.ipynb:593: WARNING: expected an indented block after function definition on line 139 (<unknown>, line 152) in document 'guide/diff_ops'
 Parsed source in `python` block:
 concatenations: def D(f):
     """
@@ -412,63 +546,19 @@ block source:   def Hessian(
                     parallel: bool = False,
                     **diff_kwargs,
                 ) -> pyct.OpT:
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/algebra.ipynb:18: WARNING: invalid syntax (<unknown>, line 1) in document 'guide/algebra'
-Parsed source in `python` block:
-block source: >> op1 + op2  # Addition of two operators
-              >> op1 * op2  # Composition of two operators
-              >> op ** 3    # Exponentiation of an operator
-              >> op.argscale(c)  # Dilation by a scalar 'c'
-              >> op.argshift(x)  # Shifting by a vector 'x'
-              >> 4 * op  # Scaling by a scalar
-              >> op.T  # Transposing
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/algebra.ipynb:54: WARNING: invalid syntax (<unknown>, line 1) in document 'guide/algebra'
-Parsed source in `python` block:
-block source: >> h = f * L
-              >> h.grad(x) = L.jacobian(x).adjoint(f.grad(L(x)))
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/algebra.ipynb:63: WARNING: cannot assign to function call here. Maybe you meant '==' instead of '='? (<unknown>, line 1) in document 'guide/algebra'
-Parsed source in `python` block:
-block source: op.apply(arr) = lhs.apply(rhs.apply(arr))
-              op.lipschitz = lhs.lipschitz * rhs.lipschitz
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/algebra.ipynb:70: WARNING: cannot assign to function call here. Maybe you meant '==' instead of '='? (<unknown>, line 1) in document 'guide/algebra'
-Parsed source in `python` block:
-block source: op.prox(arr, tau) = rhs.adjoint(lhs.prox(rhs.apply(arr), tau))
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/algebra.ipynb:76: WARNING: cannot assign to function call here. Maybe you meant '==' instead of '='? (<unknown>, line 1) in document 'guide/algebra'
-Parsed source in `python` block:
-block source: op.jacobian(arr) = lhs.jacobian(rhs.apply(arr)) * rhs.jacobian(arr)
-              op.diff_lipschitz =
-                  linear * linear  => 0
-                  linear * diff    => lhs.lipschitz * rhs.diff_lipschitz
-                  diff   * linear  => lhs.diff_lipschitz * (rhs.lipschitz ** 2)
-                  diff   * diff    => infty
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/algebra.ipynb:87: WARNING: cannot assign to function call here. Maybe you meant '==' instead of '='? (<unknown>, line 1) in document 'guide/algebra'
-Parsed source in `python` block:
-block source: op.grad(arr) = lhs.grad(rhs.apply(arr)) @ rhs.jacobian(arr).asarray()
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/algebra.ipynb:98: WARNING: invalid syntax (<unknown>, line 1) in document 'guide/algebra'
-Parsed source in `python` block:
-block source: >> coo_block(([A(500,1000), B(1,1000), C(500,500), D(1,3)],  # data
-                 ...      [[0, 1, 0, 2],  # i
-                 ...       [0, 0, 2, 1],  # j
-                          ]),grid_shape=(3, 3))
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/algorithms.ipynb:66: WARNING: invalid syntax (<unknown>, line 1) in document 'guide/algorithms'
-Parsed source in `python` block:
-block source: >> K = vstack([K_1, ..., K_J])
-              >> H = hstack([h_1, ..., h_J])
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/funcs.ipynb:129: WARNING: Title underline too short.
-
-Implicit Functionals: The Undercover Agents 🕵️‍♀️
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-/Users/mmjasime/Documents/Github/pyxu/doc/guide/funcs.ipynb:129: WARNING: Title underline too short.
-
-Implicit Functionals: The Undercover Agents 🕵️‍♀️
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/interop/jax.py:docstring of pyxu.operator.interop.jax._from_jax:: WARNING: py:class reference target not found: pyxu.operator.interop.jax.JaxArray
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/interop/jax.py:docstring of pyxu.operator.interop.jax._to_jax:: WARNING: py:class reference target not found: pyxu.operator.interop.jax.JaxArray
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/blocks.py:docstring of pyxu.operator.blocks.coo_block:33: WARNING: py:mod reference target not found: pyxu.operator.blocks
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/linop/pad.py:docstring of pyxu.operator.linop.pad.Pad.__init__:10: WARNING: py:class reference target not found: pyxu.operator.linop.pad.Pad.WidthSpec
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/linop/filter.py:docstring of pyxu.operator.linop.filter.MovingAverage:30: WARNING: py:class reference target not found: pyxu.operator.linop.filter.IndexSpec
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: (Integer
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: Integer)
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: ((Integer
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: Integer)
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: (Integer
-/Users/mmjasime/Documents/Github/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: Integer))
+/home/sep/Documents/Repositories/pyxu/doc/references.rst:5: WARNING: Citation [ProxAlg] is not referenced.
+/home/sep/Documents/Repositories/pyxu/doc/references.rst:8: WARNING: Citation [ProxSplit] is not referenced.
+/home/sep/Documents/Repositories/pyxu/doc/references.rst:19: WARNING: Citation [P2] is not referenced.
+/home/sep/Documents/Repositories/pyxu/doc/references.rst:20: WARNING: Citation [GaussProcesses] is not referenced.
+/home/sep/Documents/Repositories/pyxu/doc/references.rst:21: WARNING: Citation [SubGauss] is not referenced.
+/home/sep/Documents/Repositories/pyxu/doc/references.rst:29: WARNING: Citation [UQ_MCMC] is not referenced.
+/home/sep/Documents/Repositories/pyxu/src/pyxu/operator/blocks.py:docstring of pyxu.operator.blocks.coo_block:33: WARNING: py:mod reference target not found: pyxu.operator.blocks
+/home/sep/Documents/Repositories/pyxu/src/pyxu/operator/linop/pad.py:docstring of pyxu.operator.linop.pad.Pad.__init__:10: WARNING: py:class reference target not found: pyxu.operator.linop.pad.Pad.WidthSpec
+/home/sep/Documents/Repositories/pyxu/src/pyxu/operator/linop/filter.py:docstring of pyxu.operator.linop.filter.MovingAverage:30: WARNING: py:class reference target not found: pyxu.operator.linop.filter.IndexSpec
+/home/sep/Documents/Repositories/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: (Integer
+/home/sep/Documents/Repositories/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: Integer)
+/home/sep/Documents/Repositories/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: ((Integer
+/home/sep/Documents/Repositories/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: Integer)
+/home/sep/Documents/Repositories/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: (Integer
+/home/sep/Documents/Repositories/pyxu/src/pyxu/operator/linop/diff.py:docstring of pyxu.operator.linop.diff.Hessian:65: WARNING: py:class reference target not found: Integer))
+/home/sep/Documents/Repositories/pyxu/doc/examples/contributing.ipynb:42: WARNING: Lexing literal_block '!pip install pyxu-gradient-descent' as "python" resulted in an error at token: '!'. Retrying in relaxed mode.
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diff --git a/_downloads/01d31b53f3906f9c7594bb738943953e/linop-4_01.pdf b/_downloads/01d31b53f3906f9c7594bb738943953e/linop-4_01.pdf
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diff --git a/_downloads/0e4825835a3d6d1b8ed46f992d78d573/linop-3_00.pdf b/_downloads/0e4825835a3d6d1b8ed46f992d78d573/linop-3_00.pdf
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diff --git a/_downloads/0f65a5f8726612599305eeb053b028a0/linop-13_01.pdf b/_downloads/0f65a5f8726612599305eeb053b028a0/linop-13_01.pdf
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diff --git a/_downloads/176694d4afd8c703e2f166119010b4a5/operator-12.py b/_downloads/176694d4afd8c703e2f166119010b4a5/operator-12.py
deleted file mode 100644
index 8a895bdc..00000000
--- a/_downloads/176694d4afd8c703e2f166119010b4a5/operator-12.py
+++ /dev/null
@@ -1,27 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import DirectionalLaplacian
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-z = peaks(xx, yy)
-directions1 = np.zeros(shape=(2, z.size))
-directions1[0, :z.size // 2] = 1
-directions1[1, z.size // 2:] = 1
-directions2 = np.zeros(shape=(2, z.size))
-directions2[1, :z.size // 2] = -1
-directions2[0, z.size // 2:] = -1
-arg_shape = z.shape
-dop = DirectionalLaplacian(arg_shape=arg_shape, directions=[directions1, directions2])
-out = dop.unravel(dop(z.ravel()))
-plt.figure()
-h = plt.pcolormesh(xx, yy, z, shading='auto')
-plt.quiver(x, x, directions1[1].reshape(arg_shape), directions1[0].reshape(xx.shape))
-plt.quiver(x, x, directions2[1].reshape(arg_shape), directions2[0].reshape(xx.shape), color='red')
-plt.colorbar(h)
-plt.title('Signal and directions of derivatives')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out.squeeze(), shading='auto')
-plt.colorbar(h)
-plt.title('Directional Laplacian')
\ No newline at end of file
diff --git a/_downloads/17ea64344184b13eb3942803c2022ec7/linop-9.pdf b/_downloads/17ea64344184b13eb3942803c2022ec7/linop-9.pdf
index ce8e9671e0325a3664dcdc130b870dd685b9f7ef..f154ca06552aa4e3fe21d2c8c53f0c5b42db2479 100644
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diff --git a/_downloads/191962a7e06446281208e5b3542ba6d8/operator-13_02.png b/_downloads/191962a7e06446281208e5b3542ba6d8/operator-13_02.png
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diff --git a/_downloads/1cd8e614728fc68270743fa172a043f0/linop-11_00.pdf b/_downloads/1cd8e614728fc68270743fa172a043f0/linop-11_00.pdf
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diff --git a/_downloads/1e56b08165a1aaab1d61109119a49a7f/opt-2.py b/_downloads/1e56b08165a1aaab1d61109119a49a7f/opt-2.py
deleted file mode 100644
index 50219928..00000000
--- a/_downloads/1e56b08165a1aaab1d61109119a49a7f/opt-2.py
+++ /dev/null
@@ -1,31 +0,0 @@
-import matplotlib.pyplot as plt
-import numpy as np
-import pyxu.operator as pxo
-from pyxu.experimental._dev import DownSampling, FirstDerivative
-from pyxu.opt.solver import PD3O
-
-x = np.repeat(np.asarray([0, 2, 1, 3, 0, 2, 0]), 10)
-N = x.size
-
-D = FirstDerivative(size=N, kind="forward")
-D.lipschitz = D.estimate_lipschitz()
-
-downsample = DownSampling(size=N, downsampling_factor=3)
-y = downsample(x)
-loss = (1 / 2) * pxo.SquaredL2Norm(y.size).argshift(-y)
-F = loss * downsample
-F.diff_lipschitz = F.estimate_diff_lipschitz()
-
-pd3o = PD3O(f=F, g=0.01 * pxo.L1Norm(N), h=0.1 * pxo.L1Norm(N), K=D)
-x0, z0 = np.zeros((2, N))
-pd3o.fit(x0=x0, z0=z0)
-x_recons = pd3o.solution()[0]
-
-plt.figure()
-plt.stem(x, linefmt="C0-", markerfmt="C0o")
-mask_ids = np.where(downsample.downsampling_mask)[0]
-markerline, stemlines, baseline = plt.stem(mask_ids, y, linefmt="C3-", markerfmt="C3o")
-markerline.set_markerfacecolor("none")
-plt.stem(x_recons, linefmt="C1--", markerfmt="C1s")
-plt.legend(["Ground truth", "Observation", "PD3O Estimate"])
-plt.show()
\ No newline at end of file
diff --git a/_downloads/1f117a6a28d0313d35ba2f9b8f29caee/linop-8.pdf b/_downloads/1f117a6a28d0313d35ba2f9b8f29caee/linop-8.pdf
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diff --git a/_downloads/23893637b3327ac8e6693fb7ff55df1e/linop-21_01.pdf b/_downloads/23893637b3327ac8e6693fb7ff55df1e/linop-21_01.pdf
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delta 21
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delta 21
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diff --git a/_downloads/2567cfd1b90b151e14d7b845b313e372/operator-13_03.png b/_downloads/2567cfd1b90b151e14d7b845b313e372/operator-13_03.png
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diff --git a/_downloads/2a27831b457a8e11354eed9aa36db333/operator-13_03.pdf b/_downloads/2a27831b457a8e11354eed9aa36db333/operator-13_03.pdf
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diff --git a/_downloads/32a76fb4fe0570a9a6b22a68761ff535/experimental-sampler-1_00_00.pdf b/_downloads/32a76fb4fe0570a9a6b22a68761ff535/experimental-sampler-1_00_00.pdf
index ca3af06c748670f041c97a8dc84b36bd11f1296d..04d305430c156d293054082111bf42a91c32386e 100644
GIT binary patch
delta 7671
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diff --git a/_downloads/346e1717be7da8fa867cbbe2294f196a/operator-21_02.pdf b/_downloads/346e1717be7da8fa867cbbe2294f196a/operator-21_02.pdf
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diff --git a/_downloads/40fedab1780635b89af691e5c4ea11fb/operator-18.py b/_downloads/40fedab1780635b89af691e5c4ea11fb/operator-18.py
deleted file mode 100644
index c6cfdede..00000000
--- a/_downloads/40fedab1780635b89af691e5c4ea11fb/operator-18.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Sobel
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-sobel = Sobel(arg_shape)
-out = sobel(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/_downloads/427c29d9fe06f23074682a0c3cb7f952/operator-15.png b/_downloads/427c29d9fe06f23074682a0c3cb7f952/operator-15.png
deleted file mode 100644
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diff --git a/_downloads/468910fa079d504203df7361bc14fe4f/operator-1_01.pdf b/_downloads/468910fa079d504203df7361bc14fe4f/operator-1_01.pdf
index 77e1513b218cafb0fe1663b7372117c91b9efa7a..31cffbd8dc16433896553c17e24f7ff0bc336b9b 100644
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delta 20
bcmbOcG$Uw3uqwNep^=e^f#v2X)qTtWN3I52

diff --git a/_downloads/46ba4351fee97ccd2e3d0aba89e7413d/linop-14.pdf b/_downloads/46ba4351fee97ccd2e3d0aba89e7413d/linop-14.pdf
index 17baa0aee30ce0969ecf1c8561634bd2f6db6e7e..ab53dfa2c59b1195ef29cc40e4d0d13c70e0a444 100644
GIT binary patch
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delta 22
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diff --git a/_downloads/4769d18f8e2c0bf193e34be59a343ebb/opt-3.py b/_downloads/4769d18f8e2c0bf193e34be59a343ebb/opt-3.py
deleted file mode 100644
index 2b58eeeb..00000000
--- a/_downloads/4769d18f8e2c0bf193e34be59a343ebb/opt-3.py
+++ /dev/null
@@ -1,58 +0,0 @@
-import matplotlib.pyplot as plt
-import numpy as np
-import pyxu.abc as pxa
-import pyxu.operator as pxo
-import scipy as sp
-from pyxu.opt.solver import ADMM
-
-N = 100  # Dimension of the problem
-
-# Generate piecewise-linear ground truth
-x_gt = np.array([10, 25, 60, 90])  # Knot locations
-a_gt = np.array([2, -4, 3, -2])  # Amplitudes of the knots
-gt = np.zeros(N)  # Ground-truth signal
-for n in range(len(x_gt)):
-    gt[x_gt[n] :] += a_gt[n] * np.arange(N - x_gt[n]) / N
-
-# Generate data (noisy samples at random locations)
-M = 20  # Number of data points
-rng = np.random.default_rng(seed=0)
-x_samp = rng.choice(np.arange(N // M), size=M) + np.arange(N, step=N // M)  # sampling locations
-sigma = 2 * 1e-2  # noise variance
-y = gt[x_samp] + sigma * rng.standard_normal(size=M)  # noisy data points
-
-# Data-fidelity term
-subsamp_mat = sp.sparse.lil_matrix((M, N))
-for i in range(M):
-    subsamp_mat[i, x_samp[i]] = 1
-G = pxa.LinOp.from_array(subsamp_mat.tocsr())
-F = 1 / 2 * pxo.SquaredL2Norm(dim=y.size).argshift(-y) * G
-F.diff_lipschitz = F.estimate_diff_lipschitz(method="svd")
-
-# Regularization term (promotes sparse second derivatives)
-deriv_mat = sp.sparse.diags(diagonals=[1, -2, 1], offsets=[0, 1, 2], shape=(N - 2, N))
-D = pxa.LinOp.from_array(deriv_mat)
-_lambda = 1e-1  # regularization parameter
-H = _lambda * pxo.L1Norm(dim=D.codim)
-
-# Solver for ADMM
-tau = 1 / _lambda  # internal ADMM parameter
-# Inverse operator to solve the linear system
-A_inv = sp.linalg.inv(G.gram().asarray() + (1 / tau) * D.gram().asarray())
-
-def solver_ADMM(arr, tau):
-    b = (1 / tau) * D.adjoint(arr) + G.adjoint(y)
-    return A_inv @ b.squeeze()
-
-
-# Solve optimization problem
-admm = ADMM(f=F, h=H, K=D, solver=solver_ADMM,show_progress=False)  # with solver
-admm.fit(x0=np.zeros(N), tau=tau)
-x_opt = admm.solution()  # reconstructed signal
-
-# Plots
-plt.figure()
-plt.plot(np.arange(N), gt, label="Ground truth")
-plt.plot(x_samp, y, "kx", label="Noisy data points")
-plt.plot(np.arange(N), x_opt, label="Reconstructed signal")
-plt.legend()
\ No newline at end of file
diff --git a/_downloads/4835132393171dc4fee6fa57fd1d6c6a/experimental-1_01_00.hires.png b/_downloads/4835132393171dc4fee6fa57fd1d6c6a/experimental-1_01_00.hires.png
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diff --git a/_downloads/5420c90dcdf9b097dbed8ebf47bc7a03/util-2.pdf b/_downloads/5420c90dcdf9b097dbed8ebf47bc7a03/util-2.pdf
index 0c6a330bea0c8f2e256e1d36ec72b9ea02a5583e..a4a41f07bccee8533c0a011275dca1481f171250 100644
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diff --git a/_downloads/557f177f4b474935fc904081afacebf3/operator-3.py b/_downloads/557f177f4b474935fc904081afacebf3/operator-3.py
deleted file mode 100644
index 725e0ddf..00000000
--- a/_downloads/557f177f4b474935fc904081afacebf3/operator-3.py
+++ /dev/null
@@ -1,40 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import PartialDerivative
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # Shape of our image
-# Specify derivative order at each direction
-df_dx = (1, 0)  # Compute derivative of order 1 in first dimension
-d2f_dy2 = (0, 2)  # Compute derivative of order 2 in second dimension
-d3f_dxdy2 = (1, 2)  # Compute derivative of order 1 in first dimension and der. of order 2 in second dimension
-# Instantiate derivative operators
-sigma = 2.0
-diff1 = PartialDerivative.gaussian_derivative(order=df_dx, arg_shape=arg_shape, sigma=sigma / np.sqrt(2))
-diff2 = PartialDerivative.gaussian_derivative(order=d2f_dy2, arg_shape=arg_shape, sigma=sigma / np.sqrt(2))
-diff = PartialDerivative.gaussian_derivative(order=d3f_dxdy2, arg_shape=arg_shape, sigma=sigma)
-# Compute derivatives
-out1 = (diff1 * diff2)(image.ravel()).reshape(arg_shape)
-out2 = diff(image.ravel()).reshape(arg_shape)
-# Plot derivatives
-fig, axs = plt.subplots(1, 3, figsize=(15, 4))
-im = axs[0].imshow(image)
-axs[0].axis("off")
-axs[0].set_title("f(x,y)")
-plt.colorbar(im, ax=axs[0])
-axs[1].imshow(out1)
-axs[1].axis("off")
-axs[1].set_title(r"$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$")
-plt.colorbar(im, ax=axs[1])
-
-axs[2].imshow(out2)
-axs[2].axis("off")
-axs[2].set_title(r"$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$")
-plt.colorbar(im, ax=axs[2])
-
-# Test approximation error
-plt.figure()
-plt.imshow(abs(out1 - out2) / abs(out2)), plt.colorbar()
\ No newline at end of file
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diff --git a/_downloads/5822ec21ae4dcb79a8910f34bb426b2a/operator-15.py b/_downloads/5822ec21ae4dcb79a8910f34bb426b2a/operator-15.py
deleted file mode 100644
index 6af655cf..00000000
--- a/_downloads/5822ec21ae4dcb79a8910f34bb426b2a/operator-15.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Gaussian
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-gaussian = Gaussian(arg_shape, sigma=3)
-out = gaussian(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/_downloads/59794358488e15e2bf1ca40d5f99cb9e/operator-12_01.pdf b/_downloads/59794358488e15e2bf1ca40d5f99cb9e/operator-12_01.pdf
deleted file mode 100644
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diff --git a/_downloads/5bc77603e37ab6857e35a64c763b0285/operator-13.py b/_downloads/5bc77603e37ab6857e35a64c763b0285/operator-13.py
deleted file mode 100644
index ddc93cd0..00000000
--- a/_downloads/5bc77603e37ab6857e35a64c763b0285/operator-13.py
+++ /dev/null
@@ -1,35 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import DirectionalHessian
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-z = peaks(xx, yy)
-directions1 = np.zeros(shape=(2, z.size))
-directions1[0, :z.size // 2] = 1
-directions1[1, z.size // 2:] = 1
-directions2 = np.zeros(shape=(2, z.size))
-directions2[1, :z.size // 2] = -1
-directions2[0, z.size // 2:] = -1
-arg_shape = z.shape
-d_hess = DirectionalHessian(arg_shape=arg_shape, directions=[directions1, directions2])
-out = d_hess.unravel(d_hess(z.ravel()))
-plt.figure()
-h = plt.pcolormesh(xx, yy, z, shading='auto')
-plt.quiver(x, x, directions1[1].reshape(arg_shape), directions1[0].reshape(xx.shape))
-plt.quiver(x, x, directions2[1].reshape(arg_shape), directions2[0].reshape(xx.shape), color='red')
-plt.colorbar(h)
-plt.title(r'Signal $\mathbf{f}$ and directions of derivatives')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[0], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla^2_{\mathbf{v}_0} \mathbf{f}$')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[1], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla_{\mathbf{v}_0} \nabla_{\mathbf{v}_{1}} \mathbf{f}$')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[2], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla^2_{\mathbf{v}_1} \mathbf{f}$')
\ No newline at end of file
diff --git a/_downloads/5be70851f96b004b61b84e14faba6d02/util-1.pdf b/_downloads/5be70851f96b004b61b84e14faba6d02/util-1.pdf
index 94a15e574fd4f4c70e85dfcccdb9b2356700db8c..8e452f2d4ce3b044ecfa34357349f9002e096827 100644
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diff --git a/_downloads/5c238fb268b33a8da224f181740013f5/operator-3_00.hires.png b/_downloads/5c238fb268b33a8da224f181740013f5/operator-3_00.hires.png
deleted file mode 100644
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diff --git a/_downloads/5e5b9b1c67e25e4482d76496b68f3b68/experimental-1.py b/_downloads/5e5b9b1c67e25e4482d76496b68f3b68/experimental-1.py
deleted file mode 100644
index d5ab99f6..00000000
--- a/_downloads/5e5b9b1c67e25e4482d76496b68f3b68/experimental-1.py
+++ /dev/null
@@ -1,70 +0,0 @@
-import matplotlib.pyplot as plt
-import numpy as np
-import pyxu.experimental.sampler as pxe_sampler
-import pyxu.operator as pxo
-import scipy as sp
-
-f = pxo.SquaredL2Norm(dim=1) / 2  # To sample 1D normal distribution (mean 0, variance 1)
-ula = pxe_sampler.ULA(f=f)  # Sampler with maximum step size
-ula_lb = pxe_sampler.ULA(f=f, gamma=1e-1)  # Sampler with small step size
-
-gen_ula = ula.samples(x0=np.zeros(1))
-gen_ula_lb = ula_lb.samples(x0=np.zeros(1))
-n_burn_in = int(1e3)  # Number of burn-in iterations
-for i in range(n_burn_in):
-    next(gen_ula)
-    next(gen_ula_lb)
-
-# Online statistics objects
-mean_ula = pxe_sampler.OnlineMoment(order=1)
-mean_ula_lb = pxe_sampler.OnlineMoment(order=1)
-var_ula = pxe_sampler.OnlineVariance()
-var_ula_lb = pxe_sampler.OnlineVariance()
-
-n = int(1e4)  # Number of samples
-samples_ula = np.zeros(n)
-samples_ula_lb = np.zeros(n)
-for i in range(n):
-    sample = next(gen_ula)
-    sample_lb = next(gen_ula_lb)
-    samples_ula[i] = sample
-    samples_ula_lb[i] = sample_lb
-    mean = float(mean_ula.update(sample))
-    var = float(var_ula.update(sample))
-    mean_lb = float(mean_ula_lb.update(sample_lb))
-    var_lb = float(var_ula_lb.update(sample_lb))
-
-# Theoretical variances of biased stationary distributions of ULA
-biased_var = 1 / (1 - ula._gamma / 2)
-biased_var_lb = 1 / (1 - ula_lb._gamma / 2)
-
-# Quantify goodness of fit of empirical distribution with theoretical distribution (Cramér-von Mises test)
-cvm = sp.stats.cramervonmises(samples_ula, "norm", args=(0, np.sqrt(biased_var)))
-cvm_lb = sp.stats.cramervonmises(samples_ula_lb, "norm", args=(0, np.sqrt(biased_var_lb)))
-
-# Plots
-grid = np.linspace(-4, 4, 1000)
-
-plt.figure()
-plt.title(
-    f"ULA samples (large step size) \n Empirical mean: {mean:.3f} (theoretical: 0) \n "
-    f"Empirical variance: {var:.3f} (theoretical: {biased_var:.3f}) \n"
-    f"Cramér-von Mises goodness of fit: {cvm.statistic:.3f}"
-)
-plt.hist(samples_ula, range=(min(grid), max(grid)), bins=100, density=True)
-plt.plot(grid, sp.stats.norm.pdf(grid), label=r"$p(x)$")
-plt.plot(grid, sp.stats.norm.pdf(grid, scale=np.sqrt(biased_var)), label=r"$p_{\gamma_1}(x)$")
-plt.legend()
-plt.show()
-
-plt.figure()
-plt.title(
-    f"ULA samples (small step size) \n Empirical mean: {mean_lb:.3f} (theoretical: 0) \n "
-    f"Empirical variance: {var_lb:.3f} (theoretical: {biased_var_lb:.3f}) \n"
-    f"Cramér-von Mises goodness of fit: {cvm_lb.statistic:.3f}"
-)
-plt.hist(samples_ula_lb, range=(min(grid), max(grid)), bins=100, density=True)
-plt.plot(grid, sp.stats.norm.pdf(grid), label=r"$p(x)$")
-plt.plot(grid, sp.stats.norm.pdf(grid, scale=np.sqrt(biased_var_lb)), label=r"$p_{\gamma_2}(x)$")
-plt.legend()
-plt.show()
\ No newline at end of file
diff --git a/_downloads/5ebda40b456c165df2ad890040597b6f/linop-15.pdf b/_downloads/5ebda40b456c165df2ad890040597b6f/linop-15.pdf
index 935f624363c9647e6bc7acca9114cb32ba735061..97673b8e69197bc995bdebdaf29427d0769c9f09 100644
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diff --git a/_downloads/5f62c6bb5301ff3e2502fc8625ddc3e8/linop-19.pdf b/_downloads/5f62c6bb5301ff3e2502fc8625ddc3e8/linop-19.pdf
deleted file mode 100644
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diff --git a/_downloads/67094c89382ad81380a52906901bb725/operator-17.py b/_downloads/67094c89382ad81380a52906901bb725/operator-17.py
deleted file mode 100644
index 74ffad5c..00000000
--- a/_downloads/67094c89382ad81380a52906901bb725/operator-17.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Laplace
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-laplace = Laplace(arg_shape)
-out = laplace(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/_downloads/673d72fb29625abae78650b04ff992cf/operator-21_00.pdf b/_downloads/673d72fb29625abae78650b04ff992cf/operator-21_00.pdf
deleted file mode 100644
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diff --git a/_downloads/73bedc7b7248ca036824dc8463b36828/operator-17.pdf b/_downloads/73bedc7b7248ca036824dc8463b36828/operator-17.pdf
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diff --git a/_downloads/7a311f51d351b440032a25d77b6b0f15/operator-21.py b/_downloads/7a311f51d351b440032a25d77b6b0f15/operator-21.py
deleted file mode 100644
index 9ef935ea..00000000
--- a/_downloads/7a311f51d351b440032a25d77b6b0f15/operator-21.py
+++ /dev/null
@@ -1,45 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import StructureTensor
-from pyxu.util.misc import peaks
-
-# Define input image
-n = 1000
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-nsamples = 2
-arg_shape = image.shape  # (1000, 1000)
-images = np.tile(image, (nsamples, 1, 1)).reshape(nsamples, -1)
-print(images.shape)  # (2, 1000000)
-# Instantiate structure tensor operator
-structure_tensor = StructureTensor(arg_shape=arg_shape)
-
-outputs = structure_tensor(images)
-print(outputs.shape)  # (2, 3000000)
-# Plot
-outputs = structure_tensor.unravel(outputs)
-print(outputs.shape)  # (2, 3, 1000, 1000)
-plt.figure()
-plt.imshow(images[0].reshape(arg_shape))
-plt.colorbar()
-plt.title("Image")
-plt.axis("off")
-
-plt.figure()
-plt.imshow(outputs[0][0].reshape(arg_shape))
-plt.colorbar()
-plt.title(r"$\hat{S}_{xx}$")
-plt.axis("off")
-
-plt.figure()
-plt.imshow(outputs[0][1].reshape(arg_shape))
-plt.colorbar()
-plt.title(r"$\hat{S}_{xy}$")
-plt.axis("off")
-
-plt.figure()
-plt.imshow(outputs[0][2].reshape(arg_shape))
-plt.colorbar()
-plt.title(r"$\hat{S}_{yy}$")
-plt.axis("off")
\ No newline at end of file
diff --git a/_downloads/7a45a92466c43f54218138bd4c5bfb33/opt-1.pdf b/_downloads/7a45a92466c43f54218138bd4c5bfb33/opt-1.pdf
deleted file mode 100644
index 8c3fe5590d8b1a2812594344525549aa32371580..0000000000000000000000000000000000000000
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diff --git a/_downloads/7b093b841c4187795b2b3e7fe37a35fb/linop-21_03.pdf b/_downloads/7b093b841c4187795b2b3e7fe37a35fb/linop-21_03.pdf
index 41bb5eada7a660cfcdc58c35173e2dada5f0da12..52382b7dea7c804042947cee636aa68ed3c69641 100644
GIT binary patch
delta 21
dcmaFAneqK*#tkRK*h~#94J}PKpAS=D1^{aD2vh(7

delta 21
dcmaFAneqK*#tkRK*o+K~j7&^6pAS=D1^{Y$2u1(^

diff --git a/_downloads/7bf4f564a15100201d0a1e7baafafa52/opt-solver-2.pdf b/_downloads/7bf4f564a15100201d0a1e7baafafa52/opt-solver-2.pdf
index 87e6c096f536229ded68e76358732433ba2e55bb..ab401ccb10fbb7dbd5b779152a2bf0fcfbc2509e 100644
GIT binary patch
delta 3928
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delta 3938
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diff --git a/_downloads/80e8d2262c83f8aa3286c318c355a06b/operator-11_00.pdf b/_downloads/80e8d2262c83f8aa3286c318c355a06b/operator-11_00.pdf
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diff --git a/_downloads/821591bde9f2c4bb83a1dbdf85716dce/operator-19.py b/_downloads/821591bde9f2c4bb83a1dbdf85716dce/operator-19.py
deleted file mode 100644
index 4e36ae88..00000000
--- a/_downloads/821591bde9f2c4bb83a1dbdf85716dce/operator-19.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Prewitt
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-prewitt = Prewitt(arg_shape)
-out = prewitt(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/_downloads/830c6cf1ca9ddce08ef358693dbce351/operator-15.pdf b/_downloads/830c6cf1ca9ddce08ef358693dbce351/operator-15.pdf
deleted file mode 100644
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diff --git a/_downloads/8860ae0fe6ee3c63137f67234c7ff9a8/experimental-1_01_00.pdf b/_downloads/8860ae0fe6ee3c63137f67234c7ff9a8/experimental-1_01_00.pdf
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diff --git a/_downloads/89cf7e77837a5c3249511293b70d7aa2/linop-13_00.pdf b/_downloads/89cf7e77837a5c3249511293b70d7aa2/linop-13_00.pdf
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diff --git a/_downloads/8b725cf748f1669bc44a24d333409c47/linop-12_02.pdf b/_downloads/8b725cf748f1669bc44a24d333409c47/linop-12_02.pdf
index 094c32580c68214239669913291f53751347c66a..afba84cf82473833a1cb489a7135d95e9a0b8652 100644
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diff --git a/_downloads/8b75e17542eb060a859009378ccf739e/operator-6.py b/_downloads/8b75e17542eb060a859009378ccf739e/operator-6.py
deleted file mode 100644
index 088a74fe..00000000
--- a/_downloads/8b75e17542eb060a859009378ccf739e/operator-6.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Jacobian
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-image = np.tile(peaks(xx, yy), (3, 1, 1))
-jac = Jacobian(arg_shape=image.shape[1:], n_channels=image.shape[0])
-out = jac.unravel(jac(image.ravel()))
-fig, axes = plt.subplots(3, 2, figsize=(10, 15))
-for i in range(3):
-    for j in range(2):
-        axes[i, j].imshow(out[i, j].T, cmap=["Reds", "Greens", "Blues"][j])
-        axes[i, j].set_title(f"$\partial I_{{{['R', 'G', 'B'][j]}}}/\partial{{{['x', 'y'][j]}}}$")
-plt.suptitle("Jacobian")
\ No newline at end of file
diff --git a/_downloads/8f59a997c178a3e2bb89f1f4ce7dc2b0/operator-4_01.png b/_downloads/8f59a997c178a3e2bb89f1f4ce7dc2b0/operator-4_01.png
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diff --git a/_downloads/9029f349dcba6220309b295a9140982b/operator-2.py b/_downloads/9029f349dcba6220309b295a9140982b/operator-2.py
deleted file mode 100644
index fb8d4844..00000000
--- a/_downloads/9029f349dcba6220309b295a9140982b/operator-2.py
+++ /dev/null
@@ -1,43 +0,0 @@
-import numpy as np
-import pyxu.operator as pxo
-
-rng = np.random.default_rng(2)
-D, M, N = 2, 500, 200
-rnd_points = lambda _: rng.normal(scale=rng.uniform(0.25, 0.5, size=(D,)), size=(_, D))
-rnd_offset = lambda: rng.uniform(-1, 1, size=(D,))
-scale = 20
-x = np.concatenate(
-    [
-        rnd_points(M) + rnd_offset() * scale,
-        rnd_points(M) + rnd_offset() * scale,
-        rnd_points(M) + rnd_offset() * scale,
-        rnd_points(M) + rnd_offset() * scale,
-        rnd_points(M) + rnd_offset() * scale,
-    ],
-    axis=0,
-)
-z = np.concatenate(
-    [
-        rnd_points(N) + rnd_offset() * scale,
-        rnd_points(N) + rnd_offset() * scale,
-        rnd_points(N) + rnd_offset() * scale,
-        rnd_points(N) + rnd_offset() * scale,
-        rnd_points(N) + rnd_offset() * scale,
-    ],
-    axis=0,
-)
-
-kwargs = dict(
-    x=x,
-    z=z,
-    isign=-1,
-    eps=1e-3,
-)
-A = pxo.NUFFT.type3(**kwargs, chunked=True)
-x_chunks, z_chunks = A.auto_chunk(
-    max_mem=.1,
-    max_anisotropy=1,
-)
-A.allocate(x_chunks, z_chunks)
-fig = A.diagnostic_plot('x')
-fig.show()
\ No newline at end of file
diff --git a/_downloads/90b6ede7cd0b624bf04b02a069518152/operator-13_00.pdf b/_downloads/90b6ede7cd0b624bf04b02a069518152/operator-13_00.pdf
deleted file mode 100644
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diff --git a/_downloads/91bc70ed73eba97c728b782748cb547d/experimental-sampler-1_01_00.pdf b/_downloads/91bc70ed73eba97c728b782748cb547d/experimental-sampler-1_01_00.pdf
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diff --git a/_downloads/9c8347663ec88378aaae5057c1ae3264/operator-1.py b/_downloads/9c8347663ec88378aaae5057c1ae3264/operator-1.py
deleted file mode 100644
index 2fb312ed..00000000
--- a/_downloads/9c8347663ec88378aaae5057c1ae3264/operator-1.py
+++ /dev/null
@@ -1,14 +0,0 @@
-import numpy as np
-import pyxu.operator as pxo
-import matplotlib.pyplot as plt
-
-rng = np.random.default_rng(0)
-D, M, N = 1, 2, 3  # D denotes the dimension of the data
-x = np.fmod(rng.normal(size=(M, D)), 2 * np.pi)
-A = pxo.NUFFT.type1(
-    x, N,
-    isign=-1,
-    eps=1e-9
-)
-A.plot_kernel()
-plt.show()
\ No newline at end of file
diff --git a/_downloads/9db61dbdbb51645a825c3d21408069d0/opt-1.hires.png b/_downloads/9db61dbdbb51645a825c3d21408069d0/opt-1.hires.png
deleted file mode 100644
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diff --git a/_downloads/a30e3ded8c1066a4592a760dd92364c9/operator-7.py b/_downloads/a30e3ded8c1066a4592a760dd92364c9/operator-7.py
deleted file mode 100644
index df749166..00000000
--- a/_downloads/a30e3ded8c1066a4592a760dd92364c9/operator-7.py
+++ /dev/null
@@ -1,25 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Gradient, Divergence, Laplacian
-from pyxu.util.misc import peaks
-
-n = 100
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # (1000, 1000)
-grad = Gradient(arg_shape=arg_shape)
-div = Divergence(arg_shape=arg_shape)
-# Construct Laplacian via composition
-laplacian1 = div * grad
-# Compare to default Laplacian
-laplacian2 = Laplacian(arg_shape=arg_shape)
-output1 = laplacian1(image.ravel())
-output2 = laplacian2(image.ravel())
-fig, axes = plt.subplots(1, 2, figsize=(10, 5))
-im = axes[0].imshow(np.log(abs(output1)).reshape(*arg_shape))
-axes[0].set_title("Laplacian via composition")
-plt.colorbar(im, ax=axes[0])
-im = axes[1].imshow(np.log(abs(output1)).reshape(*arg_shape))
-axes[1].set_title("Default Laplacian")
-plt.colorbar(im, ax=axes[1])
\ No newline at end of file
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diff --git a/_downloads/a7fbcf236aa04c1f2f0fe84dd0beb567/linop-17.pdf b/_downloads/a7fbcf236aa04c1f2f0fe84dd0beb567/linop-17.pdf
index 2d02bb88192da341f0d5a26b533a393bc73148e2..feac06258a0776cdb9ba2f7efc6c2a94a7c28e03 100644
GIT binary patch
delta 22
ecmaF6jp^++rVY~5*^LcNP0dU!HY-i{W&r?dfd}6J

delta 22
ecmaF6jp^++rVY~5*^LYh3=B;SHY-i{W&r?cz6Zwu

diff --git a/_downloads/a8991112e97556caf0e2fd5883613b0a/operator-21_02.png b/_downloads/a8991112e97556caf0e2fd5883613b0a/operator-21_02.png
deleted file mode 100644
index 202a34b9b1e4e3bc6a835eed65ad88792c75d0fc..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

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diff --git a/_downloads/a9f1d15500139a62d3908b04a52bc416/linop-10_00.pdf b/_downloads/a9f1d15500139a62d3908b04a52bc416/linop-10_00.pdf
index a839ce52638955d86c774d0aa9665bda6d9adf0e..665448b8c3229a25e70362b7c874fdfdea5bd59f 100644
GIT binary patch
delta 22
ecmdmeih1`b<_)%w*i8*A4J{4LH@iIg&IAB%l?f>T

delta 22
ecmdmeih1`b<_)%w*o_R0j7$v8HoH9f&IAB%5eXXr

diff --git a/_downloads/aa08cf4e2cef61b518aa64b10c1817a9/abc-1_01.pdf b/_downloads/aa08cf4e2cef61b518aa64b10c1817a9/abc-1_01.pdf
index 46a3305389766dc58321ede82c2527237a52ea43..4f600ce013c5c06cf12f53f9cbe2e5e7092d9c11 100644
GIT binary patch
delta 20
bcmbOcG$Uw3uqwN$fu*6Pf$8Qb)qTtWNE8NS

delta 20
bcmbOcG$Uw3uqwNufu*UbiP7dL)qTtWNAd<?

diff --git a/_downloads/ac2d8e4fa5ab3cfce5066292ea2e5ee4/operator-13_00.png b/_downloads/ac2d8e4fa5ab3cfce5066292ea2e5ee4/operator-13_00.png
deleted file mode 100644
index 2999731422f860a63c090c7d4729371a9d263a68..0000000000000000000000000000000000000000
GIT binary patch
literal 0
HcmV?d00001

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diff --git a/_downloads/ad2f7e24bddbd17a6cfa96e6423ca673/experimental-1_00_00.pdf b/_downloads/ad2f7e24bddbd17a6cfa96e6423ca673/experimental-1_00_00.pdf
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diff --git a/_downloads/b0e4014986a0f5921e51c57c3f1d2893/operator-4_02.pdf b/_downloads/b0e4014986a0f5921e51c57c3f1d2893/operator-4_02.pdf
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diff --git a/_downloads/b1cab852cc8994069d3eb7349822e126/linop-13_02.pdf b/_downloads/b1cab852cc8994069d3eb7349822e126/linop-13_02.pdf
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diff --git a/_downloads/b2643be9761ce6a5244d11d98408529f/linop-13.pdf b/_downloads/b2643be9761ce6a5244d11d98408529f/linop-13.pdf
index 0ce8ee284f3c47260ca4dc5ef7ca9994f0fac582..a6ff73fca2172b6d894706e27f3201c678cdc743 100644
GIT binary patch
delta 22
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diff --git a/_downloads/b5b8151ee0b479d40092a5e2c7ba8055/operator-11_02.pdf b/_downloads/b5b8151ee0b479d40092a5e2c7ba8055/operator-11_02.pdf
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diff --git a/_downloads/b720f3f70e5d870af630b0311b862bdc/operator-16.py b/_downloads/b720f3f70e5d870af630b0311b862bdc/operator-16.py
deleted file mode 100644
index 7650f6fb..00000000
--- a/_downloads/b720f3f70e5d870af630b0311b862bdc/operator-16.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import DoG
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-dog = DoG(arg_shape, low_sigma=3)
-out = dog(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/_downloads/b793257364ec7e73fe09d6ac0cf897bb/linop-3.pdf b/_downloads/b793257364ec7e73fe09d6ac0cf897bb/linop-3.pdf
index 8062c6e664f8cf045052b7a379e2c04709d72b8c..f0fb7c0de0d72f34943695aaca4f7d809d931c39 100644
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diff --git a/_downloads/b9ab671fb0a7f18372db2008f8f175b3/operator-2.png b/_downloads/b9ab671fb0a7f18372db2008f8f175b3/operator-2.png
deleted file mode 100644
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diff --git a/_downloads/beadf23da07c5206cde021558c7f49fa/linop-3_01.pdf b/_downloads/beadf23da07c5206cde021558c7f49fa/linop-3_01.pdf
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diff --git a/_downloads/c287d657992e4ff9fb0cd17bed7a0b5b/operator-4_01.pdf b/_downloads/c287d657992e4ff9fb0cd17bed7a0b5b/operator-4_01.pdf
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diff --git a/_downloads/c6b377da5d37f9a1a7bd869cb238734f/operator-4.py b/_downloads/c6b377da5d37f9a1a7bd869cb238734f/operator-4.py
deleted file mode 100644
index bfe7ebc3..00000000
--- a/_downloads/c6b377da5d37f9a1a7bd869cb238734f/operator-4.py
+++ /dev/null
@@ -1,33 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import PartialDerivative
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # Shape of our image
-# Specify derivative order at each direction
-df_dx = (1, 0) # Compute derivative of order 1 in first dimension
-d2f_dy2 = (0, 2) # Compute derivative of order 2 in second dimension
-d3f_dxdy2 = (1, 2) # Compute derivative of order 1 in first dimension and der. of order 2 in second dimension
-# Instantiate derivative operators
-diff1 = PartialDerivative.gaussian_derivative(order=df_dx, arg_shape=arg_shape, sigma=2.0)
-diff2 = PartialDerivative.gaussian_derivative(order=d2f_dy2, arg_shape=arg_shape, sigma=2.0)
-diff = PartialDerivative.gaussian_derivative(order=d3f_dxdy2, arg_shape=arg_shape, sigma=2.0)
-# Compute derivatives
-out1 = (diff1 * diff2)(image.ravel()).reshape(arg_shape)
-out2 = diff(image.ravel()).reshape(arg_shape)
-plt.figure()
-plt.imshow(image),
-plt.axis('off')
-plt.colorbar()
-plt.title('f(x,y)')
-plt.figure()
-plt.imshow(out1.T)
-plt.axis('off')
-plt.title(r'$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$')
-plt.figure()
-plt.imshow(out2.T)
-plt.axis('off')
-plt.title(r'$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$')
\ No newline at end of file
diff --git a/_downloads/c6cc146e09111e224dd32387b5f48af9/operator-11_01.hires.png b/_downloads/c6cc146e09111e224dd32387b5f48af9/operator-11_01.hires.png
deleted file mode 100644
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diff --git a/_downloads/c722cabc6093f717e47975d57ffbc907/operator-5.py b/_downloads/c722cabc6093f717e47975d57ffbc907/operator-5.py
deleted file mode 100644
index caacd6b1..00000000
--- a/_downloads/c722cabc6093f717e47975d57ffbc907/operator-5.py
+++ /dev/null
@@ -1,34 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Gradient
-from pyxu.util.misc import peaks
-
-# Define input image
-n = 100
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # (1000, 1000)
-# Instantiate gradient operator
-grad = Gradient(arg_shape=arg_shape)
-
-# Compute gradients
-output = grad(image.ravel()) # shape = (2000000, )
-df_dx, df_dy = grad.unravel(output) # shape = (2, 1000, 1000)
-
-# Plot image
-fig, axs = plt.subplots(1, 3, figsize=(15, 4))
-im = axs[0].imshow(image)
-axs[0].set_title("Image")
-axs[0].axis("off")
-plt.colorbar(im, ax=axs[0])
-
-# Plot gradient
-im = axs[1].imshow(df_dx)
-axs[1].set_title(r"$\partial f/ \partial x$")
-axs[1].axis("off")
-plt.colorbar(im, ax=axs[1])
-im = axs[2].imshow(df_dy)
-axs[2].set_title(r"$\partial f/ \partial y$")
-axs[2].axis("off")
-plt.colorbar(im, ax=axs[2])
\ No newline at end of file
diff --git a/_downloads/c8a864597bcad6d39da2ef420e9ea684/linop-19_00.pdf b/_downloads/c8a864597bcad6d39da2ef420e9ea684/linop-19_00.pdf
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diff --git a/_downloads/cac3dcf5082691d7fec7aafb5a70b646/operator-8.py b/_downloads/cac3dcf5082691d7fec7aafb5a70b646/operator-8.py
deleted file mode 100644
index a64c708c..00000000
--- a/_downloads/cac3dcf5082691d7fec7aafb5a70b646/operator-8.py
+++ /dev/null
@@ -1,38 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Hessian, PartialDerivative
-from pyxu.util.misc import peaks
-
-n = 100
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # (1000, 1000)
-
-# Instantiate Hessian operator
-hessian = Hessian(arg_shape=arg_shape, directions="all")
-# Compute Hessian
-output = hessian(image.ravel()) # shape = (300000,)
-d2f_dx2, d2f_dxdy, d2f_dy2 = hessian.unravel(output)
-
-# Plot
-fig, axs = plt.subplots(1, 4, figsize=(20, 4))
-im = axs[0].imshow(image)
-plt.colorbar(im, ax=axs[0])
-axs[0].set_title("Image")
-axs[0].axis("off")
-
-im = axs[1].imshow(d2f_dx2)
-plt.colorbar(im, ax=axs[1])
-axs[1].set_title(r"$\partial^{2} f/ \partial x^{2}$")
-axs[1].axis("off")
-
-im = axs[2].imshow(d2f_dxdy)
-plt.colorbar(im, ax=axs[2])
-axs[2].set_title(r"$\partial^{2} f/ \partial x\partial y$")
-axs[2].axis("off")
-
-im = axs[3].imshow(d2f_dy2)
-plt.colorbar(im, ax=axs[3])
-axs[3].set_title(r"$\partial^{2} f/ \partial y^{2}$")
-axs[3].axis("off")
\ No newline at end of file
diff --git a/_downloads/cb592e426f343abde6179a6c6c588c24/operator-8.png b/_downloads/cb592e426f343abde6179a6c6c588c24/operator-8.png
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diff --git a/_downloads/d033201855f1ac9d7e8eb509601ad103/operator-20.py b/_downloads/d033201855f1ac9d7e8eb509601ad103/operator-20.py
deleted file mode 100644
index e2a1b717..00000000
--- a/_downloads/d033201855f1ac9d7e8eb509601ad103/operator-20.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Scharr
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-scharr = Scharr(arg_shape)
-out = scharr(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/_downloads/d1d43d473b0f4368b7c6e91e21b490e0/operator-5.hires.png b/_downloads/d1d43d473b0f4368b7c6e91e21b490e0/operator-5.hires.png
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diff --git a/_downloads/d95682f2902576513757e8747a4f94d8/operator-9.py b/_downloads/d95682f2902576513757e8747a4f94d8/operator-9.py
deleted file mode 100644
index ccb1eef9..00000000
--- a/_downloads/d95682f2902576513757e8747a4f94d8/operator-9.py
+++ /dev/null
@@ -1,29 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Laplacian
-from pyxu.util.misc import peaks
-
-# Define input image
-n = 100
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-
-arg_shape = image.shape  # (1000, 1000)
-# Compute Laplacian
-laplacian = Laplacian(arg_shape=arg_shape)
-output = laplacian(image.ravel())
-output = laplacian.unravel(output) # shape = (1, 1000, 1000)
-# Plot
-fig, axs = plt.subplots(1, 2, figsize=(10, 4))
-im = axs[0].imshow(image)
-plt.colorbar(im, ax=axs[0])
-axs[0].set_title("Image")
-axs[0].axis("off")
-
-im = axs[1].imshow(output.squeeze())
-plt.colorbar(im, ax=axs[1])
-axs[1].set_title(r"$\partial^{2} f/ \partial x^{2}+\partial^{2} f/ \partial y^{2}$")
-axs[1].axis("off")
-
-fig.show()
\ No newline at end of file
diff --git a/_downloads/db9ac5fbbfe21a45f644cc919f758da2/opt-solver-1.pdf b/_downloads/db9ac5fbbfe21a45f644cc919f758da2/opt-solver-1.pdf
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diff --git a/_downloads/ddb65118b9c2654fdc8b8c39e75cc610/operator-12_00.pdf b/_downloads/ddb65118b9c2654fdc8b8c39e75cc610/operator-12_00.pdf
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diff --git a/_downloads/e0eefa74af9eff0db39630aafbdd32db/linop-11_01.pdf b/_downloads/e0eefa74af9eff0db39630aafbdd32db/linop-11_01.pdf
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diff --git a/_downloads/e1a75dcc78d38d076dc2ecbd8c33f9ad/linop-11.py b/_downloads/e1a75dcc78d38d076dc2ecbd8c33f9ad/linop-11.py
index 725e0ddf..9b92fec1 100644
--- a/_downloads/e1a75dcc78d38d076dc2ecbd8c33f9ad/linop-11.py
+++ b/_downloads/e1a75dcc78d38d076dc2ecbd8c33f9ad/linop-11.py
@@ -35,6 +35,6 @@
 axs[2].set_title(r"$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$")
 plt.colorbar(im, ax=axs[2])
 
-# Test approximation error
+# Check approximation error
 plt.figure()
-plt.imshow(abs(out1 - out2) / abs(out2)), plt.colorbar()
\ No newline at end of file
+plt.imshow(abs(out1 - out2)), plt.colorbar()
\ No newline at end of file
diff --git a/_downloads/e1c2f45952876293feb161611e3c2d06/linop-19.png b/_downloads/e1c2f45952876293feb161611e3c2d06/linop-19.png
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diff --git a/_downloads/ebda9c8427d0061add5c36d23ac72518/operator-21_03.pdf b/_downloads/ebda9c8427d0061add5c36d23ac72518/operator-21_03.pdf
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diff --git a/_downloads/ec62b0e358ee5c0b4fe48a7f14c93a09/operator-3_00.pdf b/_downloads/ec62b0e358ee5c0b4fe48a7f14c93a09/operator-3_00.pdf
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diff --git a/_downloads/ee22dc0a66baaeda24d579f4dd50f185/operator-13_01.pdf b/_downloads/ee22dc0a66baaeda24d579f4dd50f185/operator-13_01.pdf
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diff --git a/_downloads/eff18b5fef44d9c0d77331121a291e8f/operator-11.py b/_downloads/eff18b5fef44d9c0d77331121a291e8f/operator-11.py
deleted file mode 100644
index 06c3a954..00000000
--- a/_downloads/eff18b5fef44d9c0d77331121a291e8f/operator-11.py
+++ /dev/null
@@ -1,31 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import DirectionalGradient
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-z = peaks(xx, yy)
-directions1 = np.zeros(shape=(2, z.size))
-directions1[0, :z.size // 2] = 1
-directions1[1, z.size // 2:] = 1
-directions2 = np.zeros(shape=(2, z.size))
-directions2[1, :z.size // 2] = -1
-directions2[0, z.size // 2:] = -1
-arg_shape = z.shape
-dop = DirectionalGradient(arg_shape=arg_shape, directions=[directions1, directions2])
-out = dop.unravel(dop(z.ravel()))
-plt.figure()
-h = plt.pcolormesh(xx, yy, z, shading='auto')
-plt.quiver(x, x, directions1[1].reshape(arg_shape), directions1[0].reshape(xx.shape))
-plt.quiver(x, x, directions2[1].reshape(arg_shape), directions2[0].reshape(xx.shape), color='red')
-plt.colorbar(h)
-plt.title(r'Signal $\mathbf{f}$ and directions of derivatives')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[0], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla_{\mathbf{v}_0} \mathbf{f}$')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[1], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla_{\mathbf{v}_1} \mathbf{f}$')
\ No newline at end of file
diff --git a/_downloads/f2dd49c204e444011bf0c8ee51349779/opt-1.py b/_downloads/f2dd49c204e444011bf0c8ee51349779/opt-1.py
deleted file mode 100644
index 982b2492..00000000
--- a/_downloads/f2dd49c204e444011bf0c8ee51349779/opt-1.py
+++ /dev/null
@@ -1,31 +0,0 @@
-import matplotlib.pyplot as plt
-import numpy as np
-import pyxu.operator as pxo
-from pyxu.experimental._dev import DownSampling, FirstDerivative
-from pyxu.opt.solver import CV
-
-x = np.repeat(np.asarray([0, 2, 1, 3, 0, 2, 0]), 10)
-N = x.size
-
-D = FirstDerivative(size=N, kind="forward")
-D.lipschitz = D.estimate_lipschitz()
-
-downsample = DownSampling(size=N, downsampling_factor=3)
-y = downsample(x)
-loss = (1 / 2) * pxo.SquaredL2Norm(y.size).argshift(-y)
-F = loss * downsample
-F.diff_lipschitz = F.estimate_diff_lipschitz()
-
-cv = CV(f=F, g=0.01 * pxo.L1Norm(N), h=0.1 * pxo.L1Norm(N), K=D)
-x0, z0 = np.zeros((2, N))
-cv.fit(x0=x0, z0=z0)
-x_recons = cv.solution()[0]
-
-plt.figure()
-plt.stem(x, linefmt="C0-", markerfmt="C0o")
-mask_ids = np.where(downsample.downsampling_mask)[0]
-markerline, stemlines, baseline = plt.stem(mask_ids, y, linefmt="C3-", markerfmt="C3o")
-markerline.set_markerfacecolor("none")
-plt.stem(x_recons, linefmt="C1--", markerfmt="C1s")
-plt.legend(["Ground truth", "Observation", "CV Estimate"])
-plt.show()
\ No newline at end of file
diff --git a/_downloads/f32070409f4c8c535a15508855b9e463/linop-21_02.pdf b/_downloads/f32070409f4c8c535a15508855b9e463/linop-21_02.pdf
index 9a068ceb8ba10a7eaaacb85591adb51c32623e91..b65f4c88bbc9333d29e25e5e146efc65856aea1a 100644
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diff --git a/_downloads/f363b074be57f30d62e32feccedb67e8/experimental-sampler-1_00_00.png b/_downloads/f363b074be57f30d62e32feccedb67e8/experimental-sampler-1_00_00.png
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diff --git a/_downloads/f54ac688c85e54a5c4e01ac51d047db1/operator-10.py b/_downloads/f54ac688c85e54a5c4e01ac51d047db1/operator-10.py
deleted file mode 100644
index 1f191681..00000000
--- a/_downloads/f54ac688c85e54a5c4e01ac51d047db1/operator-10.py
+++ /dev/null
@@ -1,29 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import DirectionalDerivative
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-z = peaks(xx, yy)
-directions = np.zeros(shape=(2, z.size))
-directions[0, : z.size // 2] = 1
-directions[1, z.size // 2:] = 1
-dop = DirectionalDerivative(arg_shape=z.shape, order=1, directions=directions)
-out = dop.unravel(dop(z.ravel()))
-dop2 = DirectionalDerivative(arg_shape=z.shape, order=2, directions=directions)
-out2 = dop2.unravel(dop2(z.ravel()))
-fig, axs = plt.subplots(1, 3, figsize=(15, 5))
-axs = np.ravel(axs)
-h = axs[0].pcolormesh(xx, yy, z, shading="auto")
-axs[0].quiver(x, x, directions[1].reshape(xx.shape), directions[0].reshape(xx.shape))
-plt.colorbar(h, ax=axs[0])
-axs[0].set_title("Signal and directions of first derivatives")
-
-h = axs[1].pcolormesh(xx, yy, out.squeeze(), shading="auto")
-plt.colorbar(h, ax=axs[1])
-axs[1].set_title("First-order directional derivatives")
-
-h = axs[2].pcolormesh(xx, yy, out2.squeeze(), shading="auto")
-plt.colorbar(h, ax=axs[2])
-axs[2].set_title("Second-order directional derivative")
\ No newline at end of file
diff --git a/_downloads/f6fdcb1dac293e403daf6b44a63a0a98/linop-19_01.pdf b/_downloads/f6fdcb1dac293e403daf6b44a63a0a98/linop-19_01.pdf
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diff --git a/_downloads/fa1e9c492a3642cd6b2e4edb05885d27/operator-11_01.pdf b/_downloads/fa1e9c492a3642cd6b2e4edb05885d27/operator-11_01.pdf
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diff --git a/_downloads/fb2a08c73290a1f099ce4f662f384ba8/operator-3_01.pdf b/_downloads/fb2a08c73290a1f099ce4f662f384ba8/operator-3_01.pdf
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diff --git a/_downloads/feb0d965c7c0bb35ac098ec3ef67df61/operator-14.py b/_downloads/feb0d965c7c0bb35ac098ec3ef67df61/operator-14.py
deleted file mode 100644
index d7c5085f..00000000
--- a/_downloads/feb0d965c7c0bb35ac098ec3ef67df61/operator-14.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import MovingAverage
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-ma = MovingAverage(arg_shape, size=5)
-out = ma(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/_images/examples_Stencils_29_0.png b/_images/examples_Stencils_29_0.png
deleted file mode 100644
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diff --git a/_modules/collections/abc.html b/_modules/collections/abc.html
index 4eb3fab4..793a945f 100644
--- a/_modules/collections/abc.html
+++ b/_modules/collections/abc.html
@@ -27,8 +27,8 @@
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-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
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-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
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-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
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         </div>
       
       
-        <div class="navbar-item"><strong> v1.0.x </strong></div>
+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
       
         <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
     aria-label="Icon Links">
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -341,7 +341,7 @@
     
       <div class="sidebar-header-items__end">
         
-          <div class="navbar-item"><strong> v1.0.x </strong></div>
+          <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
         
           <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
     aria-label="Icon Links">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -513,15 +513,11 @@ <h1>Source code for collections.abc</h1><div class="highlight"><pre>
       
         <div class="footer-item">
   <p class="sphinx-version">
-    Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5.
+     Created with <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5, with some help from <a href="https://chat.openai.com/"> ChatGPT</a> (GPT 4).
     <br/>
   </p>
 </div>
       
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-  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
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diff --git a/_modules/index.html b/_modules/index.html
index 59c8e23d..ec426312 100644
--- a/_modules/index.html
+++ b/_modules/index.html
@@ -27,7 +27,7 @@
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-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
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-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
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-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
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     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
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diff --git a/_modules/numbers.html b/_modules/numbers.html
index 284917c5..f1a2519e 100644
--- a/_modules/numbers.html
+++ b/_modules/numbers.html
@@ -27,7 +27,7 @@
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-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
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     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
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@@ -37,13 +37,13 @@
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-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
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-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
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@@ -199,7 +199,7 @@
         </div>
       
       
-        <div class="navbar-item"><strong> v1.0.x </strong></div>
+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
       
         <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
     aria-label="Icon Links">
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -341,7 +341,7 @@
     
       <div class="sidebar-header-items__end">
         
-          <div class="navbar-item"><strong> v1.0.x </strong></div>
+          <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
         
           <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
     aria-label="Icon Links">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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@@ -598,7 +598,7 @@ <h1>Source code for numbers</h1><div class="highlight"><pre>
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 <span class="linenos">146</span>
 <div class="viewcode-block" id="Real">
-<a class="viewcode-back" href="../api/info.html#pyxu.info.ptype.Real">[docs]</a>
+<a class="viewcode-back" href="../api/info.ptype.html#pyxu.info.ptype.Real">[docs]</a>
 <span class="linenos">147</span><span class="k">class</span> <span class="nc">Real</span><span class="p">(</span><span class="n">Complex</span><span class="p">):</span>
 <span class="linenos">148</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;To Complex, Real adds the operations that work on real numbers.</span>
 <span class="linenos">149</span>
@@ -713,7 +713,7 @@ <h1>Source code for numbers</h1><div class="highlight"><pre>
 <span class="linenos">258</span>        <span class="k">return</span> <span class="mi">0</span>
 <span class="linenos">259</span>
 <div class="viewcode-block" id="Real.conjugate">
-<a class="viewcode-back" href="../api/info.html#pyxu.info.ptype.Real.conjugate">[docs]</a>
+<a class="viewcode-back" href="../api/info.ptype.html#pyxu.info.ptype.Real.conjugate">[docs]</a>
 <span class="linenos">260</span>    <span class="k">def</span> <span class="nf">conjugate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
 <span class="linenos">261</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Conjugate is a no-op for Reals.&quot;&quot;&quot;</span>
 <span class="linenos">262</span>        <span class="k">return</span> <span class="o">+</span><span class="bp">self</span></div>
@@ -909,15 +909,11 @@ <h1>Source code for numbers</h1><div class="highlight"><pre>
       
         <div class="footer-item">
   <p class="sphinx-version">
-    Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5.
+     Created with <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5, with some help from <a href="https://chat.openai.com/"> ChatGPT</a> (GPT 4).
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-  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
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-      
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diff --git a/_modules/pyxu/abc/arithmetic.html b/_modules/pyxu/abc/arithmetic.html
index f0a1273d..470a8063 100644
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-    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
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     <link rel="stylesheet" type="text/css" href="../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
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-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
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-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
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@@ -468,7 +468,7 @@ <h1>Source code for pyxu.abc.arithmetic</h1><div class="highlight"><pre>
 <span class="linenos">  15</span>
 <span class="linenos">  16</span>
 <div class="viewcode-block" id="Rule">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.arithmetic.Rule">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/arithmetic.html#pyxu.abc.arithmetic.Rule">[docs]</a>
 <span class="linenos">  17</span><span class="k">class</span> <span class="nc">Rule</span><span class="p">:</span>
 <span class="linenos">  18</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">  19</span><span class="sd">    General arithmetic rule.</span>
@@ -477,7 +477,7 @@ <h1>Source code for pyxu.abc.arithmetic</h1><div class="highlight"><pre>
 <span class="linenos">  22</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">  23</span>
 <div class="viewcode-block" id="Rule.op">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.arithmetic.Rule.op">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/arithmetic.html#pyxu.abc.arithmetic.Rule.op">[docs]</a>
 <span class="linenos">  24</span>    <span class="k">def</span> <span class="nf">op</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos">  25</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">  26</span><span class="sd">        Returns</span>
@@ -526,7 +526,7 @@ <h1>Source code for pyxu.abc.arithmetic</h1><div class="highlight"><pre>
 <span class="linenos">  67</span>
 <span class="linenos">  68</span>
 <div class="viewcode-block" id="ScaleRule">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.arithmetic.ScaleRule">[docs]</a>
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 <span class="linenos">  69</span><span class="k">class</span> <span class="nc">ScaleRule</span><span class="p">(</span><span class="n">Rule</span><span class="p">):</span>
 <span class="linenos">  70</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">  71</span><span class="sd">    Arithmetic rules for element-wise scaling: :math:`B(x) = \alpha A(x)`.</span>
@@ -727,7 +727,7 @@ <h1>Source code for pyxu.abc.arithmetic</h1><div class="highlight"><pre>
 <span class="linenos"> 265</span>
 <span class="linenos"> 266</span>
 <div class="viewcode-block" id="ArgScaleRule">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.arithmetic.ArgScaleRule">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/arithmetic.html#pyxu.abc.arithmetic.ArgScaleRule">[docs]</a>
 <span class="linenos"> 267</span><span class="k">class</span> <span class="nc">ArgScaleRule</span><span class="p">(</span><span class="n">Rule</span><span class="p">):</span>
 <span class="linenos"> 268</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 269</span><span class="sd">    Arithmetic rules for element-wise parameter scaling: :math:`B(x) = A(\alpha x)`.</span>
@@ -950,7 +950,7 @@ <h1>Source code for pyxu.abc.arithmetic</h1><div class="highlight"><pre>
 <span class="linenos"> 485</span>
 <span class="linenos"> 486</span>
 <div class="viewcode-block" id="ArgShiftRule">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.arithmetic.ArgShiftRule">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/arithmetic.html#pyxu.abc.arithmetic.ArgShiftRule">[docs]</a>
 <span class="linenos"> 487</span><span class="k">class</span> <span class="nc">ArgShiftRule</span><span class="p">(</span><span class="n">Rule</span><span class="p">):</span>
 <span class="linenos"> 488</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 489</span><span class="sd">    Arithmetic rules for parameter shifting: :math:`B(x) = A(x - c)`.</span>
@@ -1143,7 +1143,7 @@ <h1>Source code for pyxu.abc.arithmetic</h1><div class="highlight"><pre>
 <span class="linenos"> 675</span>
 <span class="linenos"> 676</span>
 <div class="viewcode-block" id="AddRule">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.arithmetic.AddRule">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/arithmetic.html#pyxu.abc.arithmetic.AddRule">[docs]</a>
 <span class="linenos"> 677</span><span class="k">class</span> <span class="nc">AddRule</span><span class="p">(</span><span class="n">Rule</span><span class="p">):</span>
 <span class="linenos"> 678</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 679</span><span class="sd">    Arithmetic rules for operator addition: :math:`C(x) = A(x) + B(x)`.</span>
@@ -1515,7 +1515,7 @@ <h1>Source code for pyxu.abc.arithmetic</h1><div class="highlight"><pre>
 <span class="linenos">1044</span>
 <span class="linenos">1045</span>
 <div class="viewcode-block" id="ChainRule">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.arithmetic.ChainRule">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/arithmetic.html#pyxu.abc.arithmetic.ChainRule">[docs]</a>
 <span class="linenos">1046</span><span class="k">class</span> <span class="nc">ChainRule</span><span class="p">(</span><span class="n">Rule</span><span class="p">):</span>
 <span class="linenos">1047</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1048</span><span class="sd">    Arithmetic rules for operator composition: :math:`C(x) = (A \circ B)(x)`.</span>
@@ -1837,7 +1837,7 @@ <h1>Source code for pyxu.abc.arithmetic</h1><div class="highlight"><pre>
 <span class="linenos">1363</span>
 <span class="linenos">1364</span>
 <div class="viewcode-block" id="PowerRule">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.arithmetic.PowerRule">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/arithmetic.html#pyxu.abc.arithmetic.PowerRule">[docs]</a>
 <span class="linenos">1365</span><span class="k">class</span> <span class="nc">PowerRule</span><span class="p">(</span><span class="n">Rule</span><span class="p">):</span>
 <span class="linenos">1366</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1367</span><span class="sd">    Arithmetic rules for operator exponentiation: :math:`B(x) = A^{k}(x)`.</span>
@@ -1882,7 +1882,7 @@ <h1>Source code for pyxu.abc.arithmetic</h1><div class="highlight"><pre>
 <span class="linenos">1405</span>
 <span class="linenos">1406</span>
 <div class="viewcode-block" id="TransposeRule">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.arithmetic.TransposeRule">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/arithmetic.html#pyxu.abc.arithmetic.TransposeRule">[docs]</a>
 <span class="linenos">1407</span><span class="k">class</span> <span class="nc">TransposeRule</span><span class="p">(</span><span class="n">Rule</span><span class="p">):</span>
 <span class="linenos">1408</span>    <span class="c1"># Not strictly-speaking an arithmetic method, but the logic behind constructing transposed</span>
 <span class="linenos">1409</span>    <span class="c1"># operators is identical to arithmetic methods.</span>
diff --git a/_modules/pyxu/abc/operator.html b/_modules/pyxu/abc/operator.html
index 142b14ff..052ec986 100644
--- a/_modules/pyxu/abc/operator.html
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+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
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-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
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@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -471,7 +471,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">  18</span>
 <span class="linenos">  19</span>
 <div class="viewcode-block" id="Property">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Property">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Property">[docs]</a>
 <span class="linenos">  20</span><span class="k">class</span> <span class="nc">Property</span><span class="p">(</span><span class="n">enum</span><span class="o">.</span><span class="n">Enum</span><span class="p">):</span>
 <span class="linenos">  21</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">  22</span><span class="sd">    Mathematical property.</span>
@@ -496,7 +496,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">  41</span>    <span class="n">QUADRATIC</span> <span class="o">=</span> <span class="n">enum</span><span class="o">.</span><span class="n">auto</span><span class="p">()</span>
 <span class="linenos">  42</span>
 <div class="viewcode-block" id="Property.arithmetic_methods">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Property.arithmetic_methods">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Property.arithmetic_methods">[docs]</a>
 <span class="linenos">  43</span>    <span class="k">def</span> <span class="nf">arithmetic_methods</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Set</span><span class="p">[</span><span class="nb">str</span><span class="p">]:</span>
 <span class="linenos">  44</span>        <span class="s2">&quot;Instance methods affected by arithmetic operations.&quot;</span>
 <span class="linenos">  45</span>        <span class="n">data</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
@@ -537,7 +537,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">  78</span>
 <span class="linenos">  79</span>
 <div class="viewcode-block" id="Operator">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator">[docs]</a>
 <span class="linenos">  80</span><span class="k">class</span> <span class="nc">Operator</span><span class="p">:</span>
 <span class="linenos">  81</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">  82</span><span class="sd">    Abstract Base Class for Pyxu operators.</span>
@@ -556,7 +556,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">  95</span>    <span class="n">__array_priority__</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span>
 <span class="linenos">  96</span>
 <div class="viewcode-block" id="Operator.__init__">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.__init__">[docs]</a>
 <span class="linenos">  97</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">):</span>
 <span class="linenos">  98</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">  99</span><span class="sd">        Parameters</span>
@@ -594,7 +594,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 130</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
 <span class="linenos"> 131</span>
 <div class="viewcode-block" id="Operator.properties">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.properties">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.properties">[docs]</a>
 <span class="linenos"> 132</span>    <span class="nd">@classmethod</span>
 <span class="linenos"> 133</span>    <span class="k">def</span> <span class="nf">properties</span><span class="p">(</span><span class="bp">cls</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Set</span><span class="p">[</span><span class="n">Property</span><span class="p">]:</span>
 <span class="linenos"> 134</span>        <span class="s2">&quot;Mathematical properties of the operator.&quot;</span>
@@ -602,7 +602,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos"> 136</span>
 <div class="viewcode-block" id="Operator.has">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.has">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.has">[docs]</a>
 <span class="linenos"> 137</span>    <span class="nd">@classmethod</span>
 <span class="linenos"> 138</span>    <span class="k">def</span> <span class="nf">has</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">prop</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Union</span><span class="p">[</span><span class="n">Property</span><span class="p">,</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Collection</span><span class="p">[</span><span class="n">Property</span><span class="p">]])</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
 <span class="linenos"> 139</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
@@ -614,7 +614,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos"> 145</span>
 <div class="viewcode-block" id="Operator.asop">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.asop">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.asop">[docs]</a>
 <span class="linenos"> 146</span>    <span class="k">def</span> <span class="nf">asop</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cast_to</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpC</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 147</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 148</span><span class="sd">        Recast an :py:class:`~pyxu.abc.Operator` (or subclass thereof) to another :py:class:`~pyxu.abc.Operator`.</span>
@@ -677,7 +677,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 204</span>
 <span class="linenos"> 205</span>    <span class="c1"># Operator Arithmetic -----------------------------------------------------</span>
 <div class="viewcode-block" id="Operator.__add__">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.__add__">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.__add__">[docs]</a>
 <span class="linenos"> 206</span>    <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 207</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 208</span><span class="sd">        Add two operators.</span>
@@ -714,7 +714,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos"> 239</span>
 <div class="viewcode-block" id="Operator.__sub__">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.__sub__">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.__sub__">[docs]</a>
 <span class="linenos"> 240</span>    <span class="k">def</span> <span class="fm">__sub__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 241</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 242</span><span class="sd">        Subtract two operators.</span>
@@ -740,7 +740,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos"> 262</span>
 <div class="viewcode-block" id="Operator.__neg__">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.__neg__">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.__neg__">[docs]</a>
 <span class="linenos"> 263</span>    <span class="k">def</span> <span class="fm">__neg__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 264</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 265</span><span class="sd">        Negate an operator.</span>
@@ -756,7 +756,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos"> 275</span>
 <div class="viewcode-block" id="Operator.__mul__">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.__mul__">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.__mul__">[docs]</a>
 <span class="linenos"> 276</span>    <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Union</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 277</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 278</span><span class="sd">        Compose two operators, or scale an operator by a constant.</span>
@@ -811,7 +811,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 326</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
 <span class="linenos"> 327</span>
 <div class="viewcode-block" id="Operator.__pow__">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.__pow__">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.__pow__">[docs]</a>
 <span class="linenos"> 328</span>    <span class="k">def</span> <span class="fm">__pow__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">k</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 329</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 330</span><span class="sd">        Exponentiate an operator, i.e. compose it with itself.</span>
@@ -851,7 +851,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 363</span>        <span class="k">return</span> <span class="bp">NotImplemented</span>
 <span class="linenos"> 364</span>
 <div class="viewcode-block" id="Operator.argscale">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.argscale">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.argscale">[docs]</a>
 <span class="linenos"> 365</span>    <span class="k">def</span> <span class="nf">argscale</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">scalar</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 366</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 367</span><span class="sd">        Scale operator&#39;s domain.</span>
@@ -876,7 +876,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos"> 386</span>
 <div class="viewcode-block" id="Operator.argshift">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.argshift">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.argshift">[docs]</a>
 <span class="linenos"> 387</span>    <span class="k">def</span> <span class="nf">argshift</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">shift</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Union</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 388</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 389</span><span class="sd">        Shift operator&#39;s domain.</span>
@@ -913,7 +913,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 419</span>            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;No operator found with properties </span><span class="si">{</span><span class="n">prop</span><span class="si">}</span><span class="s2">.&quot;</span><span class="p">)</span>
 <span class="linenos"> 420</span>
 <div class="viewcode-block" id="Operator.squeeze">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.squeeze">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.squeeze">[docs]</a>
 <span class="linenos"> 421</span>    <span class="k">def</span> <span class="nf">squeeze</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 422</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 423</span><span class="sd">        Cast an :py:class:`~pyxu.abc.Operator` to the right core operator sub-type given codomain dimension.</span>
@@ -953,7 +953,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 456</span>        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="p">,)</span>
 <span class="linenos"> 457</span>
 <div class="viewcode-block" id="Operator.expr">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Operator.expr">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Operator.expr">[docs]</a>
 <span class="linenos"> 458</span>    <span class="k">def</span> <span class="nf">expr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">level</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">strip</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
 <span class="linenos"> 459</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 460</span><span class="sd">        Pretty-Print the expression representation of the operator.</span>
@@ -1014,7 +1014,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 513</span>
 <span class="linenos"> 514</span>
 <div class="viewcode-block" id="Map">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Map">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Map">[docs]</a>
 <span class="linenos"> 515</span><span class="k">class</span> <span class="nc">Map</span><span class="p">(</span><span class="n">Operator</span><span class="p">):</span>
 <span class="linenos"> 516</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 517</span><span class="sd">    Base class for real-valued maps :math:`\mathbf{f}: \mathbb{R}^{M} \to \mathbb{R}^{N}`.</span>
@@ -1026,7 +1026,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 523</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos"> 524</span>
 <div class="viewcode-block" id="Map.properties">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Map.properties">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Map.properties">[docs]</a>
 <span class="linenos"> 525</span>    <span class="nd">@classmethod</span>
 <span class="linenos"> 526</span>    <span class="k">def</span> <span class="nf">properties</span><span class="p">(</span><span class="bp">cls</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Set</span><span class="p">[</span><span class="n">Property</span><span class="p">]:</span>
 <span class="linenos"> 527</span>        <span class="n">p</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">properties</span><span class="p">())</span>
@@ -1039,7 +1039,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 533</span>        <span class="bp">self</span><span class="o">.</span><span class="n">lipschitz</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span>
 <span class="linenos"> 534</span>
 <div class="viewcode-block" id="Map.apply">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Map.apply">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Map.apply">[docs]</a>
 <span class="linenos"> 535</span>    <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos"> 536</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 537</span><span class="sd">        Evaluate operator at specified point(s).</span>
@@ -1058,7 +1058,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos"> 550</span>
 <div class="viewcode-block" id="Map.__call__">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Map.__call__">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Map.__call__">[docs]</a>
 <span class="linenos"> 551</span>    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos"> 552</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 553</span><span class="sd">        Alias for :py:meth:`~pyxu.abc.Map.apply`.</span>
@@ -1126,7 +1126,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 614</span>            <span class="bp">self</span><span class="o">.</span><span class="n">estimate_lipschitz</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_estimate_lipschitz</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span>
 <span class="linenos"> 615</span>
 <div class="viewcode-block" id="Map.estimate_lipschitz">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Map.estimate_lipschitz">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Map.estimate_lipschitz">[docs]</a>
 <span class="linenos"> 616</span>    <span class="k">def</span> <span class="nf">estimate_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
 <span class="linenos"> 617</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 618</span><span class="sd">        Compute a Lipschitz constant of the operator.</span>
@@ -1162,7 +1162,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 646</span>
 <span class="linenos"> 647</span>
 <div class="viewcode-block" id="Func">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Func">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Func">[docs]</a>
 <span class="linenos"> 648</span><span class="k">class</span> <span class="nc">Func</span><span class="p">(</span><span class="n">Map</span><span class="p">):</span>
 <span class="linenos"> 649</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 650</span><span class="sd">    Base class for real-valued functionals :math:`f: \mathbb{R}^{M} \to \mathbb{R}\cup\{+\infty\}`.</span>
@@ -1184,7 +1184,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 666</span>        <span class="k">assert</span> <span class="bp">self</span><span class="o">.</span><span class="n">codim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;shape: expected (1, n), got </span><span class="si">{</span><span class="n">shape</span><span class="si">}</span><span class="s2">.&quot;</span>
 <span class="linenos"> 667</span>
 <div class="viewcode-block" id="Func.asloss">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.Func.asloss">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.Func.asloss">[docs]</a>
 <span class="linenos"> 668</span>    <span class="k">def</span> <span class="nf">asloss</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 669</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 670</span><span class="sd">        Transform a functional into a loss functional.</span>
@@ -1209,7 +1209,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 687</span>
 <span class="linenos"> 688</span>
 <div class="viewcode-block" id="DiffMap">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.DiffMap">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.DiffMap">[docs]</a>
 <span class="linenos"> 689</span><span class="k">class</span> <span class="nc">DiffMap</span><span class="p">(</span><span class="n">Map</span><span class="p">):</span>
 <span class="linenos"> 690</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 691</span><span class="sd">    Base class for real-valued differentiable maps :math:`\mathbf{f}: \mathbb{R}^{M} \to \mathbb{R}^{N}`.</span>
@@ -1234,7 +1234,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 710</span>        <span class="bp">self</span><span class="o">.</span><span class="n">diff_lipschitz</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span>
 <span class="linenos"> 711</span>
 <div class="viewcode-block" id="DiffMap.jacobian">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.DiffMap.jacobian">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.DiffMap.jacobian">[docs]</a>
 <span class="linenos"> 712</span>    <span class="k">def</span> <span class="nf">jacobian</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 713</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 714</span><span class="sd">        Evaluate the Jacobian of :math:`\mathbf{f}` at the specified point.</span>
@@ -1339,7 +1339,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 812</span>            <span class="bp">self</span><span class="o">.</span><span class="n">estimate_diff_lipschitz</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_estimate_diff_lipschitz</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span>
 <span class="linenos"> 813</span>
 <div class="viewcode-block" id="DiffMap.estimate_diff_lipschitz">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.DiffMap.estimate_diff_lipschitz">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.DiffMap.estimate_diff_lipschitz">[docs]</a>
 <span class="linenos"> 814</span>    <span class="k">def</span> <span class="nf">estimate_diff_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
 <span class="linenos"> 815</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 816</span><span class="sd">        Compute a Lipschitz constant of :py:meth:`~pyxu.abc.DiffMap.jacobian`.</span>
@@ -1375,7 +1375,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 844</span>
 <span class="linenos"> 845</span>
 <div class="viewcode-block" id="ProxFunc">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.ProxFunc">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.ProxFunc">[docs]</a>
 <span class="linenos"> 846</span><span class="k">class</span> <span class="nc">ProxFunc</span><span class="p">(</span><span class="n">Func</span><span class="p">):</span>
 <span class="linenos"> 847</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 848</span><span class="sd">    Base class for real-valued proximable functionals :math:`f: \mathbb{R}^{M} \to \mathbb{R} \cup \{+\infty\}`.</span>
@@ -1400,7 +1400,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos"> 867</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">shape</span><span class="p">)</span>
 <span class="linenos"> 868</span>
 <div class="viewcode-block" id="ProxFunc.prox">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.ProxFunc.prox">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.ProxFunc.prox">[docs]</a>
 <span class="linenos"> 869</span>    <span class="k">def</span> <span class="nf">prox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">tau</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos"> 870</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 871</span><span class="sd">        Evaluate proximity operator of :math:`\tau f` at specified point(s).</span>
@@ -1434,7 +1434,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos"> 899</span>
 <div class="viewcode-block" id="ProxFunc.fenchel_prox">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.ProxFunc.fenchel_prox">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.ProxFunc.fenchel_prox">[docs]</a>
 <span class="linenos"> 900</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;sigma&quot;</span><span class="p">))</span>
 <span class="linenos"> 901</span>    <span class="k">def</span> <span class="nf">fenchel_prox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">sigma</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos"> 902</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
@@ -1479,7 +1479,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos"> 941</span>
 <div class="viewcode-block" id="ProxFunc.moreau_envelope">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.ProxFunc.moreau_envelope">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.ProxFunc.moreau_envelope">[docs]</a>
 <span class="linenos"> 942</span>    <span class="k">def</span> <span class="nf">moreau_envelope</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mu</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 943</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 944</span><span class="sd">        Approximate proximable functional :math:`f` by its *Moreau envelope* :math:`f^{\mu}`.</span>
@@ -1609,7 +1609,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1066</span>
 <span class="linenos">1067</span>
 <div class="viewcode-block" id="DiffFunc">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.DiffFunc">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.DiffFunc">[docs]</a>
 <span class="linenos">1068</span><span class="k">class</span> <span class="nc">DiffFunc</span><span class="p">(</span><span class="n">DiffMap</span><span class="p">,</span> <span class="n">Func</span><span class="p">):</span>
 <span class="linenos">1069</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1070</span><span class="sd">    Base class for real-valued differentiable functionals :math:`f: \mathbb{R}^{M} \to \mathbb{R}`.</span>
@@ -1638,7 +1638,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1093</span>        <span class="k">return</span> <span class="n">LinFunc</span><span class="o">.</span><span class="n">from_array</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="n">arr</span><span class="p">))</span>
 <span class="linenos">1094</span>
 <div class="viewcode-block" id="DiffFunc.grad">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.DiffFunc.grad">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.DiffFunc.grad">[docs]</a>
 <span class="linenos">1095</span>    <span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos">1096</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1097</span><span class="sd">        Evaluate operator gradient at specified point(s).</span>
@@ -1674,7 +1674,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1125</span>
 <span class="linenos">1126</span>
 <div class="viewcode-block" id="ProxDiffFunc">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.ProxDiffFunc">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.ProxDiffFunc">[docs]</a>
 <span class="linenos">1127</span><span class="k">class</span> <span class="nc">ProxDiffFunc</span><span class="p">(</span><span class="n">ProxFunc</span><span class="p">,</span> <span class="n">DiffFunc</span><span class="p">):</span>
 <span class="linenos">1128</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1129</span><span class="sd">    Base class for real-valued differentiable *and* proximable functionals :math:`f:\mathbb{R}^{M} \to \mathbb{R}`.</span>
@@ -1701,7 +1701,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1149</span>
 <span class="linenos">1150</span>
 <div class="viewcode-block" id="QuadraticFunc">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.QuadraticFunc">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.QuadraticFunc">[docs]</a>
 <span class="linenos">1151</span><span class="k">class</span> <span class="nc">QuadraticFunc</span><span class="p">(</span><span class="n">ProxDiffFunc</span><span class="p">):</span>
 <span class="linenos">1152</span>    <span class="c1"># This is a special abstract base class with more __init__ parameters than `shape`.</span>
 <span class="linenos">1153</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
@@ -1755,7 +1755,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1201</span>        <span class="k">return</span> <span class="nb">frozenset</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
 <span class="linenos">1202</span>
 <div class="viewcode-block" id="QuadraticFunc.__init__">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.QuadraticFunc.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.QuadraticFunc.__init__">[docs]</a>
 <span class="linenos">1203</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
 <span class="linenos">1204</span>        <span class="bp">self</span><span class="p">,</span>
 <span class="linenos">1205</span>        <span class="n">shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span>
@@ -1839,7 +1839,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1282</span>        <span class="k">return</span> <span class="n">dL</span>
 <span class="linenos">1283</span>
 <div class="viewcode-block" id="QuadraticFunc._quad_spec">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.QuadraticFunc._quad_spec">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.QuadraticFunc._quad_spec">[docs]</a>
 <span class="linenos">1284</span>    <span class="k">def</span> <span class="nf">_quad_spec</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
 <span class="linenos">1285</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1286</span><span class="sd">        Canonical quadratic parameterization.</span>
@@ -1852,7 +1852,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1291</span>
 <span class="linenos">1292</span>
 <div class="viewcode-block" id="LinOp">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp">[docs]</a>
 <span class="linenos">1293</span><span class="k">class</span> <span class="nc">LinOp</span><span class="p">(</span><span class="n">DiffMap</span><span class="p">):</span>
 <span class="linenos">1294</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1295</span><span class="sd">    Base class for real-valued linear operators :math:`\mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{N}`.</span>
@@ -1889,7 +1889,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1326</span>        <span class="bp">self</span><span class="o">.</span><span class="n">diff_lipschitz</span> <span class="o">=</span> <span class="mi">0</span>
 <span class="linenos">1327</span>
 <div class="viewcode-block" id="LinOp.adjoint">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.adjoint">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.adjoint">[docs]</a>
 <span class="linenos">1328</span>    <span class="k">def</span> <span class="nf">adjoint</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos">1329</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1330</span><span class="sd">        Evaluate operator adjoint at specified point(s).</span>
@@ -1933,7 +1933,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1367</span>        <span class="k">return</span> <span class="n">arithmetic</span><span class="o">.</span><span class="n">TransposeRule</span><span class="p">(</span><span class="n">op</span><span class="o">=</span><span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
 <span class="linenos">1368</span>
 <div class="viewcode-block" id="LinOp.to_sciop">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.to_sciop">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.to_sciop">[docs]</a>
 <span class="linenos">1369</span>    <span class="k">def</span> <span class="nf">to_sciop</span><span class="p">(</span>
 <span class="linenos">1370</span>        <span class="bp">self</span><span class="p">,</span>
 <span class="linenos">1371</span>        <span class="n">dtype</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">DType</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
@@ -1983,7 +1983,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos">1415</span>
 <div class="viewcode-block" id="LinOp.estimate_lipschitz">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.estimate_lipschitz">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.estimate_lipschitz">[docs]</a>
 <span class="linenos">1416</span>    <span class="k">def</span> <span class="nf">estimate_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
 <span class="linenos">1417</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1418</span><span class="sd">        Compute a Lipschitz constant of the operator.</span>
@@ -2055,7 +2055,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos">1484</span>
 <div class="viewcode-block" id="LinOp.svdvals">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.svdvals">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.svdvals">[docs]</a>
 <span class="linenos">1485</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">()</span>
 <span class="linenos">1486</span>    <span class="k">def</span> <span class="nf">svdvals</span><span class="p">(</span>
 <span class="linenos">1487</span>        <span class="bp">self</span><span class="p">,</span>
@@ -2130,7 +2130,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos">1556</span>
 <div class="viewcode-block" id="LinOp.asarray">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.asarray">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.asarray">[docs]</a>
 <span class="linenos">1557</span>    <span class="k">def</span> <span class="nf">asarray</span><span class="p">(</span>
 <span class="linenos">1558</span>        <span class="bp">self</span><span class="p">,</span>
 <span class="linenos">1559</span>        <span class="n">xp</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">ArrayModule</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
@@ -2168,7 +2168,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos">1591</span>
 <div class="viewcode-block" id="LinOp.gram">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.gram">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.gram">[docs]</a>
 <span class="linenos">1592</span>    <span class="k">def</span> <span class="nf">gram</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos">1593</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1594</span><span class="sd">        Gram operator :math:`\mathbf{A}^{\ast} \mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{M}`.</span>
@@ -2194,7 +2194,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos">1614</span>
 <div class="viewcode-block" id="LinOp.cogram">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.cogram">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.cogram">[docs]</a>
 <span class="linenos">1615</span>    <span class="k">def</span> <span class="nf">cogram</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos">1616</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1617</span><span class="sd">        Co-Gram operator :math:`\mathbf{A}\mathbf{A}^{\ast}:\mathbb{R}^{N} \to \mathbb{R}^{N}`.</span>
@@ -2220,7 +2220,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos">1637</span>
 <div class="viewcode-block" id="LinOp.pinv">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.pinv">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.pinv">[docs]</a>
 <span class="linenos">1638</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;damp&quot;</span><span class="p">))</span>
 <span class="linenos">1639</span>    <span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span>
 <span class="linenos">1640</span>        <span class="bp">self</span><span class="p">,</span>
@@ -2306,7 +2306,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos">1720</span>
 <div class="viewcode-block" id="LinOp.dagger">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.dagger">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.dagger">[docs]</a>
 <span class="linenos">1721</span>    <span class="k">def</span> <span class="nf">dagger</span><span class="p">(</span>
 <span class="linenos">1722</span>        <span class="bp">self</span><span class="p">,</span>
 <span class="linenos">1723</span>        <span class="n">damp</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span>
@@ -2368,7 +2368,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 
 <span class="linenos">1779</span>
 <div class="viewcode-block" id="LinOp.from_array">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinOp.from_array">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinOp.from_array">[docs]</a>
 <span class="linenos">1780</span>    <span class="nd">@classmethod</span>
 <span class="linenos">1781</span>    <span class="k">def</span> <span class="nf">from_array</span><span class="p">(</span>
 <span class="linenos">1782</span>        <span class="bp">cls</span><span class="p">,</span>
@@ -2398,7 +2398,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1804</span>
 <span class="linenos">1805</span>
 <div class="viewcode-block" id="SquareOp">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.SquareOp">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.SquareOp">[docs]</a>
 <span class="linenos">1806</span><span class="k">class</span> <span class="nc">SquareOp</span><span class="p">(</span><span class="n">LinOp</span><span class="p">):</span>
 <span class="linenos">1807</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1808</span><span class="sd">    Base class for *square* linear operators, i.e. :math:`\mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{M}`</span>
@@ -2416,7 +2416,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1820</span>        <span class="k">assert</span> <span class="bp">self</span><span class="o">.</span><span class="n">dim</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">codim</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;shape: expected (M, M), got </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s2">.&quot;</span>
 <span class="linenos">1821</span>
 <div class="viewcode-block" id="SquareOp.trace">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.SquareOp.trace">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.SquareOp.trace">[docs]</a>
 <span class="linenos">1822</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">()</span>
 <span class="linenos">1823</span>    <span class="k">def</span> <span class="nf">trace</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
 <span class="linenos">1824</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
@@ -2464,7 +2464,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1864</span>
 <span class="linenos">1865</span>
 <div class="viewcode-block" id="NormalOp">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.NormalOp">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.NormalOp">[docs]</a>
 <span class="linenos">1866</span><span class="k">class</span> <span class="nc">NormalOp</span><span class="p">(</span><span class="n">SquareOp</span><span class="p">):</span>
 <span class="linenos">1867</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1868</span><span class="sd">    Base class for *normal* operators.</span>
@@ -2486,7 +2486,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1883</span>
 <span class="linenos">1884</span>
 <div class="viewcode-block" id="SelfAdjointOp">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.SelfAdjointOp">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.SelfAdjointOp">[docs]</a>
 <span class="linenos">1885</span><span class="k">class</span> <span class="nc">SelfAdjointOp</span><span class="p">(</span><span class="n">NormalOp</span><span class="p">):</span>
 <span class="linenos">1886</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1887</span><span class="sd">    Base class for *self-adjoint* operators.</span>
@@ -2506,7 +2506,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1900</span>
 <span class="linenos">1901</span>
 <div class="viewcode-block" id="UnitOp">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.UnitOp">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.UnitOp">[docs]</a>
 <span class="linenos">1902</span><span class="k">class</span> <span class="nc">UnitOp</span><span class="p">(</span><span class="n">NormalOp</span><span class="p">):</span>
 <span class="linenos">1903</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1904</span><span class="sd">    Base class for *unitary* operators.</span>
@@ -2555,7 +2555,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1946</span>
 <span class="linenos">1947</span>
 <div class="viewcode-block" id="ProjOp">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.ProjOp">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.ProjOp">[docs]</a>
 <span class="linenos">1948</span><span class="k">class</span> <span class="nc">ProjOp</span><span class="p">(</span><span class="n">SquareOp</span><span class="p">):</span>
 <span class="linenos">1949</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1950</span><span class="sd">    Base class for *projection* operators.</span>
@@ -2572,7 +2572,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">1960</span>
 <span class="linenos">1961</span>
 <div class="viewcode-block" id="OrthProjOp">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.OrthProjOp">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.OrthProjOp">[docs]</a>
 <span class="linenos">1962</span><span class="k">class</span> <span class="nc">OrthProjOp</span><span class="p">(</span><span class="n">ProjOp</span><span class="p">,</span> <span class="n">SelfAdjointOp</span><span class="p">):</span>
 <span class="linenos">1963</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1964</span><span class="sd">    Base class for *orthogonal projection* operators.</span>
@@ -2616,7 +2616,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">2001</span>
 <span class="linenos">2002</span>
 <div class="viewcode-block" id="PosDefOp">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.PosDefOp">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.PosDefOp">[docs]</a>
 <span class="linenos">2003</span><span class="k">class</span> <span class="nc">PosDefOp</span><span class="p">(</span><span class="n">SelfAdjointOp</span><span class="p">):</span>
 <span class="linenos">2004</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">2005</span><span class="sd">    Base class for *positive-definite* operators.</span>
@@ -2631,7 +2631,7 @@ <h1>Source code for pyxu.abc.operator</h1><div class="highlight"><pre>
 <span class="linenos">2013</span>
 <span class="linenos">2014</span>
 <div class="viewcode-block" id="LinFunc">
-<a class="viewcode-back" href="../../../api/abc.html#pyxu.abc.LinFunc">[docs]</a>
+<a class="viewcode-back" href="../../../api/abc/operator.html#pyxu.abc.LinFunc">[docs]</a>
 <span class="linenos">2015</span><span class="k">class</span> <span class="nc">LinFunc</span><span class="p">(</span><span class="n">ProxDiffFunc</span><span class="p">,</span> <span class="n">LinOp</span><span class="p">):</span>
 <span class="linenos">2016</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">2017</span><span class="sd">    Base class for real-valued linear functionals :math:`f: \mathbb{R}^{M} \to \mathbb{R}`.</span>
diff --git a/_modules/pyxu/abc/solver.html b/_modules/pyxu/abc/solver.html
index 68fb9ae7..dd9b39d6 100644
--- a/_modules/pyxu/abc/solver.html
+++ b/_modules/pyxu/abc/solver.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
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     <link rel="stylesheet" type="text/css" href="../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
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     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
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-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
diff --git a/_modules/pyxu/experimental/sampler/_sampler.html b/_modules/pyxu/experimental/sampler/_sampler.html
index a706a264..516bd0b3 100644
--- a/_modules/pyxu/experimental/sampler/_sampler.html
+++ b/_modules/pyxu/experimental/sampler/_sampler.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/copybutton.css?v=76b2166b" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
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     <link rel="stylesheet" type="text/css" href="../../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../../_static/clipboard.min.js?v=a7894cd8"></script>
diff --git a/_modules/pyxu/experimental/sampler/statistics.html b/_modules/pyxu/experimental/sampler/statistics.html
index 6d1e2675..76bb0274 100644
--- a/_modules/pyxu/experimental/sampler/statistics.html
+++ b/_modules/pyxu/experimental/sampler/statistics.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/copybutton.css?v=76b2166b" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
     <link rel="stylesheet" type="text/css" href="../../../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
diff --git a/_modules/pyxu/info/deps.html b/_modules/pyxu/info/deps.html
index a9eceb5b..0d517e92 100644
--- a/_modules/pyxu/info/deps.html
+++ b/_modules/pyxu/info/deps.html
@@ -27,7 +27,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../../_static/copybutton.css?v=76b2166b" />
@@ -37,13 +37,13 @@
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -199,7 +199,7 @@
         </div>
       
       
-        <div class="navbar-item"><strong> v1.0.x </strong></div>
+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
       
         <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
     aria-label="Icon Links">
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -341,7 +341,7 @@
     
       <div class="sidebar-header-items__end">
         
-          <div class="navbar-item"><strong> v1.0.x </strong></div>
+          <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
         
           <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
     aria-label="Icon Links">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -475,7 +475,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 <span class="linenos"> 22</span>
 <span class="linenos"> 23</span>
 <div class="viewcode-block" id="NDArrayInfo">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.NDArrayInfo">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.NDArrayInfo">[docs]</a>
 <span class="linenos"> 24</span><span class="nd">@enum</span><span class="o">.</span><span class="n">unique</span>
 <span class="linenos"> 25</span><span class="k">class</span> <span class="nc">NDArrayInfo</span><span class="p">(</span><span class="n">enum</span><span class="o">.</span><span class="n">Enum</span><span class="p">):</span>
 <span class="linenos"> 26</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
@@ -487,7 +487,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 <span class="linenos"> 32</span>    <span class="n">CUPY</span> <span class="o">=</span> <span class="n">enum</span><span class="o">.</span><span class="n">auto</span><span class="p">()</span>
 <span class="linenos"> 33</span>
 <div class="viewcode-block" id="NDArrayInfo.default">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.NDArrayInfo.default">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.NDArrayInfo.default">[docs]</a>
 <span class="linenos"> 34</span>    <span class="nd">@classmethod</span>
 <span class="linenos"> 35</span>    <span class="k">def</span> <span class="nf">default</span><span class="p">(</span><span class="bp">cls</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s2">&quot;NDArrayInfo&quot;</span><span class="p">:</span>
 <span class="linenos"> 36</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Default array backend to use.&quot;&quot;&quot;</span>
@@ -495,7 +495,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 
 <span class="linenos"> 38</span>
 <div class="viewcode-block" id="NDArrayInfo.type">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.NDArrayInfo.type">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.NDArrayInfo.type">[docs]</a>
 <span class="linenos"> 39</span>    <span class="k">def</span> <span class="nf">type</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">type</span><span class="p">:</span>
 <span class="linenos"> 40</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Array type associated to a backend.&quot;&quot;&quot;</span>
 <span class="linenos"> 41</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">==</span> <span class="s2">&quot;NUMPY&quot;</span><span class="p">:</span>
@@ -509,7 +509,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 
 <span class="linenos"> 49</span>
 <div class="viewcode-block" id="NDArrayInfo.from_obj">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.NDArrayInfo.from_obj">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.NDArrayInfo.from_obj">[docs]</a>
 <span class="linenos"> 50</span>    <span class="nd">@classmethod</span>
 <span class="linenos"> 51</span>    <span class="k">def</span> <span class="nf">from_obj</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">obj</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s2">&quot;NDArrayInfo&quot;</span><span class="p">:</span>
 <span class="linenos"> 52</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Find array backend associated to `obj`.&quot;&quot;&quot;</span>
@@ -521,7 +521,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 
 <span class="linenos"> 58</span>
 <div class="viewcode-block" id="NDArrayInfo.from_flag">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.NDArrayInfo.from_flag">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.NDArrayInfo.from_flag">[docs]</a>
 <span class="linenos"> 59</span>    <span class="nd">@classmethod</span>
 <span class="linenos"> 60</span>    <span class="k">def</span> <span class="nf">from_flag</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">gpu</span><span class="p">:</span> <span class="nb">bool</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s2">&quot;NDArrayInfo&quot;</span><span class="p">:</span>
 <span class="linenos"> 61</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Find array backend suitable for in-memory CPU/GPU computing.&quot;&quot;&quot;</span>
@@ -532,7 +532,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 
 <span class="linenos"> 66</span>
 <div class="viewcode-block" id="NDArrayInfo.module">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.NDArrayInfo.module">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.NDArrayInfo.module">[docs]</a>
 <span class="linenos"> 67</span>    <span class="k">def</span> <span class="nf">module</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">linalg</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">:</span>
 <span class="linenos"> 68</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 69</span><span class="sd">        Python module associated to an array backend.</span>
@@ -559,7 +559,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 <span class="linenos"> 88</span>
 <span class="linenos"> 89</span>
 <div class="viewcode-block" id="SparseArrayInfo">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.SparseArrayInfo">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.SparseArrayInfo">[docs]</a>
 <span class="linenos"> 90</span><span class="nd">@enum</span><span class="o">.</span><span class="n">unique</span>
 <span class="linenos"> 91</span><span class="k">class</span> <span class="nc">SparseArrayInfo</span><span class="p">(</span><span class="n">enum</span><span class="o">.</span><span class="n">Enum</span><span class="p">):</span>
 <span class="linenos"> 92</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
@@ -571,7 +571,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 <span class="linenos"> 98</span>    <span class="n">CUPY_SPARSE</span> <span class="o">=</span> <span class="n">enum</span><span class="o">.</span><span class="n">auto</span><span class="p">()</span>
 <span class="linenos"> 99</span>
 <div class="viewcode-block" id="SparseArrayInfo.default">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.SparseArrayInfo.default">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.SparseArrayInfo.default">[docs]</a>
 <span class="linenos">100</span>    <span class="nd">@classmethod</span>
 <span class="linenos">101</span>    <span class="k">def</span> <span class="nf">default</span><span class="p">(</span><span class="bp">cls</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s2">&quot;SparseArrayInfo&quot;</span><span class="p">:</span>
 <span class="linenos">102</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Default array backend to use.&quot;&quot;&quot;</span>
@@ -579,7 +579,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 
 <span class="linenos">104</span>
 <div class="viewcode-block" id="SparseArrayInfo.type">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.SparseArrayInfo.type">[docs]</a>
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 <span class="linenos">105</span>    <span class="k">def</span> <span class="nf">type</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">type</span><span class="p">:</span>
 <span class="linenos">106</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Array type associated to a backend.&quot;&quot;&quot;</span>
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@@ -594,7 +594,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 
 <span class="linenos">116</span>
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-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.SparseArrayInfo.from_obj">[docs]</a>
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 <span class="linenos">117</span>    <span class="nd">@classmethod</span>
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 <span class="linenos">119</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Find array backend associated to `obj`.&quot;&quot;&quot;</span>
@@ -606,7 +606,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 
 <span class="linenos">125</span>
 <div class="viewcode-block" id="SparseArrayInfo.module">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.SparseArrayInfo.module">[docs]</a>
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 <span class="linenos">126</span>    <span class="k">def</span> <span class="nf">module</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">linalg</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">:</span>
 <span class="linenos">127</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">128</span><span class="sd">        Python module associated to an array backend.</span>
@@ -633,7 +633,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 <span class="linenos">147</span>
 <span class="linenos">148</span>
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-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.supported_array_types">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.supported_array_types">[docs]</a>
 <span class="linenos">149</span><span class="k">def</span> <span class="nf">supported_array_types</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Collection</span><span class="p">[</span><span class="nb">type</span><span class="p">]:</span>
 <span class="linenos">150</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;List of all supported dense array types in current Pyxu install.&quot;&quot;&quot;</span>
 <span class="linenos">151</span>    <span class="n">data</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
@@ -645,7 +645,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
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 <span class="linenos">157</span>
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-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.supported_array_modules">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.supported_array_modules">[docs]</a>
 <span class="linenos">158</span><span class="k">def</span> <span class="nf">supported_array_modules</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Collection</span><span class="p">[</span><span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">]:</span>
 <span class="linenos">159</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;List of all supported dense array modules in current Pyxu install.&quot;&quot;&quot;</span>
 <span class="linenos">160</span>    <span class="n">data</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
@@ -657,7 +657,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 <span class="linenos">165</span>
 <span class="linenos">166</span>
 <div class="viewcode-block" id="supported_sparse_types">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.supported_sparse_types">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.supported_sparse_types">[docs]</a>
 <span class="linenos">167</span><span class="k">def</span> <span class="nf">supported_sparse_types</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Collection</span><span class="p">[</span><span class="nb">type</span><span class="p">]:</span>
 <span class="linenos">168</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;List of all supported sparse array types in current Pyxu install.&quot;&quot;&quot;</span>
 <span class="linenos">169</span>    <span class="n">data</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
@@ -669,7 +669,7 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
 <span class="linenos">174</span>
 <span class="linenos">175</span>
 <div class="viewcode-block" id="supported_sparse_modules">
-<a class="viewcode-back" href="../../../api/info.html#pyxu.info.deps.supported_sparse_modules">[docs]</a>
+<a class="viewcode-back" href="../../../api/info.deps.html#pyxu.info.deps.supported_sparse_modules">[docs]</a>
 <span class="linenos">176</span><span class="k">def</span> <span class="nf">supported_sparse_modules</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Collection</span><span class="p">[</span><span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">]:</span>
 <span class="linenos">177</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;List of all supported sparse array modules in current Pyxu install.&quot;&quot;&quot;</span>
 <span class="linenos">178</span>    <span class="n">data</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
@@ -759,15 +759,11 @@ <h1>Source code for pyxu.info.deps</h1><div class="highlight"><pre>
       
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   <p class="sphinx-version">
-    Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5.
+     Created with <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5, with some help from <a href="https://chat.openai.com/"> ChatGPT</a> (GPT 4).
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-  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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@@ -378,7 +378,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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diff --git a/_modules/pyxu/info/warning.html b/_modules/pyxu/info/warning.html
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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diff --git a/_modules/pyxu/math/linesearch.html b/_modules/pyxu/math/linesearch.html
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-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
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 <link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
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     <script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -236,7 +236,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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diff --git a/_modules/pyxu/operator/blocks.html b/_modules/pyxu/operator/blocks.html
index ee3f59d0..9c892e5d 100644
--- a/_modules/pyxu/operator/blocks.html
+++ b/_modules/pyxu/operator/blocks.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
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-    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
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@@ -37,13 +37,13 @@
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     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
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 <link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
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     <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
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@@ -236,7 +236,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
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@@ -464,1014 +464,1017 @@ <h1>Source code for pyxu.operator.blocks</h1><div class="highlight"><pre>
 <span class="linenos">  11</span><span class="kn">import</span> <span class="nn">pyxu.info.ptype</span> <span class="k">as</span> <span class="nn">pxt</span>
 <span class="linenos">  12</span><span class="kn">import</span> <span class="nn">pyxu.runtime</span> <span class="k">as</span> <span class="nn">pxrt</span>
 <span class="linenos">  13</span><span class="kn">import</span> <span class="nn">pyxu.util</span> <span class="k">as</span> <span class="nn">pxu</span>
-<span class="linenos">  14</span>
-<span class="linenos">  15</span><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
-<span class="linenos">  16</span>    <span class="s2">&quot;stack&quot;</span><span class="p">,</span>
-<span class="linenos">  17</span>    <span class="s2">&quot;vstack&quot;</span><span class="p">,</span>
-<span class="linenos">  18</span>    <span class="s2">&quot;hstack&quot;</span><span class="p">,</span>
-<span class="linenos">  19</span>    <span class="s2">&quot;block_diag&quot;</span><span class="p">,</span>
-<span class="linenos">  20</span>    <span class="s2">&quot;block&quot;</span><span class="p">,</span>
-<span class="linenos">  21</span>    <span class="s2">&quot;coo_block&quot;</span><span class="p">,</span>
-<span class="linenos">  22</span><span class="p">]</span>
-<span class="linenos">  23</span>
-<span class="linenos">  24</span><span class="c1"># Arithmetic methods/attributes of [hstack, vstack, block_diag, coo_block]() are very similar. To avoid excessive</span>
-<span class="linenos">  25</span><span class="c1"># copy/paste-ing the same implementation everywhere, these functions piggy-back on _COOBlock() for most computations.</span>
-<span class="linenos">  26</span><span class="c1"># When a more efficient implementation is known however, it is overridden in [hstack, vstack, block_diag]() as needed.</span>
-<span class="linenos">  27</span>
-<span class="linenos">  28</span>
+<span class="linenos">  14</span><span class="kn">from</span> <span class="nn">pyxu.info.plugin</span> <span class="kn">import</span> <span class="n">_load_entry_points</span>
+<span class="linenos">  15</span>
+<span class="linenos">  16</span><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
+<span class="linenos">  17</span>    <span class="s2">&quot;stack&quot;</span><span class="p">,</span>
+<span class="linenos">  18</span>    <span class="s2">&quot;vstack&quot;</span><span class="p">,</span>
+<span class="linenos">  19</span>    <span class="s2">&quot;hstack&quot;</span><span class="p">,</span>
+<span class="linenos">  20</span>    <span class="s2">&quot;block_diag&quot;</span><span class="p">,</span>
+<span class="linenos">  21</span>    <span class="s2">&quot;block&quot;</span><span class="p">,</span>
+<span class="linenos">  22</span>    <span class="s2">&quot;coo_block&quot;</span><span class="p">,</span>
+<span class="linenos">  23</span><span class="p">]</span>
+<span class="linenos">  24</span>
+<span class="linenos">  25</span><span class="n">__all__</span> <span class="o">=</span> <span class="n">_load_entry_points</span><span class="p">(</span><span class="nb">globals</span><span class="p">(),</span> <span class="n">group</span><span class="o">=</span><span class="s2">&quot;pyxu.opt.blocks&quot;</span><span class="p">,</span> <span class="n">names</span><span class="o">=</span><span class="n">__all__</span><span class="p">)</span>
+<span class="linenos">  26</span>
+<span class="linenos">  27</span><span class="c1"># Arithmetic methods/attributes of [hstack, vstack, block_diag, coo_block]() are very similar. To avoid excessive</span>
+<span class="linenos">  28</span><span class="c1"># copy/paste-ing the same implementation everywhere, these functions piggy-back on _COOBlock() for most computations.</span>
+<span class="linenos">  29</span><span class="c1"># When a more efficient implementation is known however, it is overridden in [hstack, vstack, block_diag]() as needed.</span>
+<span class="linenos">  30</span>
+<span class="linenos">  31</span>
 <div class="viewcode-block" id="stack">
-<a class="viewcode-back" href="../../../api/operator.html#pyxu.operator.stack">[docs]</a>
-<span class="linenos">  29</span><span class="k">def</span> <span class="nf">stack</span><span class="p">(</span>
-<span class="linenos">  30</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
-<span class="linenos">  31</span>    <span class="n">axis</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
-<span class="linenos">  32</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
-<span class="linenos">  33</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos">  34</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">  35</span><span class="sd">    Construct a stacked operator.</span>
-<span class="linenos">  36</span>
-<span class="linenos">  37</span><span class="sd">    A stacked-operator :math:`V: \mathbb{R}^{d} \to \mathbb{R}^{c}` is an operator containing (vertically or</span>
-<span class="linenos">  38</span><span class="sd">    horizontally) blocks of smaller operators :math:`\{O_{1}, \ldots, O_{N}\}`.</span>
+<a class="viewcode-back" href="../../../api/operator/blocks.html#pyxu.operator.stack">[docs]</a>
+<span class="linenos">  32</span><span class="k">def</span> <span class="nf">stack</span><span class="p">(</span>
+<span class="linenos">  33</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
+<span class="linenos">  34</span>    <span class="n">axis</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
+<span class="linenos">  35</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
+<span class="linenos">  36</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos">  37</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">  38</span><span class="sd">    Construct a stacked operator.</span>
 <span class="linenos">  39</span>
-<span class="linenos">  40</span><span class="sd">    This is a convenience function around :py:func:`~pyxu.operator.hstack` and :py:func:`~pyxu.operator.vstack`.</span>
-<span class="linenos">  41</span>
-<span class="linenos">  42</span><span class="sd">    Parameters</span>
-<span class="linenos">  43</span><span class="sd">    ----------</span>
-<span class="linenos">  44</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` )</span>
-<span class="linenos">  45</span><span class="sd">        [op1(c1, d1), ..., opN(cN, dN)] operators to join.</span>
-<span class="linenos">  46</span><span class="sd">    axis: Integer</span>
-<span class="linenos">  47</span><span class="sd">        The axis along which operators will be joined, i.e.</span>
-<span class="linenos">  48</span>
-<span class="linenos">  49</span><span class="sd">        * 0: stack vertically (row-wise)</span>
-<span class="linenos">  50</span><span class="sd">        * 1: stack horizontally (column-wise)</span>
-<span class="linenos">  51</span><span class="sd">    kwargs</span>
-<span class="linenos">  52</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
-<span class="linenos">  53</span>
-<span class="linenos">  54</span><span class="sd">    Returns</span>
-<span class="linenos">  55</span><span class="sd">    -------</span>
-<span class="linenos">  56</span><span class="sd">    op: OpT</span>
-<span class="linenos">  57</span><span class="sd">        Stacked operator.</span>
-<span class="linenos">  58</span>
-<span class="linenos">  59</span><span class="sd">    See Also</span>
-<span class="linenos">  60</span><span class="sd">    --------</span>
-<span class="linenos">  61</span><span class="sd">    :py:func:`~pyxu.operator.hstack`,</span>
-<span class="linenos">  62</span><span class="sd">    :py:func:`~pyxu.operator.vstack`.</span>
-<span class="linenos">  63</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">  64</span>    <span class="n">axis</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">axis</span><span class="p">)</span>
-<span class="linenos">  65</span>    <span class="k">assert</span> <span class="n">axis</span> <span class="ow">in</span> <span class="p">{</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">},</span> <span class="sa">f</span><span class="s2">&quot;axis: out-of-bounds axis &#39;</span><span class="si">{</span><span class="n">axis</span><span class="si">}</span><span class="s2">&#39;.&quot;</span>
-<span class="linenos">  66</span>
-<span class="linenos">  67</span>    <span class="n">f</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">:</span> <span class="n">vstack</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span> <span class="n">hstack</span><span class="p">}[</span><span class="n">axis</span><span class="p">]</span>
-<span class="linenos">  68</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">ops</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos">  69</span>    <span class="k">return</span> <span class="n">op</span></div>
+<span class="linenos">  40</span><span class="sd">    A stacked-operator :math:`V: \mathbb{R}^{d} \to \mathbb{R}^{c}` is an operator containing (vertically or</span>
+<span class="linenos">  41</span><span class="sd">    horizontally) blocks of smaller operators :math:`\{O_{1}, \ldots, O_{N}\}`.</span>
+<span class="linenos">  42</span>
+<span class="linenos">  43</span><span class="sd">    This is a convenience function around :py:func:`~pyxu.operator.hstack` and :py:func:`~pyxu.operator.vstack`.</span>
+<span class="linenos">  44</span>
+<span class="linenos">  45</span><span class="sd">    Parameters</span>
+<span class="linenos">  46</span><span class="sd">    ----------</span>
+<span class="linenos">  47</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` )</span>
+<span class="linenos">  48</span><span class="sd">        [op1(c1, d1), ..., opN(cN, dN)] operators to join.</span>
+<span class="linenos">  49</span><span class="sd">    axis: Integer</span>
+<span class="linenos">  50</span><span class="sd">        The axis along which operators will be joined, i.e.</span>
+<span class="linenos">  51</span>
+<span class="linenos">  52</span><span class="sd">        * 0: stack vertically (row-wise)</span>
+<span class="linenos">  53</span><span class="sd">        * 1: stack horizontally (column-wise)</span>
+<span class="linenos">  54</span><span class="sd">    kwargs</span>
+<span class="linenos">  55</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
+<span class="linenos">  56</span>
+<span class="linenos">  57</span><span class="sd">    Returns</span>
+<span class="linenos">  58</span><span class="sd">    -------</span>
+<span class="linenos">  59</span><span class="sd">    op: OpT</span>
+<span class="linenos">  60</span><span class="sd">        Stacked operator.</span>
+<span class="linenos">  61</span>
+<span class="linenos">  62</span><span class="sd">    See Also</span>
+<span class="linenos">  63</span><span class="sd">    --------</span>
+<span class="linenos">  64</span><span class="sd">    :py:func:`~pyxu.operator.hstack`,</span>
+<span class="linenos">  65</span><span class="sd">    :py:func:`~pyxu.operator.vstack`.</span>
+<span class="linenos">  66</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">  67</span>    <span class="n">axis</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">axis</span><span class="p">)</span>
+<span class="linenos">  68</span>    <span class="k">assert</span> <span class="n">axis</span> <span class="ow">in</span> <span class="p">{</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">},</span> <span class="sa">f</span><span class="s2">&quot;axis: out-of-bounds axis &#39;</span><span class="si">{</span><span class="n">axis</span><span class="si">}</span><span class="s2">&#39;.&quot;</span>
+<span class="linenos">  69</span>
+<span class="linenos">  70</span>    <span class="n">f</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">:</span> <span class="n">vstack</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span> <span class="n">hstack</span><span class="p">}[</span><span class="n">axis</span><span class="p">]</span>
+<span class="linenos">  71</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">ops</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos">  72</span>    <span class="k">return</span> <span class="n">op</span></div>
 
-<span class="linenos">  70</span>
-<span class="linenos">  71</span>
+<span class="linenos">  73</span>
+<span class="linenos">  74</span>
 <div class="viewcode-block" id="vstack">
-<a class="viewcode-back" href="../../../api/operator.html#pyxu.operator.vstack">[docs]</a>
-<span class="linenos">  72</span><span class="k">def</span> <span class="nf">vstack</span><span class="p">(</span>
-<span class="linenos">  73</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
-<span class="linenos">  74</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
-<span class="linenos">  75</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos">  76</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">  77</span><span class="sd">    Construct a vertically-stacked operator.</span>
-<span class="linenos">  78</span>
-<span class="linenos">  79</span><span class="sd">    A vstacked-operator :math:`V: \mathbb{R}^{d} \to \mathbb{R}^{c_{1} + \cdots + c_{N}}` is an operator containing</span>
-<span class="linenos">  80</span><span class="sd">    (vertically) blocks of smaller operators :math:`\{O_{1}: \mathbb{R}^{d} \to \mathbb{R}^{c_{1}}, \ldots, O_{N}:</span>
-<span class="linenos">  81</span><span class="sd">    \mathbb{R}^{d} \to \mathbb{R}^{c_{N}}\}`, i.e.</span>
-<span class="linenos">  82</span>
-<span class="linenos">  83</span><span class="sd">    .. math::</span>
-<span class="linenos">  84</span>
-<span class="linenos">  85</span><span class="sd">       V</span>
-<span class="linenos">  86</span><span class="sd">       =</span>
-<span class="linenos">  87</span><span class="sd">       \left[</span>
-<span class="linenos">  88</span><span class="sd">           \begin{array}{c}</span>
-<span class="linenos">  89</span><span class="sd">               O_{1}  \\</span>
-<span class="linenos">  90</span><span class="sd">               \vdots \\</span>
-<span class="linenos">  91</span><span class="sd">               O_{N}  \\</span>
-<span class="linenos">  92</span><span class="sd">           \end{array}</span>
-<span class="linenos">  93</span><span class="sd">       \right]</span>
-<span class="linenos">  94</span>
-<span class="linenos">  95</span><span class="sd">    Parameters</span>
-<span class="linenos">  96</span><span class="sd">    ----------</span>
-<span class="linenos">  97</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` )</span>
-<span class="linenos">  98</span><span class="sd">        [op1(c1, d), ..., opN(cN, d)] operators to concatenate.</span>
-<span class="linenos">  99</span><span class="sd">    kwargs</span>
-<span class="linenos"> 100</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
-<span class="linenos"> 101</span>
-<span class="linenos"> 102</span><span class="sd">    Returns</span>
-<span class="linenos"> 103</span><span class="sd">    -------</span>
-<span class="linenos"> 104</span><span class="sd">    op: OpT</span>
-<span class="linenos"> 105</span><span class="sd">        Vertically-stacked (c1+...+cN, d) operator.</span>
-<span class="linenos"> 106</span>
-<span class="linenos"> 107</span><span class="sd">    Notes</span>
-<span class="linenos"> 108</span><span class="sd">    -----</span>
-<span class="linenos"> 109</span><span class="sd">    * All sub-operator domains must have compatible shapes, i.e. all integer-valued ``dim`` s must be identical.</span>
-<span class="linenos"> 110</span>
-<span class="linenos"> 111</span><span class="sd">    See Also</span>
-<span class="linenos"> 112</span><span class="sd">    --------</span>
-<span class="linenos"> 113</span><span class="sd">    :py:func:`~pyxu.operator.hstack`,</span>
-<span class="linenos"> 114</span><span class="sd">    :py:func:`~pyxu.operator.stack`.</span>
-<span class="linenos"> 115</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 116</span>
-<span class="linenos"> 117</span>    <span class="k">def</span> <span class="nf">op_expr</span><span class="p">(</span><span class="n">_</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
-<span class="linenos"> 118</span>        <span class="n">N_row</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-<span class="linenos"> 119</span>        <span class="n">ops</span> <span class="o">=</span> <span class="p">[</span><span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">)]</span>
-<span class="linenos"> 120</span>        <span class="k">return</span> <span class="p">(</span><span class="s2">&quot;vstack&quot;</span><span class="p">,</span> <span class="o">*</span><span class="n">ops</span><span class="p">)</span>
-<span class="linenos"> 121</span>
-<span class="linenos"> 122</span>    <span class="n">N_data</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ops</span><span class="p">)</span>
-<span class="linenos"> 123</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
-<span class="linenos"> 124</span>        <span class="n">ops</span><span class="o">=</span><span class="p">(</span>
-<span class="linenos"> 125</span>            <span class="n">ops</span><span class="p">,</span>  <span class="c1"># data</span>
-<span class="linenos"> 126</span>            <span class="p">(</span>
-<span class="linenos"> 127</span>                <span class="nb">tuple</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_data</span><span class="p">)),</span>  <span class="c1"># i</span>
-<span class="linenos"> 128</span>                <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">N_data</span><span class="p">,</span>  <span class="c1"># j</span>
-<span class="linenos"> 129</span>            <span class="p">),</span>
-<span class="linenos"> 130</span>        <span class="p">),</span>
-<span class="linenos"> 131</span>        <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_data</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span>
-<span class="linenos"> 132</span>        <span class="n">parallel</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;parallel&quot;</span><span class="p">,</span> <span class="kc">False</span><span class="p">),</span>
-<span class="linenos"> 133</span>    <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
-<span class="linenos"> 134</span>    <span class="n">op</span><span class="o">.</span><span class="n">_expr</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_expr</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
-<span class="linenos"> 135</span>    <span class="k">return</span> <span class="n">op</span></div>
+<a class="viewcode-back" href="../../../api/operator/blocks.html#pyxu.operator.vstack">[docs]</a>
+<span class="linenos">  75</span><span class="k">def</span> <span class="nf">vstack</span><span class="p">(</span>
+<span class="linenos">  76</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
+<span class="linenos">  77</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
+<span class="linenos">  78</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos">  79</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">  80</span><span class="sd">    Construct a vertically-stacked operator.</span>
+<span class="linenos">  81</span>
+<span class="linenos">  82</span><span class="sd">    A vstacked-operator :math:`V: \mathbb{R}^{d} \to \mathbb{R}^{c_{1} + \cdots + c_{N}}` is an operator containing</span>
+<span class="linenos">  83</span><span class="sd">    (vertically) blocks of smaller operators :math:`\{O_{1}: \mathbb{R}^{d} \to \mathbb{R}^{c_{1}}, \ldots, O_{N}:</span>
+<span class="linenos">  84</span><span class="sd">    \mathbb{R}^{d} \to \mathbb{R}^{c_{N}}\}`, i.e.</span>
+<span class="linenos">  85</span>
+<span class="linenos">  86</span><span class="sd">    .. math::</span>
+<span class="linenos">  87</span>
+<span class="linenos">  88</span><span class="sd">       V</span>
+<span class="linenos">  89</span><span class="sd">       =</span>
+<span class="linenos">  90</span><span class="sd">       \left[</span>
+<span class="linenos">  91</span><span class="sd">           \begin{array}{c}</span>
+<span class="linenos">  92</span><span class="sd">               O_{1}  \\</span>
+<span class="linenos">  93</span><span class="sd">               \vdots \\</span>
+<span class="linenos">  94</span><span class="sd">               O_{N}  \\</span>
+<span class="linenos">  95</span><span class="sd">           \end{array}</span>
+<span class="linenos">  96</span><span class="sd">       \right]</span>
+<span class="linenos">  97</span>
+<span class="linenos">  98</span><span class="sd">    Parameters</span>
+<span class="linenos">  99</span><span class="sd">    ----------</span>
+<span class="linenos"> 100</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` )</span>
+<span class="linenos"> 101</span><span class="sd">        [op1(c1, d), ..., opN(cN, d)] operators to concatenate.</span>
+<span class="linenos"> 102</span><span class="sd">    kwargs</span>
+<span class="linenos"> 103</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
+<span class="linenos"> 104</span>
+<span class="linenos"> 105</span><span class="sd">    Returns</span>
+<span class="linenos"> 106</span><span class="sd">    -------</span>
+<span class="linenos"> 107</span><span class="sd">    op: OpT</span>
+<span class="linenos"> 108</span><span class="sd">        Vertically-stacked (c1+...+cN, d) operator.</span>
+<span class="linenos"> 109</span>
+<span class="linenos"> 110</span><span class="sd">    Notes</span>
+<span class="linenos"> 111</span><span class="sd">    -----</span>
+<span class="linenos"> 112</span><span class="sd">    * All sub-operator domains must have compatible shapes, i.e. all integer-valued ``dim`` s must be identical.</span>
+<span class="linenos"> 113</span>
+<span class="linenos"> 114</span><span class="sd">    See Also</span>
+<span class="linenos"> 115</span><span class="sd">    --------</span>
+<span class="linenos"> 116</span><span class="sd">    :py:func:`~pyxu.operator.hstack`,</span>
+<span class="linenos"> 117</span><span class="sd">    :py:func:`~pyxu.operator.stack`.</span>
+<span class="linenos"> 118</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 119</span>
+<span class="linenos"> 120</span>    <span class="k">def</span> <span class="nf">op_expr</span><span class="p">(</span><span class="n">_</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
+<span class="linenos"> 121</span>        <span class="n">N_row</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<span class="linenos"> 122</span>        <span class="n">ops</span> <span class="o">=</span> <span class="p">[</span><span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">)]</span>
+<span class="linenos"> 123</span>        <span class="k">return</span> <span class="p">(</span><span class="s2">&quot;vstack&quot;</span><span class="p">,</span> <span class="o">*</span><span class="n">ops</span><span class="p">)</span>
+<span class="linenos"> 124</span>
+<span class="linenos"> 125</span>    <span class="n">N_data</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ops</span><span class="p">)</span>
+<span class="linenos"> 126</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
+<span class="linenos"> 127</span>        <span class="n">ops</span><span class="o">=</span><span class="p">(</span>
+<span class="linenos"> 128</span>            <span class="n">ops</span><span class="p">,</span>  <span class="c1"># data</span>
+<span class="linenos"> 129</span>            <span class="p">(</span>
+<span class="linenos"> 130</span>                <span class="nb">tuple</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_data</span><span class="p">)),</span>  <span class="c1"># i</span>
+<span class="linenos"> 131</span>                <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">N_data</span><span class="p">,</span>  <span class="c1"># j</span>
+<span class="linenos"> 132</span>            <span class="p">),</span>
+<span class="linenos"> 133</span>        <span class="p">),</span>
+<span class="linenos"> 134</span>        <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_data</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span>
+<span class="linenos"> 135</span>        <span class="n">parallel</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;parallel&quot;</span><span class="p">,</span> <span class="kc">False</span><span class="p">),</span>
+<span class="linenos"> 136</span>    <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
+<span class="linenos"> 137</span>    <span class="n">op</span><span class="o">.</span><span class="n">_expr</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_expr</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
+<span class="linenos"> 138</span>    <span class="k">return</span> <span class="n">op</span></div>
 
-<span class="linenos"> 136</span>
-<span class="linenos"> 137</span>
+<span class="linenos"> 139</span>
+<span class="linenos"> 140</span>
 <div class="viewcode-block" id="hstack">
-<a class="viewcode-back" href="../../../api/operator.html#pyxu.operator.hstack">[docs]</a>
-<span class="linenos"> 138</span><span class="k">def</span> <span class="nf">hstack</span><span class="p">(</span>
-<span class="linenos"> 139</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
-<span class="linenos"> 140</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
-<span class="linenos"> 141</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos"> 142</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 143</span><span class="sd">    Construct a horizontally-stacked operator.</span>
-<span class="linenos"> 144</span>
-<span class="linenos"> 145</span><span class="sd">    A hstacked-operator :math:`H: \mathbb{R}^{d_{1} + \cdots + d_{N}} \to \mathbb{R}^{c}` is an operator containing</span>
-<span class="linenos"> 146</span><span class="sd">    (horizontally) blocks of smaller operators :math:`\{O_{1}: \mathbb{R}^{d_{1}} \to \mathbb{R}^{c}, \ldots, O_{N}:</span>
-<span class="linenos"> 147</span><span class="sd">    \mathbb{R}^{d_{N}} \to \mathbb{R}^{c}\}`, i.e.</span>
-<span class="linenos"> 148</span>
-<span class="linenos"> 149</span><span class="sd">    .. math::</span>
-<span class="linenos"> 150</span>
-<span class="linenos"> 151</span><span class="sd">       H</span>
-<span class="linenos"> 152</span><span class="sd">       =</span>
-<span class="linenos"> 153</span><span class="sd">       \left[</span>
-<span class="linenos"> 154</span><span class="sd">           \begin{array}{ccc}</span>
-<span class="linenos"> 155</span><span class="sd">               O_{1} &amp; \cdots &amp; O_{N}</span>
-<span class="linenos"> 156</span><span class="sd">           \end{array}</span>
-<span class="linenos"> 157</span><span class="sd">       \right]</span>
-<span class="linenos"> 158</span>
-<span class="linenos"> 159</span><span class="sd">    Parameters</span>
-<span class="linenos"> 160</span><span class="sd">    ----------</span>
-<span class="linenos"> 161</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` )</span>
-<span class="linenos"> 162</span><span class="sd">        [op1(c, d1), ..., opN(c, dN)] operators to concatenate.</span>
-<span class="linenos"> 163</span><span class="sd">    kwargs</span>
-<span class="linenos"> 164</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
-<span class="linenos"> 165</span>
-<span class="linenos"> 166</span><span class="sd">    Returns</span>
-<span class="linenos"> 167</span><span class="sd">    -------</span>
-<span class="linenos"> 168</span><span class="sd">    op: OpT</span>
-<span class="linenos"> 169</span><span class="sd">        Horizontally-stacked (c, d1+....+dN) operator.</span>
-<span class="linenos"> 170</span>
-<span class="linenos"> 171</span><span class="sd">    Notes</span>
-<span class="linenos"> 172</span><span class="sd">    -----</span>
-<span class="linenos"> 173</span><span class="sd">    * All sub-operator domains must have compatible shapes, i.e. all ``codim`` s must be identical.</span>
-<span class="linenos"> 174</span>
-<span class="linenos"> 175</span><span class="sd">    See Also</span>
-<span class="linenos"> 176</span><span class="sd">    --------</span>
-<span class="linenos"> 177</span><span class="sd">    :py:func:`~pyxu.operator.vstack`,</span>
-<span class="linenos"> 178</span><span class="sd">    :py:func:`~pyxu.operator.stack`.</span>
-<span class="linenos"> 179</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 180</span>
-<span class="linenos"> 181</span>    <span class="k">def</span> <span class="nf">op_expr</span><span class="p">(</span><span class="n">_</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
-<span class="linenos"> 182</span>        <span class="n">N_col</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
-<span class="linenos"> 183</span>        <span class="n">ops</span> <span class="o">=</span> <span class="p">[</span><span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">)]</span>
-<span class="linenos"> 184</span>        <span class="k">return</span> <span class="p">(</span><span class="s2">&quot;hstack&quot;</span><span class="p">,</span> <span class="o">*</span><span class="n">ops</span><span class="p">)</span>
-<span class="linenos"> 185</span>
-<span class="linenos"> 186</span>    <span class="n">N_data</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ops</span><span class="p">)</span>
-<span class="linenos"> 187</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
-<span class="linenos"> 188</span>        <span class="n">ops</span><span class="o">=</span><span class="p">(</span>
-<span class="linenos"> 189</span>            <span class="n">ops</span><span class="p">,</span>  <span class="c1"># data</span>
-<span class="linenos"> 190</span>            <span class="p">(</span>
-<span class="linenos"> 191</span>                <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">N_data</span><span class="p">,</span>  <span class="c1"># i</span>
-<span class="linenos"> 192</span>                <span class="nb">tuple</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_data</span><span class="p">)),</span>  <span class="c1"># j</span>
-<span class="linenos"> 193</span>            <span class="p">),</span>
-<span class="linenos"> 194</span>        <span class="p">),</span>
-<span class="linenos"> 195</span>        <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">N_data</span><span class="p">),</span>
-<span class="linenos"> 196</span>        <span class="n">parallel</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;parallel&quot;</span><span class="p">,</span> <span class="kc">False</span><span class="p">),</span>
-<span class="linenos"> 197</span>    <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
-<span class="linenos"> 198</span>    <span class="n">op</span><span class="o">.</span><span class="n">_expr</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_expr</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
-<span class="linenos"> 199</span>    <span class="k">return</span> <span class="n">op</span></div>
+<a class="viewcode-back" href="../../../api/operator/blocks.html#pyxu.operator.hstack">[docs]</a>
+<span class="linenos"> 141</span><span class="k">def</span> <span class="nf">hstack</span><span class="p">(</span>
+<span class="linenos"> 142</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
+<span class="linenos"> 143</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
+<span class="linenos"> 144</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos"> 145</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 146</span><span class="sd">    Construct a horizontally-stacked operator.</span>
+<span class="linenos"> 147</span>
+<span class="linenos"> 148</span><span class="sd">    A hstacked-operator :math:`H: \mathbb{R}^{d_{1} + \cdots + d_{N}} \to \mathbb{R}^{c}` is an operator containing</span>
+<span class="linenos"> 149</span><span class="sd">    (horizontally) blocks of smaller operators :math:`\{O_{1}: \mathbb{R}^{d_{1}} \to \mathbb{R}^{c}, \ldots, O_{N}:</span>
+<span class="linenos"> 150</span><span class="sd">    \mathbb{R}^{d_{N}} \to \mathbb{R}^{c}\}`, i.e.</span>
+<span class="linenos"> 151</span>
+<span class="linenos"> 152</span><span class="sd">    .. math::</span>
+<span class="linenos"> 153</span>
+<span class="linenos"> 154</span><span class="sd">       H</span>
+<span class="linenos"> 155</span><span class="sd">       =</span>
+<span class="linenos"> 156</span><span class="sd">       \left[</span>
+<span class="linenos"> 157</span><span class="sd">           \begin{array}{ccc}</span>
+<span class="linenos"> 158</span><span class="sd">               O_{1} &amp; \cdots &amp; O_{N}</span>
+<span class="linenos"> 159</span><span class="sd">           \end{array}</span>
+<span class="linenos"> 160</span><span class="sd">       \right]</span>
+<span class="linenos"> 161</span>
+<span class="linenos"> 162</span><span class="sd">    Parameters</span>
+<span class="linenos"> 163</span><span class="sd">    ----------</span>
+<span class="linenos"> 164</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` )</span>
+<span class="linenos"> 165</span><span class="sd">        [op1(c, d1), ..., opN(c, dN)] operators to concatenate.</span>
+<span class="linenos"> 166</span><span class="sd">    kwargs</span>
+<span class="linenos"> 167</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
+<span class="linenos"> 168</span>
+<span class="linenos"> 169</span><span class="sd">    Returns</span>
+<span class="linenos"> 170</span><span class="sd">    -------</span>
+<span class="linenos"> 171</span><span class="sd">    op: OpT</span>
+<span class="linenos"> 172</span><span class="sd">        Horizontally-stacked (c, d1+....+dN) operator.</span>
+<span class="linenos"> 173</span>
+<span class="linenos"> 174</span><span class="sd">    Notes</span>
+<span class="linenos"> 175</span><span class="sd">    -----</span>
+<span class="linenos"> 176</span><span class="sd">    * All sub-operator domains must have compatible shapes, i.e. all ``codim`` s must be identical.</span>
+<span class="linenos"> 177</span>
+<span class="linenos"> 178</span><span class="sd">    See Also</span>
+<span class="linenos"> 179</span><span class="sd">    --------</span>
+<span class="linenos"> 180</span><span class="sd">    :py:func:`~pyxu.operator.vstack`,</span>
+<span class="linenos"> 181</span><span class="sd">    :py:func:`~pyxu.operator.stack`.</span>
+<span class="linenos"> 182</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 183</span>
+<span class="linenos"> 184</span>    <span class="k">def</span> <span class="nf">op_expr</span><span class="p">(</span><span class="n">_</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
+<span class="linenos"> 185</span>        <span class="n">N_col</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+<span class="linenos"> 186</span>        <span class="n">ops</span> <span class="o">=</span> <span class="p">[</span><span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">)]</span>
+<span class="linenos"> 187</span>        <span class="k">return</span> <span class="p">(</span><span class="s2">&quot;hstack&quot;</span><span class="p">,</span> <span class="o">*</span><span class="n">ops</span><span class="p">)</span>
+<span class="linenos"> 188</span>
+<span class="linenos"> 189</span>    <span class="n">N_data</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ops</span><span class="p">)</span>
+<span class="linenos"> 190</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
+<span class="linenos"> 191</span>        <span class="n">ops</span><span class="o">=</span><span class="p">(</span>
+<span class="linenos"> 192</span>            <span class="n">ops</span><span class="p">,</span>  <span class="c1"># data</span>
+<span class="linenos"> 193</span>            <span class="p">(</span>
+<span class="linenos"> 194</span>                <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">N_data</span><span class="p">,</span>  <span class="c1"># i</span>
+<span class="linenos"> 195</span>                <span class="nb">tuple</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_data</span><span class="p">)),</span>  <span class="c1"># j</span>
+<span class="linenos"> 196</span>            <span class="p">),</span>
+<span class="linenos"> 197</span>        <span class="p">),</span>
+<span class="linenos"> 198</span>        <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">N_data</span><span class="p">),</span>
+<span class="linenos"> 199</span>        <span class="n">parallel</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;parallel&quot;</span><span class="p">,</span> <span class="kc">False</span><span class="p">),</span>
+<span class="linenos"> 200</span>    <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
+<span class="linenos"> 201</span>    <span class="n">op</span><span class="o">.</span><span class="n">_expr</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_expr</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
+<span class="linenos"> 202</span>    <span class="k">return</span> <span class="n">op</span></div>
 
-<span class="linenos"> 200</span>
-<span class="linenos"> 201</span>
+<span class="linenos"> 203</span>
+<span class="linenos"> 204</span>
 <div class="viewcode-block" id="block_diag">
-<a class="viewcode-back" href="../../../api/operator.html#pyxu.operator.block_diag">[docs]</a>
-<span class="linenos"> 202</span><span class="k">def</span> <span class="nf">block_diag</span><span class="p">(</span>
-<span class="linenos"> 203</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
-<span class="linenos"> 204</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
-<span class="linenos"> 205</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos"> 206</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 207</span><span class="sd">    Construct a block-diagonal operator.</span>
-<span class="linenos"> 208</span>
-<span class="linenos"> 209</span><span class="sd">    A block-diagonal operator :math:`D: \mathbb{R}^{d_{1} + \cdots + d_{N}} \to \mathbb{R}^{c_{1} + \cdots + c_{N}}` is</span>
-<span class="linenos"> 210</span><span class="sd">    an operator containing (diagonally) blocks of smaller operators :math:`\{O_{1}: \mathbb{R}^{d_{1}} \to</span>
-<span class="linenos"> 211</span><span class="sd">    \mathbb{R}^{c_{1}}, \ldots, O_{N}: \mathbb{R}^{d_{N}} \to \mathbb{R}^{c_{N}}\}`, i.e.</span>
-<span class="linenos"> 212</span>
-<span class="linenos"> 213</span><span class="sd">    .. math::</span>
-<span class="linenos"> 214</span>
-<span class="linenos"> 215</span><span class="sd">       D</span>
-<span class="linenos"> 216</span><span class="sd">       =</span>
-<span class="linenos"> 217</span><span class="sd">       \left[</span>
-<span class="linenos"> 218</span><span class="sd">           \begin{array}{ccc}</span>
-<span class="linenos"> 219</span><span class="sd">               O_{1} &amp;        &amp;       \\</span>
-<span class="linenos"> 220</span><span class="sd">                     &amp; \ddots &amp;       \\</span>
-<span class="linenos"> 221</span><span class="sd">                     &amp;        &amp; O_{N} \\</span>
-<span class="linenos"> 222</span><span class="sd">           \end{array}</span>
-<span class="linenos"> 223</span><span class="sd">       \right]</span>
-<span class="linenos"> 224</span>
-<span class="linenos"> 225</span><span class="sd">    Parameters</span>
-<span class="linenos"> 226</span><span class="sd">    ----------</span>
-<span class="linenos"> 227</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` )</span>
-<span class="linenos"> 228</span><span class="sd">        [op1(c1, d1), ..., opN(cN, dN)] operators to concatenate.</span>
-<span class="linenos"> 229</span><span class="sd">    kwargs</span>
-<span class="linenos"> 230</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
-<span class="linenos"> 231</span>
-<span class="linenos"> 232</span><span class="sd">    Returns</span>
-<span class="linenos"> 233</span><span class="sd">    -------</span>
-<span class="linenos"> 234</span><span class="sd">    op: OpT</span>
-<span class="linenos"> 235</span><span class="sd">        Block-diagonal (c1+...+cN, d1+...+dN) operator.</span>
-<span class="linenos"> 236</span>
-<span class="linenos"> 237</span><span class="sd">    See Also</span>
-<span class="linenos"> 238</span><span class="sd">    --------</span>
-<span class="linenos"> 239</span><span class="sd">    :py:func:`~pyxu.operator.block`,</span>
-<span class="linenos"> 240</span><span class="sd">    :py:func:`~pyxu.operator.coo_block`.</span>
-<span class="linenos"> 241</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 242</span>
-<span class="linenos"> 243</span>    <span class="k">def</span> <span class="nf">op_svdvals</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 244</span>        <span class="c1"># op.svdvals(**kwargs) = [top|bottom-k]([op1.svdvals(**kwargs), ..., opN.svdvals(**kwargs)])</span>
-<span class="linenos"> 245</span>        <span class="k">if</span> <span class="ow">not</span> <span class="n">_</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
-<span class="linenos"> 246</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 247</span>
-<span class="linenos"> 248</span>        <span class="n">k</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;k&quot;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos"> 249</span>        <span class="n">which</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;which&quot;</span><span class="p">,</span> <span class="s2">&quot;LM&quot;</span><span class="p">)</span>
-<span class="linenos"> 250</span>        <span class="k">if</span> <span class="n">which</span><span class="o">.</span><span class="n">upper</span><span class="p">()</span> <span class="o">==</span> <span class="s2">&quot;SM&quot;</span><span class="p">:</span>
-<span class="linenos"> 251</span>            <span class="n">D</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">svdvals</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 252</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 253</span>            <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">svdvals</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">values</span><span class="p">()]</span>
-<span class="linenos"> 254</span>            <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">parts</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="linenos"> 255</span>            <span class="n">D</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">parts</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="kc">None</span><span class="p">)[</span><span class="o">-</span><span class="n">k</span><span class="p">:]</span>
-<span class="linenos"> 256</span>        <span class="k">return</span> <span class="n">D</span>
-<span class="linenos"> 257</span>
-<span class="linenos"> 258</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;damp&quot;</span><span class="p">))</span>
-<span class="linenos"> 259</span>    <span class="k">def</span> <span class="nf">op_pinv</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">damp</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 260</span>        <span class="c1"># op.pinv(y, damp) = concatenate([op1.pinv(y1, damp), ..., opN.pinv(yN, damp)], axis=-1)</span>
-<span class="linenos"> 261</span>        <span class="k">if</span> <span class="ow">not</span> <span class="n">_</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
-<span class="linenos"> 262</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 263</span>
-<span class="linenos"> 264</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
-<span class="linenos"> 265</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 266</span>            <span class="n">offset</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
-<span class="linenos"> 267</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">codim</span><span class="p">],</span> <span class="n">damp</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 268</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
-<span class="linenos"> 269</span>
-<span class="linenos"> 270</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
-<span class="linenos"> 271</span>        <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">parts</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">parts</span><span class="o">.</span><span class="n">keys</span><span class="p">())]</span>
-<span class="linenos"> 272</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">parts</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
-<span class="linenos"> 273</span>        <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 274</span>
-<span class="linenos"> 275</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">()</span>
-<span class="linenos"> 276</span>    <span class="k">def</span> <span class="nf">op_trace</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
-<span class="linenos"> 277</span>        <span class="c1"># op.trace(**kwargs) = if [op1,...,opN] square</span>
-<span class="linenos"> 278</span>        <span class="c1">#                          sum([op1.trace(**kwargs), ..., opN.trace(**kwargs)])</span>
-<span class="linenos"> 279</span>        <span class="c1">#                      else</span>
-<span class="linenos"> 280</span>        <span class="c1">#                          SquareOp.trace(**kwargs)</span>
-<span class="linenos"> 281</span>        <span class="k">if</span> <span class="ow">not</span> <span class="n">_</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR_SQUARE</span><span class="p">):</span>
-<span class="linenos"> 282</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 283</span>
-<span class="linenos"> 284</span>        <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR_SQUARE</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">values</span><span class="p">()):</span>
-<span class="linenos"> 285</span>            <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">trace</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">values</span><span class="p">()]</span>
-<span class="linenos"> 286</span>            <span class="n">tr</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
-<span class="linenos"> 287</span>        <span class="k">else</span><span class="p">:</span>  <span class="c1"># default fallback</span>
-<span class="linenos"> 288</span>            <span class="n">tr</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">SquareOp</span><span class="o">.</span><span class="n">trace</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 289</span>        <span class="k">return</span> <span class="n">tr</span>
-<span class="linenos"> 290</span>
-<span class="linenos"> 291</span>    <span class="k">def</span> <span class="nf">op_expr</span><span class="p">(</span><span class="n">_</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
-<span class="linenos"> 292</span>        <span class="n">ops</span> <span class="o">=</span> <span class="p">[</span><span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">keys</span><span class="p">())]</span>
-<span class="linenos"> 293</span>        <span class="k">return</span> <span class="p">(</span><span class="s2">&quot;block_diag&quot;</span><span class="p">,</span> <span class="o">*</span><span class="n">ops</span><span class="p">)</span>
-<span class="linenos"> 294</span>
-<span class="linenos"> 295</span>    <span class="n">N_data</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ops</span><span class="p">)</span>
-<span class="linenos"> 296</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
-<span class="linenos"> 297</span>        <span class="n">ops</span><span class="o">=</span><span class="p">(</span>
-<span class="linenos"> 298</span>            <span class="n">ops</span><span class="p">,</span>  <span class="c1"># data</span>
-<span class="linenos"> 299</span>            <span class="p">(</span>
-<span class="linenos"> 300</span>                <span class="nb">tuple</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_data</span><span class="p">)),</span>  <span class="c1"># i</span>
-<span class="linenos"> 301</span>                <span class="nb">tuple</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_data</span><span class="p">)),</span>  <span class="c1"># j</span>
-<span class="linenos"> 302</span>            <span class="p">),</span>
-<span class="linenos"> 303</span>        <span class="p">),</span>
-<span class="linenos"> 304</span>        <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_data</span><span class="p">,</span> <span class="n">N_data</span><span class="p">),</span>
-<span class="linenos"> 305</span>        <span class="n">parallel</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;parallel&quot;</span><span class="p">,</span> <span class="kc">False</span><span class="p">),</span>
-<span class="linenos"> 306</span>    <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
-<span class="linenos"> 307</span>    <span class="n">op</span><span class="o">.</span><span class="n">svdvals</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_svdvals</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
-<span class="linenos"> 308</span>    <span class="n">op</span><span class="o">.</span><span class="n">pinv</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_pinv</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
-<span class="linenos"> 309</span>    <span class="n">op</span><span class="o">.</span><span class="n">trace</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_trace</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
-<span class="linenos"> 310</span>    <span class="n">op</span><span class="o">.</span><span class="n">_expr</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_expr</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
-<span class="linenos"> 311</span>    <span class="k">return</span> <span class="n">op</span></div>
+<a class="viewcode-back" href="../../../api/operator/blocks.html#pyxu.operator.block_diag">[docs]</a>
+<span class="linenos"> 205</span><span class="k">def</span> <span class="nf">block_diag</span><span class="p">(</span>
+<span class="linenos"> 206</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
+<span class="linenos"> 207</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
+<span class="linenos"> 208</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos"> 209</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 210</span><span class="sd">    Construct a block-diagonal operator.</span>
+<span class="linenos"> 211</span>
+<span class="linenos"> 212</span><span class="sd">    A block-diagonal operator :math:`D: \mathbb{R}^{d_{1} + \cdots + d_{N}} \to \mathbb{R}^{c_{1} + \cdots + c_{N}}` is</span>
+<span class="linenos"> 213</span><span class="sd">    an operator containing (diagonally) blocks of smaller operators :math:`\{O_{1}: \mathbb{R}^{d_{1}} \to</span>
+<span class="linenos"> 214</span><span class="sd">    \mathbb{R}^{c_{1}}, \ldots, O_{N}: \mathbb{R}^{d_{N}} \to \mathbb{R}^{c_{N}}\}`, i.e.</span>
+<span class="linenos"> 215</span>
+<span class="linenos"> 216</span><span class="sd">    .. math::</span>
+<span class="linenos"> 217</span>
+<span class="linenos"> 218</span><span class="sd">       D</span>
+<span class="linenos"> 219</span><span class="sd">       =</span>
+<span class="linenos"> 220</span><span class="sd">       \left[</span>
+<span class="linenos"> 221</span><span class="sd">           \begin{array}{ccc}</span>
+<span class="linenos"> 222</span><span class="sd">               O_{1} &amp;        &amp;       \\</span>
+<span class="linenos"> 223</span><span class="sd">                     &amp; \ddots &amp;       \\</span>
+<span class="linenos"> 224</span><span class="sd">                     &amp;        &amp; O_{N} \\</span>
+<span class="linenos"> 225</span><span class="sd">           \end{array}</span>
+<span class="linenos"> 226</span><span class="sd">       \right]</span>
+<span class="linenos"> 227</span>
+<span class="linenos"> 228</span><span class="sd">    Parameters</span>
+<span class="linenos"> 229</span><span class="sd">    ----------</span>
+<span class="linenos"> 230</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` )</span>
+<span class="linenos"> 231</span><span class="sd">        [op1(c1, d1), ..., opN(cN, dN)] operators to concatenate.</span>
+<span class="linenos"> 232</span><span class="sd">    kwargs</span>
+<span class="linenos"> 233</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
+<span class="linenos"> 234</span>
+<span class="linenos"> 235</span><span class="sd">    Returns</span>
+<span class="linenos"> 236</span><span class="sd">    -------</span>
+<span class="linenos"> 237</span><span class="sd">    op: OpT</span>
+<span class="linenos"> 238</span><span class="sd">        Block-diagonal (c1+...+cN, d1+...+dN) operator.</span>
+<span class="linenos"> 239</span>
+<span class="linenos"> 240</span><span class="sd">    See Also</span>
+<span class="linenos"> 241</span><span class="sd">    --------</span>
+<span class="linenos"> 242</span><span class="sd">    :py:func:`~pyxu.operator.block`,</span>
+<span class="linenos"> 243</span><span class="sd">    :py:func:`~pyxu.operator.coo_block`.</span>
+<span class="linenos"> 244</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 245</span>
+<span class="linenos"> 246</span>    <span class="k">def</span> <span class="nf">op_svdvals</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 247</span>        <span class="c1"># op.svdvals(**kwargs) = [top|bottom-k]([op1.svdvals(**kwargs), ..., opN.svdvals(**kwargs)])</span>
+<span class="linenos"> 248</span>        <span class="k">if</span> <span class="ow">not</span> <span class="n">_</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
+<span class="linenos"> 249</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 250</span>
+<span class="linenos"> 251</span>        <span class="n">k</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;k&quot;</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos"> 252</span>        <span class="n">which</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;which&quot;</span><span class="p">,</span> <span class="s2">&quot;LM&quot;</span><span class="p">)</span>
+<span class="linenos"> 253</span>        <span class="k">if</span> <span class="n">which</span><span class="o">.</span><span class="n">upper</span><span class="p">()</span> <span class="o">==</span> <span class="s2">&quot;SM&quot;</span><span class="p">:</span>
+<span class="linenos"> 254</span>            <span class="n">D</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">svdvals</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos"> 255</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 256</span>            <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">svdvals</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">values</span><span class="p">()]</span>
+<span class="linenos"> 257</span>            <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">parts</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<span class="linenos"> 258</span>            <span class="n">D</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">parts</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="kc">None</span><span class="p">)[</span><span class="o">-</span><span class="n">k</span><span class="p">:]</span>
+<span class="linenos"> 259</span>        <span class="k">return</span> <span class="n">D</span>
+<span class="linenos"> 260</span>
+<span class="linenos"> 261</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;damp&quot;</span><span class="p">))</span>
+<span class="linenos"> 262</span>    <span class="k">def</span> <span class="nf">op_pinv</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">damp</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 263</span>        <span class="c1"># op.pinv(y, damp) = concatenate([op1.pinv(y1, damp), ..., opN.pinv(yN, damp)], axis=-1)</span>
+<span class="linenos"> 264</span>        <span class="k">if</span> <span class="ow">not</span> <span class="n">_</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
+<span class="linenos"> 265</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 266</span>
+<span class="linenos"> 267</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+<span class="linenos"> 268</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 269</span>            <span class="n">offset</span> <span class="o">=</span> <span class="n">_</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<span class="linenos"> 270</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">codim</span><span class="p">],</span> <span class="n">damp</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos"> 271</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
+<span class="linenos"> 272</span>
+<span class="linenos"> 273</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+<span class="linenos"> 274</span>        <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">parts</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">parts</span><span class="o">.</span><span class="n">keys</span><span class="p">())]</span>
+<span class="linenos"> 275</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">parts</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
+<span class="linenos"> 276</span>        <span class="k">return</span> <span class="n">out</span>
+<span class="linenos"> 277</span>
+<span class="linenos"> 278</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">()</span>
+<span class="linenos"> 279</span>    <span class="k">def</span> <span class="nf">op_trace</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
+<span class="linenos"> 280</span>        <span class="c1"># op.trace(**kwargs) = if [op1,...,opN] square</span>
+<span class="linenos"> 281</span>        <span class="c1">#                          sum([op1.trace(**kwargs), ..., opN.trace(**kwargs)])</span>
+<span class="linenos"> 282</span>        <span class="c1">#                      else</span>
+<span class="linenos"> 283</span>        <span class="c1">#                          SquareOp.trace(**kwargs)</span>
+<span class="linenos"> 284</span>        <span class="k">if</span> <span class="ow">not</span> <span class="n">_</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR_SQUARE</span><span class="p">):</span>
+<span class="linenos"> 285</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 286</span>
+<span class="linenos"> 287</span>        <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR_SQUARE</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">values</span><span class="p">()):</span>
+<span class="linenos"> 288</span>            <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">trace</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">values</span><span class="p">()]</span>
+<span class="linenos"> 289</span>            <span class="n">tr</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
+<span class="linenos"> 290</span>        <span class="k">else</span><span class="p">:</span>  <span class="c1"># default fallback</span>
+<span class="linenos"> 291</span>            <span class="n">tr</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">SquareOp</span><span class="o">.</span><span class="n">trace</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos"> 292</span>        <span class="k">return</span> <span class="n">tr</span>
+<span class="linenos"> 293</span>
+<span class="linenos"> 294</span>    <span class="k">def</span> <span class="nf">op_expr</span><span class="p">(</span><span class="n">_</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
+<span class="linenos"> 295</span>        <span class="n">ops</span> <span class="o">=</span> <span class="p">[</span><span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">_</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">keys</span><span class="p">())]</span>
+<span class="linenos"> 296</span>        <span class="k">return</span> <span class="p">(</span><span class="s2">&quot;block_diag&quot;</span><span class="p">,</span> <span class="o">*</span><span class="n">ops</span><span class="p">)</span>
+<span class="linenos"> 297</span>
+<span class="linenos"> 298</span>    <span class="n">N_data</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">ops</span><span class="p">)</span>
+<span class="linenos"> 299</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
+<span class="linenos"> 300</span>        <span class="n">ops</span><span class="o">=</span><span class="p">(</span>
+<span class="linenos"> 301</span>            <span class="n">ops</span><span class="p">,</span>  <span class="c1"># data</span>
+<span class="linenos"> 302</span>            <span class="p">(</span>
+<span class="linenos"> 303</span>                <span class="nb">tuple</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_data</span><span class="p">)),</span>  <span class="c1"># i</span>
+<span class="linenos"> 304</span>                <span class="nb">tuple</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_data</span><span class="p">)),</span>  <span class="c1"># j</span>
+<span class="linenos"> 305</span>            <span class="p">),</span>
+<span class="linenos"> 306</span>        <span class="p">),</span>
+<span class="linenos"> 307</span>        <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_data</span><span class="p">,</span> <span class="n">N_data</span><span class="p">),</span>
+<span class="linenos"> 308</span>        <span class="n">parallel</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;parallel&quot;</span><span class="p">,</span> <span class="kc">False</span><span class="p">),</span>
+<span class="linenos"> 309</span>    <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
+<span class="linenos"> 310</span>    <span class="n">op</span><span class="o">.</span><span class="n">svdvals</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_svdvals</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
+<span class="linenos"> 311</span>    <span class="n">op</span><span class="o">.</span><span class="n">pinv</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_pinv</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
+<span class="linenos"> 312</span>    <span class="n">op</span><span class="o">.</span><span class="n">trace</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_trace</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
+<span class="linenos"> 313</span>    <span class="n">op</span><span class="o">.</span><span class="n">_expr</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_expr</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span>
+<span class="linenos"> 314</span>    <span class="k">return</span> <span class="n">op</span></div>
 
-<span class="linenos"> 312</span>
-<span class="linenos"> 313</span>
+<span class="linenos"> 315</span>
+<span class="linenos"> 316</span>
 <div class="viewcode-block" id="block">
-<a class="viewcode-back" href="../../../api/operator.html#pyxu.operator.block">[docs]</a>
-<span class="linenos"> 314</span><span class="k">def</span> <span class="nf">block</span><span class="p">(</span>
-<span class="linenos"> 315</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">]],</span>
-<span class="linenos"> 316</span>    <span class="n">order</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
-<span class="linenos"> 317</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
-<span class="linenos"> 318</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos"> 319</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 320</span><span class="sd">    Construct a (dense) block-defined operator.</span>
-<span class="linenos"> 321</span>
-<span class="linenos"> 322</span><span class="sd">    A block-defined operator is an operator containing blocks of smaller operators.  Blocks are stacked</span>
-<span class="linenos"> 323</span><span class="sd">    horizontally/vertically in a user-specified order to obtain the final shape.</span>
+<a class="viewcode-back" href="../../../api/operator/blocks.html#pyxu.operator.block">[docs]</a>
+<span class="linenos"> 317</span><span class="k">def</span> <span class="nf">block</span><span class="p">(</span>
+<span class="linenos"> 318</span>    <span class="n">ops</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">]],</span>
+<span class="linenos"> 319</span>    <span class="n">order</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
+<span class="linenos"> 320</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
+<span class="linenos"> 321</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos"> 322</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 323</span><span class="sd">    Construct a (dense) block-defined operator.</span>
 <span class="linenos"> 324</span>
-<span class="linenos"> 325</span><span class="sd">    Parameters</span>
-<span class="linenos"> 326</span><span class="sd">    ----------</span>
-<span class="linenos"> 327</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` ) )</span>
-<span class="linenos"> 328</span><span class="sd">        2D nested sequence of (ck, dk)-shaped operators.</span>
-<span class="linenos"> 329</span><span class="sd">    order: 0, 1</span>
-<span class="linenos"> 330</span><span class="sd">        Order in which the nested operators are specified/concatenated:</span>
-<span class="linenos"> 331</span>
-<span class="linenos"> 332</span><span class="sd">        * 0: concatenate inner-most blocks via :py:func:`~pyxu.operator.vstack`, then :py:func:`~pyxu.operator.hstack`.</span>
-<span class="linenos"> 333</span><span class="sd">        * 1: concatenate inner-most blocks via :py:func:`~pyxu.operator.hstack`, then :py:func:`~pyxu.operator.vstack`.</span>
-<span class="linenos"> 334</span><span class="sd">    kwargs</span>
-<span class="linenos"> 335</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
-<span class="linenos"> 336</span>
-<span class="linenos"> 337</span><span class="sd">    Returns</span>
-<span class="linenos"> 338</span><span class="sd">    -------</span>
-<span class="linenos"> 339</span><span class="sd">    op: OpT</span>
-<span class="linenos"> 340</span><span class="sd">        Block-defined operator. (See below for examples.)</span>
-<span class="linenos"> 341</span>
-<span class="linenos"> 342</span><span class="sd">    Notes</span>
-<span class="linenos"> 343</span><span class="sd">    -----</span>
-<span class="linenos"> 344</span><span class="sd">    * Each row/column may contain a different number of operators.</span>
-<span class="linenos"> 345</span>
-<span class="linenos"> 346</span><span class="sd">    Examples</span>
-<span class="linenos"> 347</span><span class="sd">    --------</span>
+<span class="linenos"> 325</span><span class="sd">    A block-defined operator is an operator containing blocks of smaller operators.  Blocks are stacked</span>
+<span class="linenos"> 326</span><span class="sd">    horizontally/vertically in a user-specified order to obtain the final shape.</span>
+<span class="linenos"> 327</span>
+<span class="linenos"> 328</span><span class="sd">    Parameters</span>
+<span class="linenos"> 329</span><span class="sd">    ----------</span>
+<span class="linenos"> 330</span><span class="sd">    ops: :py:class:`~collections.abc.Sequence` ( :py:class:`~collections.abc.Sequence` ( :py:attr:`~pyxu.info.ptype.OpT` ) )</span>
+<span class="linenos"> 331</span><span class="sd">        2D nested sequence of (ck, dk)-shaped operators.</span>
+<span class="linenos"> 332</span><span class="sd">    order: 0, 1</span>
+<span class="linenos"> 333</span><span class="sd">        Order in which the nested operators are specified/concatenated:</span>
+<span class="linenos"> 334</span>
+<span class="linenos"> 335</span><span class="sd">        * 0: concatenate inner-most blocks via :py:func:`~pyxu.operator.vstack`, then :py:func:`~pyxu.operator.hstack`.</span>
+<span class="linenos"> 336</span><span class="sd">        * 1: concatenate inner-most blocks via :py:func:`~pyxu.operator.hstack`, then :py:func:`~pyxu.operator.vstack`.</span>
+<span class="linenos"> 337</span><span class="sd">    kwargs</span>
+<span class="linenos"> 338</span><span class="sd">        Extra keyword-arguments forwarded to :py:class:`~pyxu.operator.blocks._COOBlock`.</span>
+<span class="linenos"> 339</span>
+<span class="linenos"> 340</span><span class="sd">    Returns</span>
+<span class="linenos"> 341</span><span class="sd">    -------</span>
+<span class="linenos"> 342</span><span class="sd">    op: OpT</span>
+<span class="linenos"> 343</span><span class="sd">        Block-defined operator. (See below for examples.)</span>
+<span class="linenos"> 344</span>
+<span class="linenos"> 345</span><span class="sd">    Notes</span>
+<span class="linenos"> 346</span><span class="sd">    -----</span>
+<span class="linenos"> 347</span><span class="sd">    * Each row/column may contain a different number of operators.</span>
 <span class="linenos"> 348</span>
-<span class="linenos"> 349</span><span class="sd">    .. code::</span>
-<span class="linenos"> 350</span>
-<span class="linenos"> 351</span><span class="sd">       &gt;&gt;&gt; block(</span>
-<span class="linenos"> 352</span><span class="sd">       ...    [</span>
-<span class="linenos"> 353</span><span class="sd">       ...     [A],        # ABEEGGG</span>
-<span class="linenos"> 354</span><span class="sd">       ...     [B, C, D],  # ACEEHHH</span>
-<span class="linenos"> 355</span><span class="sd">       ...     [E, F],     # ADFFHHH</span>
-<span class="linenos"> 356</span><span class="sd">       ...     [G, H],</span>
-<span class="linenos"> 357</span><span class="sd">       ...    ],</span>
-<span class="linenos"> 358</span><span class="sd">       ...    order=0,</span>
-<span class="linenos"> 359</span><span class="sd">       ... )</span>
-<span class="linenos"> 360</span>
-<span class="linenos"> 361</span><span class="sd">       &gt;&gt;&gt; block(</span>
-<span class="linenos"> 362</span><span class="sd">       ...    [</span>
-<span class="linenos"> 363</span><span class="sd">       ...     [A, B, C, D],  # ABBCD</span>
-<span class="linenos"> 364</span><span class="sd">       ...     [E],           # EEEEE</span>
-<span class="linenos"> 365</span><span class="sd">       ...     [F, G],        # FFGGG</span>
-<span class="linenos"> 366</span><span class="sd">       ...    ],</span>
-<span class="linenos"> 367</span><span class="sd">       ...    order=1,</span>
-<span class="linenos"> 368</span><span class="sd">       ... )</span>
-<span class="linenos"> 369</span>
-<span class="linenos"> 370</span><span class="sd">    See Also</span>
-<span class="linenos"> 371</span><span class="sd">    --------</span>
-<span class="linenos"> 372</span><span class="sd">    :py:func:`~pyxu.operator.block_diag`,</span>
-<span class="linenos"> 373</span><span class="sd">    :py:func:`~pyxu.operator.coo_block`.</span>
-<span class="linenos"> 374</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 375</span>    <span class="n">order</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">order</span><span class="p">)</span>
-<span class="linenos"> 376</span>    <span class="k">assert</span> <span class="n">order</span> <span class="ow">in</span> <span class="p">{</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">},</span> <span class="sa">f</span><span class="s2">&quot;order: out-of-bounds order &#39;</span><span class="si">{</span><span class="n">order</span><span class="si">}</span><span class="s2">&#39;.&quot;</span>
-<span class="linenos"> 377</span>
-<span class="linenos"> 378</span>    <span class="n">inner</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">:</span> <span class="n">vstack</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span> <span class="n">hstack</span><span class="p">}[</span><span class="n">order</span><span class="p">]</span>
-<span class="linenos"> 379</span>    <span class="n">outer</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">:</span> <span class="n">hstack</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span> <span class="n">vstack</span><span class="p">}[</span><span class="n">order</span><span class="p">]</span>
+<span class="linenos"> 349</span><span class="sd">    Examples</span>
+<span class="linenos"> 350</span><span class="sd">    --------</span>
+<span class="linenos"> 351</span>
+<span class="linenos"> 352</span><span class="sd">    .. code::</span>
+<span class="linenos"> 353</span>
+<span class="linenos"> 354</span><span class="sd">       &gt;&gt;&gt; block(</span>
+<span class="linenos"> 355</span><span class="sd">       ...    [</span>
+<span class="linenos"> 356</span><span class="sd">       ...     [A],        # ABEEGGG</span>
+<span class="linenos"> 357</span><span class="sd">       ...     [B, C, D],  # ACEEHHH</span>
+<span class="linenos"> 358</span><span class="sd">       ...     [E, F],     # ADFFHHH</span>
+<span class="linenos"> 359</span><span class="sd">       ...     [G, H],</span>
+<span class="linenos"> 360</span><span class="sd">       ...    ],</span>
+<span class="linenos"> 361</span><span class="sd">       ...    order=0,</span>
+<span class="linenos"> 362</span><span class="sd">       ... )</span>
+<span class="linenos"> 363</span>
+<span class="linenos"> 364</span><span class="sd">       &gt;&gt;&gt; block(</span>
+<span class="linenos"> 365</span><span class="sd">       ...    [</span>
+<span class="linenos"> 366</span><span class="sd">       ...     [A, B, C, D],  # ABBCD</span>
+<span class="linenos"> 367</span><span class="sd">       ...     [E],           # EEEEE</span>
+<span class="linenos"> 368</span><span class="sd">       ...     [F, G],        # FFGGG</span>
+<span class="linenos"> 369</span><span class="sd">       ...    ],</span>
+<span class="linenos"> 370</span><span class="sd">       ...    order=1,</span>
+<span class="linenos"> 371</span><span class="sd">       ... )</span>
+<span class="linenos"> 372</span>
+<span class="linenos"> 373</span><span class="sd">    See Also</span>
+<span class="linenos"> 374</span><span class="sd">    --------</span>
+<span class="linenos"> 375</span><span class="sd">    :py:func:`~pyxu.operator.block_diag`,</span>
+<span class="linenos"> 376</span><span class="sd">    :py:func:`~pyxu.operator.coo_block`.</span>
+<span class="linenos"> 377</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 378</span>    <span class="n">order</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">order</span><span class="p">)</span>
+<span class="linenos"> 379</span>    <span class="k">assert</span> <span class="n">order</span> <span class="ow">in</span> <span class="p">{</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">},</span> <span class="sa">f</span><span class="s2">&quot;order: out-of-bounds order &#39;</span><span class="si">{</span><span class="n">order</span><span class="si">}</span><span class="s2">&#39;.&quot;</span>
 <span class="linenos"> 380</span>
-<span class="linenos"> 381</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">outer</span><span class="p">([</span><span class="n">inner</span><span class="p">(</span><span class="n">row</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">ops</span><span class="p">],</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 382</span>    <span class="k">return</span> <span class="n">op</span></div>
-
+<span class="linenos"> 381</span>    <span class="n">inner</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">:</span> <span class="n">vstack</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span> <span class="n">hstack</span><span class="p">}[</span><span class="n">order</span><span class="p">]</span>
+<span class="linenos"> 382</span>    <span class="n">outer</span> <span class="o">=</span> <span class="p">{</span><span class="mi">0</span><span class="p">:</span> <span class="n">hstack</span><span class="p">,</span> <span class="mi">1</span><span class="p">:</span> <span class="n">vstack</span><span class="p">}[</span><span class="n">order</span><span class="p">]</span>
 <span class="linenos"> 383</span>
-<span class="linenos"> 384</span>
+<span class="linenos"> 384</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">outer</span><span class="p">([</span><span class="n">inner</span><span class="p">(</span><span class="n">row</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">ops</span><span class="p">],</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos"> 385</span>    <span class="k">return</span> <span class="n">op</span></div>
+
+<span class="linenos"> 386</span>
+<span class="linenos"> 387</span>
 <div class="viewcode-block" id="coo_block">
-<a class="viewcode-back" href="../../../api/operator.html#pyxu.operator.coo_block">[docs]</a>
-<span class="linenos"> 385</span><span class="k">def</span> <span class="nf">coo_block</span><span class="p">(</span>
-<span class="linenos"> 386</span>    <span class="n">ops</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span>
-<span class="linenos"> 387</span>        <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
-<span class="linenos"> 388</span>        <span class="nb">tuple</span><span class="p">[</span>
-<span class="linenos"> 389</span>            <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">],</span>
-<span class="linenos"> 390</span>            <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">],</span>
-<span class="linenos"> 391</span>        <span class="p">],</span>
-<span class="linenos"> 392</span>    <span class="p">],</span>
-<span class="linenos"> 393</span>    <span class="n">grid_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span>
-<span class="linenos"> 394</span>    <span class="o">*</span><span class="p">,</span>
-<span class="linenos"> 395</span>    <span class="n">parallel</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
-<span class="linenos"> 396</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos"> 397</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 398</span><span class="sd">    Constuct a (possibly-sparse) block-defined operator in COOrdinate format.</span>
-<span class="linenos"> 399</span>
-<span class="linenos"> 400</span><span class="sd">    A block-defined operator is an operator containing blocks of smaller operators.  Blocks must align on a coarse grid,</span>
-<span class="linenos"> 401</span><span class="sd">    akin to the COO format used to define sparse arrays.</span>
+<a class="viewcode-back" href="../../../api/operator/blocks.html#pyxu.operator.coo_block">[docs]</a>
+<span class="linenos"> 388</span><span class="k">def</span> <span class="nf">coo_block</span><span class="p">(</span>
+<span class="linenos"> 389</span>    <span class="n">ops</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span>
+<span class="linenos"> 390</span>        <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
+<span class="linenos"> 391</span>        <span class="nb">tuple</span><span class="p">[</span>
+<span class="linenos"> 392</span>            <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">],</span>
+<span class="linenos"> 393</span>            <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">],</span>
+<span class="linenos"> 394</span>        <span class="p">],</span>
+<span class="linenos"> 395</span>    <span class="p">],</span>
+<span class="linenos"> 396</span>    <span class="n">grid_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span>
+<span class="linenos"> 397</span>    <span class="o">*</span><span class="p">,</span>
+<span class="linenos"> 398</span>    <span class="n">parallel</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
+<span class="linenos"> 399</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos"> 400</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 401</span><span class="sd">    Constuct a (possibly-sparse) block-defined operator in COOrdinate format.</span>
 <span class="linenos"> 402</span>
-<span class="linenos"> 403</span><span class="sd">    Parameters</span>
-<span class="linenos"> 404</span><span class="sd">    ----------</span>
-<span class="linenos"> 405</span><span class="sd">    ops</span>
-<span class="linenos"> 406</span><span class="sd">        (data, (i, j)) sequences defining block placement, i.e.</span>
-<span class="linenos"> 407</span>
-<span class="linenos"> 408</span><span class="sd">        * `data[:]` are :py:attr:`~pyxu.info.ptype.OpT` instances, in any order.</span>
-<span class="linenos"> 409</span><span class="sd">        * `i[:]` are the row indices of the block entries on the coarse grid.</span>
-<span class="linenos"> 410</span><span class="sd">        * `j[:]` are the column indices of the block entries on the coarse grid.</span>
-<span class="linenos"> 411</span>
-<span class="linenos"> 412</span><span class="sd">    grid_shape: OpShape</span>
-<span class="linenos"> 413</span><span class="sd">        (M, N) shape of the coarse grid.</span>
+<span class="linenos"> 403</span><span class="sd">    A block-defined operator is an operator containing blocks of smaller operators.  Blocks must align on a coarse grid,</span>
+<span class="linenos"> 404</span><span class="sd">    akin to the COO format used to define sparse arrays.</span>
+<span class="linenos"> 405</span>
+<span class="linenos"> 406</span><span class="sd">    Parameters</span>
+<span class="linenos"> 407</span><span class="sd">    ----------</span>
+<span class="linenos"> 408</span><span class="sd">    ops</span>
+<span class="linenos"> 409</span><span class="sd">        (data, (i, j)) sequences defining block placement, i.e.</span>
+<span class="linenos"> 410</span>
+<span class="linenos"> 411</span><span class="sd">        * `data[:]` are :py:attr:`~pyxu.info.ptype.OpT` instances, in any order.</span>
+<span class="linenos"> 412</span><span class="sd">        * `i[:]` are the row indices of the block entries on the coarse grid.</span>
+<span class="linenos"> 413</span><span class="sd">        * `j[:]` are the column indices of the block entries on the coarse grid.</span>
 <span class="linenos"> 414</span>
-<span class="linenos"> 415</span><span class="sd">    parallel: bool</span>
-<span class="linenos"> 416</span><span class="sd">        If ``true`` , use Dask to evaluate the following methods:</span>
+<span class="linenos"> 415</span><span class="sd">    grid_shape: OpShape</span>
+<span class="linenos"> 416</span><span class="sd">        (M, N) shape of the coarse grid.</span>
 <span class="linenos"> 417</span>
-<span class="linenos"> 418</span><span class="sd">        * ``.apply()``</span>
-<span class="linenos"> 419</span><span class="sd">        * ``.prox()``</span>
-<span class="linenos"> 420</span><span class="sd">        * ``.grad()``</span>
-<span class="linenos"> 421</span><span class="sd">        * ``.adjoint()``</span>
-<span class="linenos"> 422</span><span class="sd">        * ``.[co]gram().[apply,adjoint]()``</span>
-<span class="linenos"> 423</span>
-<span class="linenos"> 424</span><span class="sd">    Returns</span>
-<span class="linenos"> 425</span><span class="sd">    -------</span>
-<span class="linenos"> 426</span><span class="sd">    op: OpT</span>
-<span class="linenos"> 427</span><span class="sd">        Block-defined operator. (See below for examples.)</span>
-<span class="linenos"> 428</span>
-<span class="linenos"> 429</span><span class="sd">    Notes</span>
-<span class="linenos"> 430</span><span class="sd">    -----</span>
-<span class="linenos"> 431</span><span class="sd">    * Blocks on the same row/column must have the same ``codim`` / ``dim`` s.</span>
-<span class="linenos"> 432</span><span class="sd">    * Each row/column of the coarse grid **must** contain at least one entry.</span>
-<span class="linenos"> 433</span><span class="sd">    * ``parallel=True`` only parallelizes execution when inputs to listed methods are NUMPY arrays.</span>
-<span class="linenos"> 434</span>
-<span class="linenos"> 435</span><span class="sd">    .. Warning::</span>
-<span class="linenos"> 436</span>
-<span class="linenos"> 437</span><span class="sd">       When processing Dask inputs, or when ``parallel=True``, operators which are not thread-safe may produce incorrect</span>
-<span class="linenos"> 438</span><span class="sd">       results.  There is no easy way to ensure thread-safety at the level of :py:mod:`~pyxu.operator.blocks` without</span>
-<span class="linenos"> 439</span><span class="sd">       impacting performance of all operators involved.  Users are thus responsible for executing block-defined</span>
-<span class="linenos"> 440</span><span class="sd">       operators correctly, i.e., if thread-unsafe operators are involved, stick to NumPy/CuPy inputs.</span>
-<span class="linenos"> 441</span>
-<span class="linenos"> 442</span><span class="sd">    Examples</span>
-<span class="linenos"> 443</span><span class="sd">    --------</span>
+<span class="linenos"> 418</span><span class="sd">    parallel: bool</span>
+<span class="linenos"> 419</span><span class="sd">        If ``true`` , use Dask to evaluate the following methods:</span>
+<span class="linenos"> 420</span>
+<span class="linenos"> 421</span><span class="sd">        * ``.apply()``</span>
+<span class="linenos"> 422</span><span class="sd">        * ``.prox()``</span>
+<span class="linenos"> 423</span><span class="sd">        * ``.grad()``</span>
+<span class="linenos"> 424</span><span class="sd">        * ``.adjoint()``</span>
+<span class="linenos"> 425</span><span class="sd">        * ``.[co]gram().[apply,adjoint]()``</span>
+<span class="linenos"> 426</span>
+<span class="linenos"> 427</span><span class="sd">    Returns</span>
+<span class="linenos"> 428</span><span class="sd">    -------</span>
+<span class="linenos"> 429</span><span class="sd">    op: OpT</span>
+<span class="linenos"> 430</span><span class="sd">        Block-defined operator. (See below for examples.)</span>
+<span class="linenos"> 431</span>
+<span class="linenos"> 432</span><span class="sd">    Notes</span>
+<span class="linenos"> 433</span><span class="sd">    -----</span>
+<span class="linenos"> 434</span><span class="sd">    * Blocks on the same row/column must have the same ``codim`` / ``dim`` s.</span>
+<span class="linenos"> 435</span><span class="sd">    * Each row/column of the coarse grid **must** contain at least one entry.</span>
+<span class="linenos"> 436</span><span class="sd">    * ``parallel=True`` only parallelizes execution when inputs to listed methods are NUMPY arrays.</span>
+<span class="linenos"> 437</span>
+<span class="linenos"> 438</span><span class="sd">    .. Warning::</span>
+<span class="linenos"> 439</span>
+<span class="linenos"> 440</span><span class="sd">       When processing Dask inputs, or when ``parallel=True``, operators which are not thread-safe may produce incorrect</span>
+<span class="linenos"> 441</span><span class="sd">       results.  There is no easy way to ensure thread-safety at the level of :py:mod:`~pyxu.operator.blocks` without</span>
+<span class="linenos"> 442</span><span class="sd">       impacting performance of all operators involved.  Users are thus responsible for executing block-defined</span>
+<span class="linenos"> 443</span><span class="sd">       operators correctly, i.e., if thread-unsafe operators are involved, stick to NumPy/CuPy inputs.</span>
 <span class="linenos"> 444</span>
-<span class="linenos"> 445</span><span class="sd">    .. code::</span>
-<span class="linenos"> 446</span>
-<span class="linenos"> 447</span><span class="sd">       &gt;&gt;&gt; coo_block(</span>
-<span class="linenos"> 448</span><span class="sd">       ...     ([A(500,1000), B(1,1000), C(500,500), D(1,3)],  # data</span>
-<span class="linenos"> 449</span><span class="sd">       ...      [</span>
-<span class="linenos"> 450</span><span class="sd">       ...       [0, 1, 0, 2],  # i</span>
-<span class="linenos"> 451</span><span class="sd">       ...       [0, 0, 2, 1],  # j</span>
-<span class="linenos"> 452</span><span class="sd">       ...      ]),</span>
-<span class="linenos"> 453</span><span class="sd">       ...     grid_shape=(3, 3),</span>
-<span class="linenos"> 454</span><span class="sd">       ... )</span>
-<span class="linenos"> 455</span>
-<span class="linenos"> 456</span><span class="sd">       | coarse_idx |      0       |    1    |      2      |</span>
-<span class="linenos"> 457</span><span class="sd">       |------------|--------------|---------|-------------|</span>
-<span class="linenos"> 458</span><span class="sd">       |          0 | A(500, 1000) |         | C(500, 500) |</span>
-<span class="linenos"> 459</span><span class="sd">       |          1 | B(1, 1000)   |         |             |</span>
-<span class="linenos"> 460</span><span class="sd">       |          2 |              | D(1, 3) |             |</span>
-<span class="linenos"> 461</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 462</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
-<span class="linenos"> 463</span>        <span class="n">ops</span><span class="o">=</span><span class="n">ops</span><span class="p">,</span>
-<span class="linenos"> 464</span>        <span class="n">grid_shape</span><span class="o">=</span><span class="n">grid_shape</span><span class="p">,</span>
-<span class="linenos"> 465</span>        <span class="n">parallel</span><span class="o">=</span><span class="n">parallel</span><span class="p">,</span>
-<span class="linenos"> 466</span>    <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
-<span class="linenos"> 467</span>    <span class="k">return</span> <span class="n">op</span></div>
+<span class="linenos"> 445</span><span class="sd">    Examples</span>
+<span class="linenos"> 446</span><span class="sd">    --------</span>
+<span class="linenos"> 447</span>
+<span class="linenos"> 448</span><span class="sd">    .. code::</span>
+<span class="linenos"> 449</span>
+<span class="linenos"> 450</span><span class="sd">       &gt;&gt;&gt; coo_block(</span>
+<span class="linenos"> 451</span><span class="sd">       ...     ([A(500,1000), B(1,1000), C(500,500), D(1,3)],  # data</span>
+<span class="linenos"> 452</span><span class="sd">       ...      [</span>
+<span class="linenos"> 453</span><span class="sd">       ...       [0, 1, 0, 2],  # i</span>
+<span class="linenos"> 454</span><span class="sd">       ...       [0, 0, 2, 1],  # j</span>
+<span class="linenos"> 455</span><span class="sd">       ...      ]),</span>
+<span class="linenos"> 456</span><span class="sd">       ...     grid_shape=(3, 3),</span>
+<span class="linenos"> 457</span><span class="sd">       ... )</span>
+<span class="linenos"> 458</span>
+<span class="linenos"> 459</span><span class="sd">       | coarse_idx |      0       |    1    |      2      |</span>
+<span class="linenos"> 460</span><span class="sd">       |------------|--------------|---------|-------------|</span>
+<span class="linenos"> 461</span><span class="sd">       |          0 | A(500, 1000) |         | C(500, 500) |</span>
+<span class="linenos"> 462</span><span class="sd">       |          1 | B(1, 1000)   |         |             |</span>
+<span class="linenos"> 463</span><span class="sd">       |          2 |              | D(1, 3) |             |</span>
+<span class="linenos"> 464</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 465</span>    <span class="n">op</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
+<span class="linenos"> 466</span>        <span class="n">ops</span><span class="o">=</span><span class="n">ops</span><span class="p">,</span>
+<span class="linenos"> 467</span>        <span class="n">grid_shape</span><span class="o">=</span><span class="n">grid_shape</span><span class="p">,</span>
+<span class="linenos"> 468</span>        <span class="n">parallel</span><span class="o">=</span><span class="n">parallel</span><span class="p">,</span>
+<span class="linenos"> 469</span>    <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
+<span class="linenos"> 470</span>    <span class="k">return</span> <span class="n">op</span></div>
 
-<span class="linenos"> 468</span>
-<span class="linenos"> 469</span>
-<span class="linenos"> 470</span><span class="k">def</span> <span class="nf">_parallelize</span><span class="p">(</span><span class="n">func</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">:</span>
-<span class="linenos"> 471</span>    <span class="c1"># Parallelize execution of func() under conditions.</span>
-<span class="linenos"> 472</span>    <span class="c1">#</span>
-<span class="linenos"> 473</span>    <span class="c1"># * func() must be one of the arithmetic methods [apply,prox,grad,adjoint,pinv]()</span>
-<span class="linenos"> 474</span>    <span class="c1"># * the `_parallel` attribute must be attached to the instance for it to parallelize execution</span>
-<span class="linenos"> 475</span>    <span class="c1">#   over NUMPY inputs.</span>
-<span class="linenos"> 476</span>
-<span class="linenos"> 477</span>    <span class="nd">@functools</span><span class="o">.</span><span class="n">wraps</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
-<span class="linenos"> 478</span>    <span class="k">def</span> <span class="nf">wrapper</span><span class="p">(</span><span class="o">*</span><span class="n">ARGS</span><span class="p">,</span> <span class="o">**</span><span class="n">KWARGS</span><span class="p">):</span>
-<span class="linenos"> 479</span>        <span class="n">func_args</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">parse_params</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="o">*</span><span class="n">ARGS</span><span class="p">,</span> <span class="o">**</span><span class="n">KWARGS</span><span class="p">)</span>
-<span class="linenos"> 480</span>
-<span class="linenos"> 481</span>        <span class="n">arr</span> <span class="o">=</span> <span class="n">func_args</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
-<span class="linenos"> 482</span>        <span class="n">N</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span>
-<span class="linenos"> 483</span>        <span class="n">parallelize</span> <span class="o">=</span> <span class="n">ARGS</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">_parallel</span> <span class="ow">and</span> <span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">)</span>
-<span class="linenos"> 484</span>
-<span class="linenos"> 485</span>        <span class="c1"># [2022.09.26] Sepand Kashani</span>
-<span class="linenos"> 486</span>        <span class="c1"># Q: Why do we parallelize only for NUMPY inputs and not CUPY?</span>
-<span class="linenos"> 487</span>        <span class="c1"># A: Given an arithmetic method `f`, there is no obligation (for DASK inputs) to satisfy the</span>
-<span class="linenos"> 488</span>        <span class="c1">#    relation `f(arr).chunk_type == arr.chunk_type`.</span>
-<span class="linenos"> 489</span>        <span class="c1">#    In particular the relationship does not hold for LinFunc.[grad, adjoint]() unless the</span>
-<span class="linenos"> 490</span>        <span class="c1">#    user provides a special implementation for DASK inputs.</span>
-<span class="linenos"> 491</span>        <span class="c1">#    Consequence: the sum() / xp.concatenate() instructions in _COOBlock() may:</span>
-<span class="linenos"> 492</span>        <span class="c1">#    * fail due to array-type mismatch; or</span>
-<span class="linenos"> 493</span>        <span class="c1">#    * induce unnecessary CPU&lt;&gt;GPU transfers.</span>
-<span class="linenos"> 494</span>
-<span class="linenos"> 495</span>        <span class="k">if</span> <span class="n">parallelize</span><span class="p">:</span>
-<span class="linenos"> 496</span>            <span class="n">xp</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">DASK</span><span class="o">.</span><span class="n">module</span><span class="p">()</span>
-<span class="linenos"> 497</span>            <span class="n">func_args</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">arr</span><span class="o">=</span><span class="n">xp</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">arr</span><span class="o">.</span><span class="n">dtype</span><span class="p">))</span>
-<span class="linenos"> 498</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 499</span>            <span class="k">pass</span>
-<span class="linenos"> 500</span>
-<span class="linenos"> 501</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="o">**</span><span class="n">func_args</span><span class="p">)</span>
-<span class="linenos"> 502</span>        <span class="n">f</span> <span class="o">=</span> <span class="p">{</span><span class="kc">True</span><span class="p">:</span> <span class="n">pxu</span><span class="o">.</span><span class="n">compute</span><span class="p">,</span> <span class="kc">False</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">:</span> <span class="n">_</span><span class="p">}[</span><span class="n">parallelize</span><span class="p">]</span>
-<span class="linenos"> 503</span>        <span class="k">return</span> <span class="n">f</span><span class="p">(</span><span class="n">out</span><span class="p">)</span>
-<span class="linenos"> 504</span>
-<span class="linenos"> 505</span>    <span class="k">return</span> <span class="n">wrapper</span>
-<span class="linenos"> 506</span>
+<span class="linenos"> 471</span>
+<span class="linenos"> 472</span>
+<span class="linenos"> 473</span><span class="k">def</span> <span class="nf">_parallelize</span><span class="p">(</span><span class="n">func</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">:</span>
+<span class="linenos"> 474</span>    <span class="c1"># Parallelize execution of func() under conditions.</span>
+<span class="linenos"> 475</span>    <span class="c1">#</span>
+<span class="linenos"> 476</span>    <span class="c1"># * func() must be one of the arithmetic methods [apply,prox,grad,adjoint,pinv]()</span>
+<span class="linenos"> 477</span>    <span class="c1"># * the `_parallel` attribute must be attached to the instance for it to parallelize execution</span>
+<span class="linenos"> 478</span>    <span class="c1">#   over NUMPY inputs.</span>
+<span class="linenos"> 479</span>
+<span class="linenos"> 480</span>    <span class="nd">@functools</span><span class="o">.</span><span class="n">wraps</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
+<span class="linenos"> 481</span>    <span class="k">def</span> <span class="nf">wrapper</span><span class="p">(</span><span class="o">*</span><span class="n">ARGS</span><span class="p">,</span> <span class="o">**</span><span class="n">KWARGS</span><span class="p">):</span>
+<span class="linenos"> 482</span>        <span class="n">func_args</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">parse_params</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="o">*</span><span class="n">ARGS</span><span class="p">,</span> <span class="o">**</span><span class="n">KWARGS</span><span class="p">)</span>
+<span class="linenos"> 483</span>
+<span class="linenos"> 484</span>        <span class="n">arr</span> <span class="o">=</span> <span class="n">func_args</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
+<span class="linenos"> 485</span>        <span class="n">N</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span>
+<span class="linenos"> 486</span>        <span class="n">parallelize</span> <span class="o">=</span> <span class="n">ARGS</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">_parallel</span> <span class="ow">and</span> <span class="p">(</span><span class="n">N</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">)</span>
+<span class="linenos"> 487</span>
+<span class="linenos"> 488</span>        <span class="c1"># [2022.09.26] Sepand Kashani</span>
+<span class="linenos"> 489</span>        <span class="c1"># Q: Why do we parallelize only for NUMPY inputs and not CUPY?</span>
+<span class="linenos"> 490</span>        <span class="c1"># A: Given an arithmetic method `f`, there is no obligation (for DASK inputs) to satisfy the</span>
+<span class="linenos"> 491</span>        <span class="c1">#    relation `f(arr).chunk_type == arr.chunk_type`.</span>
+<span class="linenos"> 492</span>        <span class="c1">#    In particular the relationship does not hold for LinFunc.[grad, adjoint]() unless the</span>
+<span class="linenos"> 493</span>        <span class="c1">#    user provides a special implementation for DASK inputs.</span>
+<span class="linenos"> 494</span>        <span class="c1">#    Consequence: the sum() / xp.concatenate() instructions in _COOBlock() may:</span>
+<span class="linenos"> 495</span>        <span class="c1">#    * fail due to array-type mismatch; or</span>
+<span class="linenos"> 496</span>        <span class="c1">#    * induce unnecessary CPU&lt;&gt;GPU transfers.</span>
+<span class="linenos"> 497</span>
+<span class="linenos"> 498</span>        <span class="k">if</span> <span class="n">parallelize</span><span class="p">:</span>
+<span class="linenos"> 499</span>            <span class="n">xp</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">DASK</span><span class="o">.</span><span class="n">module</span><span class="p">()</span>
+<span class="linenos"> 500</span>            <span class="n">func_args</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">arr</span><span class="o">=</span><span class="n">xp</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">arr</span><span class="o">.</span><span class="n">dtype</span><span class="p">))</span>
+<span class="linenos"> 501</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 502</span>            <span class="k">pass</span>
+<span class="linenos"> 503</span>
+<span class="linenos"> 504</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="o">**</span><span class="n">func_args</span><span class="p">)</span>
+<span class="linenos"> 505</span>        <span class="n">f</span> <span class="o">=</span> <span class="p">{</span><span class="kc">True</span><span class="p">:</span> <span class="n">pxu</span><span class="o">.</span><span class="n">compute</span><span class="p">,</span> <span class="kc">False</span><span class="p">:</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">:</span> <span class="n">_</span><span class="p">}[</span><span class="n">parallelize</span><span class="p">]</span>
+<span class="linenos"> 506</span>        <span class="k">return</span> <span class="n">f</span><span class="p">(</span><span class="n">out</span><span class="p">)</span>
 <span class="linenos"> 507</span>
-<span class="linenos"> 508</span><span class="k">class</span> <span class="nc">_COOBlock</span><span class="p">:</span>  <span class="c1"># See coo_block() for a detailed description.</span>
-<span class="linenos"> 509</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
-<span class="linenos"> 510</span>        <span class="bp">self</span><span class="p">,</span>
-<span class="linenos"> 511</span>        <span class="n">ops</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span>
-<span class="linenos"> 512</span>            <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
-<span class="linenos"> 513</span>            <span class="nb">tuple</span><span class="p">[</span>
-<span class="linenos"> 514</span>                <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">],</span>
-<span class="linenos"> 515</span>                <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">],</span>
-<span class="linenos"> 516</span>            <span class="p">],</span>
-<span class="linenos"> 517</span>        <span class="p">],</span>
-<span class="linenos"> 518</span>        <span class="n">grid_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span>
-<span class="linenos"> 519</span>        <span class="n">parallel</span><span class="p">:</span> <span class="nb">bool</span><span class="p">,</span>
-<span class="linenos"> 520</span>    <span class="p">):</span>
-<span class="linenos"> 521</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">grid_shape</span><span class="p">)</span>
-<span class="linenos"> 522</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_init_spec</span><span class="p">(</span><span class="n">ops</span><span class="p">)</span>
-<span class="linenos"> 523</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span> <span class="o">=</span> <span class="nb">bool</span><span class="p">(</span><span class="n">parallel</span><span class="p">)</span>
-<span class="linenos"> 524</span>
-<span class="linenos"> 525</span>    <span class="k">def</span> <span class="nf">op</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos"> 526</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 527</span><span class="sd">        Returns</span>
-<span class="linenos"> 528</span><span class="sd">        -------</span>
-<span class="linenos"> 529</span><span class="sd">        op: pxt.OpT</span>
-<span class="linenos"> 530</span><span class="sd">            Synthesized operator given inputs to :py:meth:`~pyxu.operator.blocks._COOBlock.__init__`.</span>
-<span class="linenos"> 531</span><span class="sd">        &quot;&quot;&quot;</span>
-<span class="linenos"> 532</span>        <span class="n">blk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>
-<span class="linenos"> 533</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">blk</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<span class="linenos"> 534</span>            <span class="n">_</span><span class="p">,</span> <span class="n">op</span> <span class="o">=</span> <span class="n">blk</span><span class="o">.</span><span class="n">popitem</span><span class="p">()</span>
-<span class="linenos"> 535</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 536</span>            <span class="kn">import</span> <span class="nn">pyxu.abc.arithmetic</span> <span class="k">as</span> <span class="nn">arithmetic</span>
-<span class="linenos"> 537</span>
-<span class="linenos"> 538</span>            <span class="n">op</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_infer_op</span><span class="p">()</span>
-<span class="linenos"> 539</span>            <span class="n">op</span><span class="o">.</span><span class="n">_block</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>  <span class="c1"># embed for introspection</span>
-<span class="linenos"> 540</span>            <span class="n">op</span><span class="o">.</span><span class="n">_block_offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span>  <span class="c1"># embed for introspection</span>
-<span class="linenos"> 541</span>            <span class="n">op</span><span class="o">.</span><span class="n">_grid_shape</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span>  <span class="c1"># embed for introspection</span>
-<span class="linenos"> 542</span>            <span class="n">op</span><span class="o">.</span><span class="n">_parallel</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span>  <span class="c1"># embed for introspection</span>
-<span class="linenos"> 543</span>            <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">op</span><span class="o">.</span><span class="n">properties</span><span class="p">():</span>
-<span class="linenos"> 544</span>                <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">p</span><span class="o">.</span><span class="n">arithmetic_methods</span><span class="p">():</span>
-<span class="linenos"> 545</span>                    <span class="n">func</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span>
-<span class="linenos"> 546</span>                    <span class="nb">setattr</span><span class="p">(</span><span class="n">op</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">op</span><span class="p">))</span>
-<span class="linenos"> 547</span>            <span class="n">arithmetic</span><span class="o">.</span><span class="n">Rule</span><span class="o">.</span><span class="n">_propagate_constants</span><span class="p">(</span><span class="n">op</span><span class="p">)</span>
-<span class="linenos"> 548</span>        <span class="k">return</span> <span class="n">op</span>
-<span class="linenos"> 549</span>
-<span class="linenos"> 550</span>    <span class="k">def</span> <span class="nf">_init_spec</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ops</span><span class="p">):</span>
-<span class="linenos"> 551</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 552</span><span class="sd">        Transform input into standardized form.</span>
-<span class="linenos"> 553</span>
-<span class="linenos"> 554</span><span class="sd">        Returns</span>
-<span class="linenos"> 555</span><span class="sd">        -------</span>
-<span class="linenos"> 556</span><span class="sd">        block: (int, int) -&gt; pxt.OpT</span>
-<span class="linenos"> 557</span><span class="sd">            coarse_grid index -&gt; Operator at that location.</span>
-<span class="linenos"> 558</span><span class="sd">        block_offset: (int, int) -&gt; (int, int)</span>
-<span class="linenos"> 559</span><span class="sd">            coarse_grid index -&gt; (top-left) fine_grid index.</span>
-<span class="linenos"> 560</span><span class="sd">        &quot;&quot;&quot;</span>
-<span class="linenos"> 561</span>        <span class="n">data</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span> <span class="o">=</span> <span class="n">ops</span>
-<span class="linenos"> 562</span>        <span class="n">N_row</span><span class="p">,</span> <span class="n">N_col</span><span class="p">,</span> <span class="n">N_block</span> <span class="o">=</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
-<span class="linenos"> 563</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Incorrect COO parametrization&quot;</span>
-<span class="linenos"> 564</span>        <span class="k">assert</span> <span class="n">N_block</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">j</span><span class="p">),</span> <span class="n">msg</span>
-<span class="linenos"> 565</span>        <span class="k">assert</span> <span class="mi">0</span> <span class="o">&lt;</span> <span class="n">N_block</span> <span class="o">&lt;=</span> <span class="n">N_row</span> <span class="o">*</span> <span class="n">N_col</span><span class="p">,</span> <span class="n">msg</span>
-<span class="linenos"> 566</span>        <span class="k">assert</span> <span class="mi">0</span> <span class="o">&lt;=</span> <span class="nb">min</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="nb">max</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">N_row</span><span class="p">,</span> <span class="n">msg</span>
-<span class="linenos"> 567</span>        <span class="k">assert</span> <span class="mi">0</span> <span class="o">&lt;=</span> <span class="nb">min</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="nb">max</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">N_col</span><span class="p">,</span> <span class="n">msg</span>
-<span class="linenos"> 568</span>
-<span class="linenos"> 569</span>        <span class="c1"># block dimensions are compatible.</span>
-<span class="linenos"> 570</span>        <span class="n">row</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>  <span class="c1"># row_idx -&gt; [block]</span>
-<span class="linenos"> 571</span>        <span class="n">col</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>  <span class="c1"># col_idx -&gt; [block]</span>
-<span class="linenos"> 572</span>        <span class="k">for</span> <span class="n">d</span><span class="p">,</span> <span class="n">_i</span><span class="p">,</span> <span class="n">_j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">):</span>
-<span class="linenos"> 573</span>            <span class="n">row</span><span class="p">[</span><span class="n">_i</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
-<span class="linenos"> 574</span>            <span class="n">col</span><span class="p">[</span><span class="n">_j</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
-<span class="linenos"> 575</span>        <span class="n">msg</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">dim</span><span class="p">,</span> <span class="n">idx</span><span class="p">,</span> <span class="n">dom</span><span class="p">:</span> <span class="sa">f</span><span class="s2">&quot;All sub-operators on </span><span class="si">{</span><span class="n">dim</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">idx</span><span class="si">}</span><span class="s2"> must have same </span><span class="si">{</span><span class="n">dom</span><span class="si">}</span><span class="s2"> size.&quot;</span>
-<span class="linenos"> 576</span>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">row</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 577</span>            <span class="k">assert</span> <span class="nb">len</span><span class="p">({</span><span class="n">_</span><span class="o">.</span><span class="n">codim</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">v</span><span class="p">})</span> <span class="o">==</span> <span class="mi">1</span><span class="p">,</span> <span class="n">msg</span><span class="p">(</span><span class="s2">&quot;row&quot;</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="s2">&quot;codomain&quot;</span><span class="p">)</span>
-<span class="linenos"> 578</span>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">col</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 579</span>            <span class="k">assert</span> <span class="nb">len</span><span class="p">({</span><span class="n">_</span><span class="o">.</span><span class="n">dim</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">v</span><span class="p">})</span> <span class="o">==</span> <span class="mi">1</span><span class="p">,</span> <span class="n">msg</span><span class="p">(</span><span class="s2">&quot;column&quot;</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="s2">&quot;domain&quot;</span><span class="p">)</span>
-<span class="linenos"> 580</span>
-<span class="linenos"> 581</span>        <span class="c1"># no empty lines/columns in coarse grid.</span>
-<span class="linenos"> 582</span>        <span class="n">msg</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">:</span> <span class="sa">f</span><span class="s2">&quot;Coarse grid contains empty </span><span class="si">{</span><span class="n">_</span><span class="si">}</span><span class="s2">: cannot infer fine-grid dimensions.&quot;</span>
-<span class="linenos"> 583</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">row</span><span class="p">)</span> <span class="o">==</span> <span class="n">N_row</span><span class="p">,</span> <span class="n">msg</span><span class="p">(</span><span class="s2">&quot;rows&quot;</span><span class="p">)</span>
-<span class="linenos"> 584</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">col</span><span class="p">)</span> <span class="o">==</span> <span class="n">N_col</span><span class="p">,</span> <span class="n">msg</span><span class="p">(</span><span class="s2">&quot;columns&quot;</span><span class="p">)</span>
-<span class="linenos"> 585</span>
-<span class="linenos"> 586</span>        <span class="c1"># ---------------------------------------------------------------------</span>
-<span class="linenos"> 587</span>        <span class="c1"># create block</span>
-<span class="linenos"> 588</span>        <span class="n">block</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>  <span class="c1"># coarse_grid(int, int) -&gt; pxt.OpT</span>
-<span class="linenos"> 589</span>        <span class="k">for</span> <span class="n">d</span><span class="p">,</span> <span class="n">_i</span><span class="p">,</span> <span class="n">_j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">):</span>
-<span class="linenos"> 590</span>            <span class="n">block</span><span class="p">[(</span><span class="n">_i</span><span class="p">,</span> <span class="n">_j</span><span class="p">)]</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
-<span class="linenos"> 591</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_block</span> <span class="o">=</span> <span class="n">block</span>
-<span class="linenos"> 592</span>
-<span class="linenos"> 593</span>        <span class="c1"># create block_offset</span>
-<span class="linenos"> 594</span>        <span class="n">block_offset</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>  <span class="c1"># coarse_grid(int, int) -&gt; fine_grid(int, int)</span>
-<span class="linenos"> 595</span>        <span class="n">row_offset</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">([</span><span class="n">row</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">codim</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">)])</span>
-<span class="linenos"> 596</span>        <span class="n">col_offset</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">([</span><span class="n">col</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">dim</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">)])</span>
-<span class="linenos"> 597</span>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">):</span>
-<span class="linenos"> 598</span>            <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">):</span>
-<span class="linenos"> 599</span>                <span class="n">_i</span> <span class="o">=</span> <span class="mi">0</span> <span class="k">if</span> <span class="p">(</span><span class="n">i</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)</span> <span class="k">else</span> <span class="n">row_offset</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
-<span class="linenos"> 600</span>                <span class="n">_j</span> <span class="o">=</span> <span class="mi">0</span> <span class="k">if</span> <span class="p">(</span><span class="n">j</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)</span> <span class="k">else</span> <span class="n">col_offset</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
-<span class="linenos"> 601</span>                <span class="n">block_offset</span><span class="p">[(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)]</span> <span class="o">=</span> <span class="n">_i</span><span class="p">,</span> <span class="n">_j</span>
-<span class="linenos"> 602</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span> <span class="o">=</span> <span class="n">block_offset</span>
-<span class="linenos"> 603</span>
-<span class="linenos"> 604</span>    <span class="k">def</span> <span class="nf">_infer_op</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos"> 605</span>        <span class="c1"># Create the abstract COO-operator to which methods will be assigned.</span>
-<span class="linenos"> 606</span>        <span class="n">blk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>  <span class="c1"># shorthand</span>
-<span class="linenos"> 607</span>
-<span class="linenos"> 608</span>        <span class="n">row</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
-<span class="linenos"> 609</span>        <span class="n">col</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
-<span class="linenos"> 610</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 611</span>            <span class="n">row</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">op</span><span class="p">)</span>
-<span class="linenos"> 612</span>            <span class="n">col</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">op</span><span class="p">)</span>
-<span class="linenos"> 613</span>        <span class="n">N_row</span><span class="p">,</span> <span class="n">N_col</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">row</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">col</span><span class="p">)</span>
-<span class="linenos"> 614</span>        <span class="n">op_codim</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">ops</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">codim</span> <span class="k">for</span> <span class="n">ops</span> <span class="ow">in</span> <span class="n">row</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
-<span class="linenos"> 615</span>        <span class="n">op_dim</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">ops</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">dim</span> <span class="k">for</span> <span class="n">ops</span> <span class="ow">in</span> <span class="n">col</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
-<span class="linenos"> 616</span>
-<span class="linenos"> 617</span>        <span class="n">P</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">Property</span>
-<span class="linenos"> 618</span>        <span class="n">properties</span> <span class="o">=</span> <span class="nb">set</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="o">*</span><span class="p">[</span><span class="nb">set</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">properties</span><span class="p">())</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">values</span><span class="p">()])</span>
-<span class="linenos"> 619</span>        <span class="k">if</span> <span class="n">op_codim</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
-<span class="linenos"> 620</span>            <span class="n">properties</span> <span class="o">-=</span> <span class="p">{</span>
-<span class="linenos"> 621</span>                <span class="n">P</span><span class="o">.</span><span class="n">FUNCTIONAL</span><span class="p">,</span>
-<span class="linenos"> 622</span>                <span class="n">P</span><span class="o">.</span><span class="n">PROXIMABLE</span><span class="p">,</span>
-<span class="linenos"> 623</span>                <span class="n">P</span><span class="o">.</span><span class="n">DIFFERENTIABLE_FUNCTION</span><span class="p">,</span>
-<span class="linenos"> 624</span>                <span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">,</span>
-<span class="linenos"> 625</span>            <span class="p">}</span>
-<span class="linenos"> 626</span>
-<span class="linenos"> 627</span>        <span class="k">if</span> <span class="nb">all</span><span class="p">(</span>  <span class="c1"># block_diag case</span>
-<span class="linenos"> 628</span>            <span class="p">[</span>
-<span class="linenos"> 629</span>                <span class="n">N_row</span> <span class="o">==</span> <span class="n">N_col</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">blk</span><span class="p">),</span>
-<span class="linenos"> 630</span>                <span class="nb">all</span><span class="p">((</span><span class="n">r</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">)),</span>
-<span class="linenos"> 631</span>            <span class="p">]</span>
-<span class="linenos"> 632</span>        <span class="p">):</span>
-<span class="linenos"> 633</span>            <span class="k">pass</span>
-<span class="linenos"> 634</span>        <span class="k">elif</span> <span class="n">op_codim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>  <span class="c1"># hstack case: special treatment of quadratics</span>
-<span class="linenos"> 635</span>            <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">values</span><span class="p">()):</span>
-<span class="linenos"> 636</span>                <span class="n">properties</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)</span>
-<span class="linenos"> 637</span>            <span class="k">elif</span> <span class="nb">any</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">values</span><span class="p">()):</span>
-<span class="linenos"> 638</span>                <span class="c1"># possible quadratic if all other terms are linear.</span>
-<span class="linenos"> 639</span>                <span class="n">non_quad</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">values</span><span class="p">()</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)]</span>
-<span class="linenos"> 640</span>                <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">non_quad</span><span class="p">):</span>
-<span class="linenos"> 641</span>                    <span class="n">properties</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)</span>
-<span class="linenos"> 642</span>        <span class="k">else</span><span class="p">:</span>  <span class="c1"># (1) vstack case or (2) arbitrary fill-in case =&gt; non-functionals</span>
-<span class="linenos"> 643</span>            <span class="n">properties</span> <span class="o">&amp;=</span> <span class="p">{</span>
-<span class="linenos"> 644</span>                <span class="n">P</span><span class="o">.</span><span class="n">CAN_EVAL</span><span class="p">,</span>
-<span class="linenos"> 645</span>                <span class="n">P</span><span class="o">.</span><span class="n">DIFFERENTIABLE</span><span class="p">,</span>
-<span class="linenos"> 646</span>                <span class="n">P</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">,</span>
-<span class="linenos"> 647</span>            <span class="p">}</span>
-<span class="linenos"> 648</span>            <span class="k">if</span> <span class="p">(</span><span class="n">op_codim</span> <span class="o">==</span> <span class="n">op_dim</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">LINEAR</span> <span class="ow">in</span> <span class="n">properties</span><span class="p">):</span>
-<span class="linenos"> 649</span>                <span class="n">properties</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">LINEAR_SQUARE</span><span class="p">)</span>
-<span class="linenos"> 650</span>
-<span class="linenos"> 651</span>        <span class="n">klass</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">Operator</span><span class="o">.</span><span class="n">_infer_operator_type</span><span class="p">(</span><span class="n">properties</span><span class="p">)</span>
-<span class="linenos"> 652</span>        <span class="n">op</span> <span class="o">=</span> <span class="n">klass</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">op_codim</span><span class="p">,</span> <span class="n">op_dim</span><span class="p">))</span>
-<span class="linenos"> 653</span>        <span class="k">return</span> <span class="n">op</span>
-<span class="linenos"> 654</span>
-<span class="linenos"> 655</span>    <span class="nd">@_parallelize</span>
-<span class="linenos"> 656</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
-<span class="linenos"> 657</span>    <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 658</span>        <span class="c1"># compute blocks</span>
-<span class="linenos"> 659</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
-<span class="linenos"> 660</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 661</span>            <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
-<span class="linenos"> 662</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">])</span>
-<span class="linenos"> 663</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
-<span class="linenos"> 664</span>
-<span class="linenos"> 665</span>        <span class="c1"># row-oriented reduction (via +)</span>
-<span class="linenos"> 666</span>        <span class="n">rows</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
-<span class="linenos"> 667</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parts</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 668</span>            <span class="n">rows</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
-<span class="linenos"> 669</span>        <span class="n">cols</span> <span class="o">=</span> <span class="p">[</span><span class="nb">sum</span><span class="p">(</span><span class="n">rows</span><span class="p">[</span><span class="n">r</span><span class="p">])</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">rows</span><span class="p">))]</span>
-<span class="linenos"> 670</span>
-<span class="linenos"> 671</span>        <span class="c1"># concatenate to super-column</span>
-<span class="linenos"> 672</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
-<span class="linenos"> 673</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">cols</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
-<span class="linenos"> 674</span>        <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 675</span>
-<span class="linenos"> 676</span>    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 677</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+<span class="linenos"> 508</span>    <span class="k">return</span> <span class="n">wrapper</span>
+<span class="linenos"> 509</span>
+<span class="linenos"> 510</span>
+<span class="linenos"> 511</span><span class="k">class</span> <span class="nc">_COOBlock</span><span class="p">:</span>  <span class="c1"># See coo_block() for a detailed description.</span>
+<span class="linenos"> 512</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
+<span class="linenos"> 513</span>        <span class="bp">self</span><span class="p">,</span>
+<span class="linenos"> 514</span>        <span class="n">ops</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span>
+<span class="linenos"> 515</span>            <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">],</span>
+<span class="linenos"> 516</span>            <span class="nb">tuple</span><span class="p">[</span>
+<span class="linenos"> 517</span>                <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">],</span>
+<span class="linenos"> 518</span>                <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">],</span>
+<span class="linenos"> 519</span>            <span class="p">],</span>
+<span class="linenos"> 520</span>        <span class="p">],</span>
+<span class="linenos"> 521</span>        <span class="n">grid_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span>
+<span class="linenos"> 522</span>        <span class="n">parallel</span><span class="p">:</span> <span class="nb">bool</span><span class="p">,</span>
+<span class="linenos"> 523</span>    <span class="p">):</span>
+<span class="linenos"> 524</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">grid_shape</span><span class="p">)</span>
+<span class="linenos"> 525</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_init_spec</span><span class="p">(</span><span class="n">ops</span><span class="p">)</span>
+<span class="linenos"> 526</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span> <span class="o">=</span> <span class="nb">bool</span><span class="p">(</span><span class="n">parallel</span><span class="p">)</span>
+<span class="linenos"> 527</span>
+<span class="linenos"> 528</span>    <span class="k">def</span> <span class="nf">op</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos"> 529</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 530</span><span class="sd">        Returns</span>
+<span class="linenos"> 531</span><span class="sd">        -------</span>
+<span class="linenos"> 532</span><span class="sd">        op: pxt.OpT</span>
+<span class="linenos"> 533</span><span class="sd">            Synthesized operator given inputs to :py:meth:`~pyxu.operator.blocks._COOBlock.__init__`.</span>
+<span class="linenos"> 534</span><span class="sd">        &quot;&quot;&quot;</span>
+<span class="linenos"> 535</span>        <span class="n">blk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>
+<span class="linenos"> 536</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">blk</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<span class="linenos"> 537</span>            <span class="n">_</span><span class="p">,</span> <span class="n">op</span> <span class="o">=</span> <span class="n">blk</span><span class="o">.</span><span class="n">popitem</span><span class="p">()</span>
+<span class="linenos"> 538</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 539</span>            <span class="kn">import</span> <span class="nn">pyxu.abc.arithmetic</span> <span class="k">as</span> <span class="nn">arithmetic</span>
+<span class="linenos"> 540</span>
+<span class="linenos"> 541</span>            <span class="n">op</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_infer_op</span><span class="p">()</span>
+<span class="linenos"> 542</span>            <span class="n">op</span><span class="o">.</span><span class="n">_block</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>  <span class="c1"># embed for introspection</span>
+<span class="linenos"> 543</span>            <span class="n">op</span><span class="o">.</span><span class="n">_block_offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span>  <span class="c1"># embed for introspection</span>
+<span class="linenos"> 544</span>            <span class="n">op</span><span class="o">.</span><span class="n">_grid_shape</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span>  <span class="c1"># embed for introspection</span>
+<span class="linenos"> 545</span>            <span class="n">op</span><span class="o">.</span><span class="n">_parallel</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span>  <span class="c1"># embed for introspection</span>
+<span class="linenos"> 546</span>            <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">op</span><span class="o">.</span><span class="n">properties</span><span class="p">():</span>
+<span class="linenos"> 547</span>                <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">p</span><span class="o">.</span><span class="n">arithmetic_methods</span><span class="p">():</span>
+<span class="linenos"> 548</span>                    <span class="n">func</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span>
+<span class="linenos"> 549</span>                    <span class="nb">setattr</span><span class="p">(</span><span class="n">op</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">op</span><span class="p">))</span>
+<span class="linenos"> 550</span>            <span class="n">arithmetic</span><span class="o">.</span><span class="n">Rule</span><span class="o">.</span><span class="n">_propagate_constants</span><span class="p">(</span><span class="n">op</span><span class="p">)</span>
+<span class="linenos"> 551</span>        <span class="k">return</span> <span class="n">op</span>
+<span class="linenos"> 552</span>
+<span class="linenos"> 553</span>    <span class="k">def</span> <span class="nf">_init_spec</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ops</span><span class="p">):</span>
+<span class="linenos"> 554</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 555</span><span class="sd">        Transform input into standardized form.</span>
+<span class="linenos"> 556</span>
+<span class="linenos"> 557</span><span class="sd">        Returns</span>
+<span class="linenos"> 558</span><span class="sd">        -------</span>
+<span class="linenos"> 559</span><span class="sd">        block: (int, int) -&gt; pxt.OpT</span>
+<span class="linenos"> 560</span><span class="sd">            coarse_grid index -&gt; Operator at that location.</span>
+<span class="linenos"> 561</span><span class="sd">        block_offset: (int, int) -&gt; (int, int)</span>
+<span class="linenos"> 562</span><span class="sd">            coarse_grid index -&gt; (top-left) fine_grid index.</span>
+<span class="linenos"> 563</span><span class="sd">        &quot;&quot;&quot;</span>
+<span class="linenos"> 564</span>        <span class="n">data</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span> <span class="o">=</span> <span class="n">ops</span>
+<span class="linenos"> 565</span>        <span class="n">N_row</span><span class="p">,</span> <span class="n">N_col</span><span class="p">,</span> <span class="n">N_block</span> <span class="o">=</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+<span class="linenos"> 566</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Incorrect COO parametrization&quot;</span>
+<span class="linenos"> 567</span>        <span class="k">assert</span> <span class="n">N_block</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">j</span><span class="p">),</span> <span class="n">msg</span>
+<span class="linenos"> 568</span>        <span class="k">assert</span> <span class="mi">0</span> <span class="o">&lt;</span> <span class="n">N_block</span> <span class="o">&lt;=</span> <span class="n">N_row</span> <span class="o">*</span> <span class="n">N_col</span><span class="p">,</span> <span class="n">msg</span>
+<span class="linenos"> 569</span>        <span class="k">assert</span> <span class="mi">0</span> <span class="o">&lt;=</span> <span class="nb">min</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="nb">max</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">N_row</span><span class="p">,</span> <span class="n">msg</span>
+<span class="linenos"> 570</span>        <span class="k">assert</span> <span class="mi">0</span> <span class="o">&lt;=</span> <span class="nb">min</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="nb">max</span><span class="p">(</span><span class="n">j</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">N_col</span><span class="p">,</span> <span class="n">msg</span>
+<span class="linenos"> 571</span>
+<span class="linenos"> 572</span>        <span class="c1"># block dimensions are compatible.</span>
+<span class="linenos"> 573</span>        <span class="n">row</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>  <span class="c1"># row_idx -&gt; [block]</span>
+<span class="linenos"> 574</span>        <span class="n">col</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>  <span class="c1"># col_idx -&gt; [block]</span>
+<span class="linenos"> 575</span>        <span class="k">for</span> <span class="n">d</span><span class="p">,</span> <span class="n">_i</span><span class="p">,</span> <span class="n">_j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">):</span>
+<span class="linenos"> 576</span>            <span class="n">row</span><span class="p">[</span><span class="n">_i</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
+<span class="linenos"> 577</span>            <span class="n">col</span><span class="p">[</span><span class="n">_j</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
+<span class="linenos"> 578</span>        <span class="n">msg</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">dim</span><span class="p">,</span> <span class="n">idx</span><span class="p">,</span> <span class="n">dom</span><span class="p">:</span> <span class="sa">f</span><span class="s2">&quot;All sub-operators on </span><span class="si">{</span><span class="n">dim</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">idx</span><span class="si">}</span><span class="s2"> must have same </span><span class="si">{</span><span class="n">dom</span><span class="si">}</span><span class="s2"> size.&quot;</span>
+<span class="linenos"> 579</span>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">row</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 580</span>            <span class="k">assert</span> <span class="nb">len</span><span class="p">({</span><span class="n">_</span><span class="o">.</span><span class="n">codim</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">v</span><span class="p">})</span> <span class="o">==</span> <span class="mi">1</span><span class="p">,</span> <span class="n">msg</span><span class="p">(</span><span class="s2">&quot;row&quot;</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="s2">&quot;codomain&quot;</span><span class="p">)</span>
+<span class="linenos"> 581</span>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">col</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 582</span>            <span class="k">assert</span> <span class="nb">len</span><span class="p">({</span><span class="n">_</span><span class="o">.</span><span class="n">dim</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">v</span><span class="p">})</span> <span class="o">==</span> <span class="mi">1</span><span class="p">,</span> <span class="n">msg</span><span class="p">(</span><span class="s2">&quot;column&quot;</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="s2">&quot;domain&quot;</span><span class="p">)</span>
+<span class="linenos"> 583</span>
+<span class="linenos"> 584</span>        <span class="c1"># no empty lines/columns in coarse grid.</span>
+<span class="linenos"> 585</span>        <span class="n">msg</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">:</span> <span class="sa">f</span><span class="s2">&quot;Coarse grid contains empty </span><span class="si">{</span><span class="n">_</span><span class="si">}</span><span class="s2">: cannot infer fine-grid dimensions.&quot;</span>
+<span class="linenos"> 586</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">row</span><span class="p">)</span> <span class="o">==</span> <span class="n">N_row</span><span class="p">,</span> <span class="n">msg</span><span class="p">(</span><span class="s2">&quot;rows&quot;</span><span class="p">)</span>
+<span class="linenos"> 587</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">col</span><span class="p">)</span> <span class="o">==</span> <span class="n">N_col</span><span class="p">,</span> <span class="n">msg</span><span class="p">(</span><span class="s2">&quot;columns&quot;</span><span class="p">)</span>
+<span class="linenos"> 588</span>
+<span class="linenos"> 589</span>        <span class="c1"># ---------------------------------------------------------------------</span>
+<span class="linenos"> 590</span>        <span class="c1"># create block</span>
+<span class="linenos"> 591</span>        <span class="n">block</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>  <span class="c1"># coarse_grid(int, int) -&gt; pxt.OpT</span>
+<span class="linenos"> 592</span>        <span class="k">for</span> <span class="n">d</span><span class="p">,</span> <span class="n">_i</span><span class="p">,</span> <span class="n">_j</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">):</span>
+<span class="linenos"> 593</span>            <span class="n">block</span><span class="p">[(</span><span class="n">_i</span><span class="p">,</span> <span class="n">_j</span><span class="p">)]</span> <span class="o">=</span> <span class="n">d</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
+<span class="linenos"> 594</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_block</span> <span class="o">=</span> <span class="n">block</span>
+<span class="linenos"> 595</span>
+<span class="linenos"> 596</span>        <span class="c1"># create block_offset</span>
+<span class="linenos"> 597</span>        <span class="n">block_offset</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>  <span class="c1"># coarse_grid(int, int) -&gt; fine_grid(int, int)</span>
+<span class="linenos"> 598</span>        <span class="n">row_offset</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">([</span><span class="n">row</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">codim</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">)])</span>
+<span class="linenos"> 599</span>        <span class="n">col_offset</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">([</span><span class="n">col</span><span class="p">[</span><span class="n">k</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">dim</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">)])</span>
+<span class="linenos"> 600</span>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">):</span>
+<span class="linenos"> 601</span>            <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">):</span>
+<span class="linenos"> 602</span>                <span class="n">_i</span> <span class="o">=</span> <span class="mi">0</span> <span class="k">if</span> <span class="p">(</span><span class="n">i</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)</span> <span class="k">else</span> <span class="n">row_offset</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+<span class="linenos"> 603</span>                <span class="n">_j</span> <span class="o">=</span> <span class="mi">0</span> <span class="k">if</span> <span class="p">(</span><span class="n">j</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)</span> <span class="k">else</span> <span class="n">col_offset</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+<span class="linenos"> 604</span>                <span class="n">block_offset</span><span class="p">[(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)]</span> <span class="o">=</span> <span class="n">_i</span><span class="p">,</span> <span class="n">_j</span>
+<span class="linenos"> 605</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span> <span class="o">=</span> <span class="n">block_offset</span>
+<span class="linenos"> 606</span>
+<span class="linenos"> 607</span>    <span class="k">def</span> <span class="nf">_infer_op</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos"> 608</span>        <span class="c1"># Create the abstract COO-operator to which methods will be assigned.</span>
+<span class="linenos"> 609</span>        <span class="n">blk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>  <span class="c1"># shorthand</span>
+<span class="linenos"> 610</span>
+<span class="linenos"> 611</span>        <span class="n">row</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
+<span class="linenos"> 612</span>        <span class="n">col</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
+<span class="linenos"> 613</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 614</span>            <span class="n">row</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">op</span><span class="p">)</span>
+<span class="linenos"> 615</span>            <span class="n">col</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">op</span><span class="p">)</span>
+<span class="linenos"> 616</span>        <span class="n">N_row</span><span class="p">,</span> <span class="n">N_col</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">row</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">col</span><span class="p">)</span>
+<span class="linenos"> 617</span>        <span class="n">op_codim</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">ops</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">codim</span> <span class="k">for</span> <span class="n">ops</span> <span class="ow">in</span> <span class="n">row</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
+<span class="linenos"> 618</span>        <span class="n">op_dim</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">ops</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">dim</span> <span class="k">for</span> <span class="n">ops</span> <span class="ow">in</span> <span class="n">col</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
+<span class="linenos"> 619</span>
+<span class="linenos"> 620</span>        <span class="n">P</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">Property</span>
+<span class="linenos"> 621</span>        <span class="n">properties</span> <span class="o">=</span> <span class="nb">set</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="o">*</span><span class="p">[</span><span class="nb">set</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">properties</span><span class="p">())</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">values</span><span class="p">()])</span>
+<span class="linenos"> 622</span>        <span class="k">if</span> <span class="n">op_codim</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
+<span class="linenos"> 623</span>            <span class="n">properties</span> <span class="o">-=</span> <span class="p">{</span>
+<span class="linenos"> 624</span>                <span class="n">P</span><span class="o">.</span><span class="n">FUNCTIONAL</span><span class="p">,</span>
+<span class="linenos"> 625</span>                <span class="n">P</span><span class="o">.</span><span class="n">PROXIMABLE</span><span class="p">,</span>
+<span class="linenos"> 626</span>                <span class="n">P</span><span class="o">.</span><span class="n">DIFFERENTIABLE_FUNCTION</span><span class="p">,</span>
+<span class="linenos"> 627</span>                <span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">,</span>
+<span class="linenos"> 628</span>            <span class="p">}</span>
+<span class="linenos"> 629</span>
+<span class="linenos"> 630</span>        <span class="k">if</span> <span class="nb">all</span><span class="p">(</span>  <span class="c1"># block_diag case</span>
+<span class="linenos"> 631</span>            <span class="p">[</span>
+<span class="linenos"> 632</span>                <span class="n">N_row</span> <span class="o">==</span> <span class="n">N_col</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">blk</span><span class="p">),</span>
+<span class="linenos"> 633</span>                <span class="nb">all</span><span class="p">((</span><span class="n">r</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">)),</span>
+<span class="linenos"> 634</span>            <span class="p">]</span>
+<span class="linenos"> 635</span>        <span class="p">):</span>
+<span class="linenos"> 636</span>            <span class="k">pass</span>
+<span class="linenos"> 637</span>        <span class="k">elif</span> <span class="n">op_codim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>  <span class="c1"># hstack case: special treatment of quadratics</span>
+<span class="linenos"> 638</span>            <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">values</span><span class="p">()):</span>
+<span class="linenos"> 639</span>                <span class="n">properties</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)</span>
+<span class="linenos"> 640</span>            <span class="k">elif</span> <span class="nb">any</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">values</span><span class="p">()):</span>
+<span class="linenos"> 641</span>                <span class="c1"># possible quadratic if all other terms are linear.</span>
+<span class="linenos"> 642</span>                <span class="n">non_quad</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">blk</span><span class="o">.</span><span class="n">values</span><span class="p">()</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)]</span>
+<span class="linenos"> 643</span>                <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">non_quad</span><span class="p">):</span>
+<span class="linenos"> 644</span>                    <span class="n">properties</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">)</span>
+<span class="linenos"> 645</span>        <span class="k">else</span><span class="p">:</span>  <span class="c1"># (1) vstack case or (2) arbitrary fill-in case =&gt; non-functionals</span>
+<span class="linenos"> 646</span>            <span class="n">properties</span> <span class="o">&amp;=</span> <span class="p">{</span>
+<span class="linenos"> 647</span>                <span class="n">P</span><span class="o">.</span><span class="n">CAN_EVAL</span><span class="p">,</span>
+<span class="linenos"> 648</span>                <span class="n">P</span><span class="o">.</span><span class="n">DIFFERENTIABLE</span><span class="p">,</span>
+<span class="linenos"> 649</span>                <span class="n">P</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">,</span>
+<span class="linenos"> 650</span>            <span class="p">}</span>
+<span class="linenos"> 651</span>            <span class="k">if</span> <span class="p">(</span><span class="n">op_codim</span> <span class="o">==</span> <span class="n">op_dim</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">LINEAR</span> <span class="ow">in</span> <span class="n">properties</span><span class="p">):</span>
+<span class="linenos"> 652</span>                <span class="n">properties</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">P</span><span class="o">.</span><span class="n">LINEAR_SQUARE</span><span class="p">)</span>
+<span class="linenos"> 653</span>
+<span class="linenos"> 654</span>        <span class="n">klass</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">Operator</span><span class="o">.</span><span class="n">_infer_operator_type</span><span class="p">(</span><span class="n">properties</span><span class="p">)</span>
+<span class="linenos"> 655</span>        <span class="n">op</span> <span class="o">=</span> <span class="n">klass</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">op_codim</span><span class="p">,</span> <span class="n">op_dim</span><span class="p">))</span>
+<span class="linenos"> 656</span>        <span class="k">return</span> <span class="n">op</span>
+<span class="linenos"> 657</span>
+<span class="linenos"> 658</span>    <span class="nd">@_parallelize</span>
+<span class="linenos"> 659</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
+<span class="linenos"> 660</span>    <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 661</span>        <span class="c1"># compute blocks</span>
+<span class="linenos"> 662</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+<span class="linenos"> 663</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 664</span>            <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
+<span class="linenos"> 665</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">])</span>
+<span class="linenos"> 666</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
+<span class="linenos"> 667</span>
+<span class="linenos"> 668</span>        <span class="c1"># row-oriented reduction (via +)</span>
+<span class="linenos"> 669</span>        <span class="n">rows</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
+<span class="linenos"> 670</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parts</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 671</span>            <span class="n">rows</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
+<span class="linenos"> 672</span>        <span class="n">cols</span> <span class="o">=</span> <span class="p">[</span><span class="nb">sum</span><span class="p">(</span><span class="n">rows</span><span class="p">[</span><span class="n">r</span><span class="p">])</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">rows</span><span class="p">))]</span>
+<span class="linenos"> 673</span>
+<span class="linenos"> 674</span>        <span class="c1"># concatenate to super-column</span>
+<span class="linenos"> 675</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+<span class="linenos"> 676</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">cols</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
+<span class="linenos"> 677</span>        <span class="k">return</span> <span class="n">out</span>
 <span class="linenos"> 678</span>
-<span class="linenos"> 679</span>    <span class="k">def</span> <span class="nf">estimate_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
-<span class="linenos"> 680</span>        <span class="n">Ls_all</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">)</span>  <span class="c1"># squared Lipschitz constant of each block.</span>
+<span class="linenos"> 679</span>    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 680</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
 <span class="linenos"> 681</span>
-<span class="linenos"> 682</span>        <span class="n">no_eval</span> <span class="o">=</span> <span class="s2">&quot;__rule&quot;</span> <span class="ow">in</span> <span class="n">kwargs</span>
-<span class="linenos"> 683</span>        <span class="k">if</span> <span class="n">no_eval</span><span class="p">:</span>
-<span class="linenos"> 684</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 685</span>                <span class="n">Ls_all</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">lipschitz</span><span class="o">**</span><span class="mi">2</span>
-<span class="linenos"> 686</span>        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
-<span class="linenos"> 687</span>            <span class="n">L</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">estimate_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 688</span>            <span class="k">return</span> <span class="n">L</span>
-<span class="linenos"> 689</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 690</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 691</span>                <span class="n">Ls_all</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">estimate_lipschitz</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
-<span class="linenos"> 692</span>
-<span class="linenos"> 693</span>        <span class="c1"># [non-linear case] Various upper bounds apply depending on how the blocks are organized:</span>
-<span class="linenos"> 694</span>        <span class="c1">#   * vertical alignment: L**2 = sum(L_k**2)</span>
-<span class="linenos"> 695</span>        <span class="c1">#   * horizontal alignment: L**2 = sum(L_k**2)</span>
-<span class="linenos"> 696</span>        <span class="c1">#   * block-diagonal alignment: L**2 = max(L_k**2)</span>
-<span class="linenos"> 697</span>        <span class="c1">#   * arbitrary 2D alignment: L**2 = sum(L_k**2)</span>
-<span class="linenos"> 698</span>        <span class="c1">#     [obtained via vertical+horizontal composition (or vice-versa)]</span>
-<span class="linenos"> 699</span>        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">Ls_all</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span> <span class="n">Ls_all</span><span class="o">.</span><span class="n">diagonal</span><span class="p">()</span><span class="o">.</span><span class="n">sum</span><span class="p">()):</span>  <span class="c1"># block-diag case</span>
-<span class="linenos"> 700</span>            <span class="n">L</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">Ls_all</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
-<span class="linenos"> 701</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 702</span>            <span class="n">L</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">Ls_all</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span>
-<span class="linenos"> 703</span>        <span class="k">return</span> <span class="n">L</span>
-<span class="linenos"> 704</span>
-<span class="linenos"> 705</span>    <span class="k">def</span> <span class="nf">_expr</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
-<span class="linenos"> 706</span>        <span class="k">class</span> <span class="nc">_Block</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Operator</span><span class="p">):</span>
-<span class="linenos"> 707</span>            <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">idx</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span> <span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">):</span>
-<span class="linenos"> 708</span>                <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">op</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
-<span class="linenos"> 709</span>                <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">_name</span>
-<span class="linenos"> 710</span>                <span class="bp">self</span><span class="o">.</span><span class="n">_idx</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
-<span class="linenos"> 711</span>                <span class="bp">self</span><span class="o">.</span><span class="n">_op</span> <span class="o">=</span> <span class="n">op</span>
-<span class="linenos"> 712</span>
-<span class="linenos"> 713</span>            <span class="k">def</span> <span class="nf">_expr</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
-<span class="linenos"> 714</span>                <span class="n">head</span> <span class="o">=</span> <span class="s2">&quot;block[&quot;</span> <span class="o">+</span> <span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_idx</span><span class="p">))</span> <span class="o">+</span> <span class="s2">&quot;]&quot;</span>
-<span class="linenos"> 715</span>                <span class="k">return</span> <span class="p">(</span><span class="n">head</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_op</span><span class="p">)</span>
-<span class="linenos"> 716</span>
-<span class="linenos"> 717</span>        <span class="c1"># head = coo_block[grid_shape]</span>
-<span class="linenos"> 718</span>        <span class="n">head</span> <span class="o">=</span> <span class="s2">&quot;coo_block[&quot;</span> <span class="o">+</span> <span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">))</span> <span class="o">+</span> <span class="s2">&quot;]&quot;</span>
+<span class="linenos"> 682</span>    <span class="k">def</span> <span class="nf">estimate_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
+<span class="linenos"> 683</span>        <span class="n">Ls_all</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">)</span>  <span class="c1"># squared Lipschitz constant of each block.</span>
+<span class="linenos"> 684</span>
+<span class="linenos"> 685</span>        <span class="n">no_eval</span> <span class="o">=</span> <span class="s2">&quot;__rule&quot;</span> <span class="ow">in</span> <span class="n">kwargs</span>
+<span class="linenos"> 686</span>        <span class="k">if</span> <span class="n">no_eval</span><span class="p">:</span>
+<span class="linenos"> 687</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 688</span>                <span class="n">Ls_all</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">lipschitz</span><span class="o">**</span><span class="mi">2</span>
+<span class="linenos"> 689</span>        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
+<span class="linenos"> 690</span>            <span class="n">L</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">estimate_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos"> 691</span>            <span class="k">return</span> <span class="n">L</span>
+<span class="linenos"> 692</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 693</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 694</span>                <span class="n">Ls_all</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">estimate_lipschitz</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
+<span class="linenos"> 695</span>
+<span class="linenos"> 696</span>        <span class="c1"># [non-linear case] Various upper bounds apply depending on how the blocks are organized:</span>
+<span class="linenos"> 697</span>        <span class="c1">#   * vertical alignment: L**2 = sum(L_k**2)</span>
+<span class="linenos"> 698</span>        <span class="c1">#   * horizontal alignment: L**2 = sum(L_k**2)</span>
+<span class="linenos"> 699</span>        <span class="c1">#   * block-diagonal alignment: L**2 = max(L_k**2)</span>
+<span class="linenos"> 700</span>        <span class="c1">#   * arbitrary 2D alignment: L**2 = sum(L_k**2)</span>
+<span class="linenos"> 701</span>        <span class="c1">#     [obtained via vertical+horizontal composition (or vice-versa)]</span>
+<span class="linenos"> 702</span>        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">Ls_all</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span> <span class="n">Ls_all</span><span class="o">.</span><span class="n">diagonal</span><span class="p">()</span><span class="o">.</span><span class="n">sum</span><span class="p">()):</span>  <span class="c1"># block-diag case</span>
+<span class="linenos"> 703</span>            <span class="n">L</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">Ls_all</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
+<span class="linenos"> 704</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 705</span>            <span class="n">L</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">Ls_all</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span>
+<span class="linenos"> 706</span>        <span class="k">return</span> <span class="n">L</span>
+<span class="linenos"> 707</span>
+<span class="linenos"> 708</span>    <span class="k">def</span> <span class="nf">_expr</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
+<span class="linenos"> 709</span>        <span class="k">class</span> <span class="nc">_Block</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Operator</span><span class="p">):</span>
+<span class="linenos"> 710</span>            <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">idx</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span> <span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">):</span>
+<span class="linenos"> 711</span>                <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">op</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
+<span class="linenos"> 712</span>                <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">_name</span>
+<span class="linenos"> 713</span>                <span class="bp">self</span><span class="o">.</span><span class="n">_idx</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
+<span class="linenos"> 714</span>                <span class="bp">self</span><span class="o">.</span><span class="n">_op</span> <span class="o">=</span> <span class="n">op</span>
+<span class="linenos"> 715</span>
+<span class="linenos"> 716</span>            <span class="k">def</span> <span class="nf">_expr</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">tuple</span><span class="p">:</span>
+<span class="linenos"> 717</span>                <span class="n">head</span> <span class="o">=</span> <span class="s2">&quot;block[&quot;</span> <span class="o">+</span> <span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_idx</span><span class="p">))</span> <span class="o">+</span> <span class="s2">&quot;]&quot;</span>
+<span class="linenos"> 718</span>                <span class="k">return</span> <span class="p">(</span><span class="n">head</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_op</span><span class="p">)</span>
 <span class="linenos"> 719</span>
-<span class="linenos"> 720</span>        <span class="c1"># tail = sequence of sub-blocks, encapsulated in _Block to obtain hierarchical view.</span>
-<span class="linenos"> 721</span>        <span class="n">tail</span> <span class="o">=</span> <span class="p">[</span><span class="n">_Block</span><span class="p">(</span><span class="n">idx</span><span class="o">=</span><span class="n">k</span><span class="p">,</span> <span class="n">op</span><span class="o">=</span><span class="n">op</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">()]</span>
-<span class="linenos"> 722</span>        <span class="k">return</span> <span class="p">(</span><span class="n">head</span><span class="p">,</span> <span class="o">*</span><span class="n">tail</span><span class="p">)</span>
-<span class="linenos"> 723</span>
-<span class="linenos"> 724</span>    <span class="nd">@_parallelize</span>
-<span class="linenos"> 725</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">))</span>
-<span class="linenos"> 726</span>    <span class="k">def</span> <span class="nf">prox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">tau</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 727</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">PROXIMABLE</span><span class="p">):</span>
-<span class="linenos"> 728</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 729</span>
-<span class="linenos"> 730</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
-<span class="linenos"> 731</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 732</span>            <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
-<span class="linenos"> 733</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">prox</span><span class="p">(</span><span class="n">arr</span><span class="o">=</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">],</span> <span class="n">tau</span><span class="o">=</span><span class="n">tau</span><span class="p">)</span>
-<span class="linenos"> 734</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
-<span class="linenos"> 735</span>
-<span class="linenos"> 736</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
-<span class="linenos"> 737</span>        <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">parts</span><span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">parts</span><span class="p">))]</span>  <span class="c1"># re-ordering</span>
-<span class="linenos"> 738</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">parts</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
-<span class="linenos"> 739</span>        <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 740</span>
-<span class="linenos"> 741</span>    <span class="k">def</span> <span class="nf">_quad_spec</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos"> 742</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">):</span>
-<span class="linenos"> 743</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 744</span>
-<span class="linenos"> 745</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
-<span class="linenos"> 746</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 747</span>            <span class="k">if</span> <span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">):</span>
-<span class="linenos"> 748</span>                <span class="n">_Q</span><span class="p">,</span> <span class="n">_c</span><span class="p">,</span> <span class="n">_t</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">_quad_spec</span><span class="p">()</span>
-<span class="linenos"> 749</span>            <span class="k">else</span><span class="p">:</span>  <span class="c1"># op is necessarily LINEAR</span>
-<span class="linenos"> 750</span>                <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">NullOp</span>
-<span class="linenos"> 751</span>
-<span class="linenos"> 752</span>                <span class="n">_Q</span> <span class="o">=</span> <span class="n">NullOp</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">,</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">))</span><span class="o">.</span><span class="n">asop</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">PosDefOp</span><span class="p">)</span>
-<span class="linenos"> 753</span>                <span class="n">_c</span> <span class="o">=</span> <span class="n">op</span>
-<span class="linenos"> 754</span>                <span class="n">_t</span> <span class="o">=</span> <span class="mi">0</span>
-<span class="linenos"> 755</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">_Q</span><span class="p">,</span> <span class="n">_c</span><span class="p">,</span> <span class="n">_t</span>
-<span class="linenos"> 756</span>
-<span class="linenos"> 757</span>        <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">parts</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">parts</span><span class="o">.</span><span class="n">keys</span><span class="p">())]</span>  <span class="c1"># re-ordering</span>
-<span class="linenos"> 758</span>        <span class="n">Q</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">t</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">parts</span><span class="p">)</span>
-<span class="linenos"> 759</span>        <span class="k">return</span> <span class="p">(</span><span class="n">block_diag</span><span class="p">(</span><span class="n">Q</span><span class="p">),</span> <span class="n">hstack</span><span class="p">(</span><span class="n">c</span><span class="p">),</span> <span class="nb">sum</span><span class="p">(</span><span class="n">t</span><span class="p">))</span>
-<span class="linenos"> 760</span>
-<span class="linenos"> 761</span>    <span class="k">def</span> <span class="nf">jacobian</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos"> 762</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">DIFFERENTIABLE</span><span class="p">):</span>
-<span class="linenos"> 763</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 764</span>
-<span class="linenos"> 765</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
-<span class="linenos"> 766</span>            <span class="n">out</span> <span class="o">=</span> <span class="bp">self</span>
-<span class="linenos"> 767</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 768</span>            <span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
-<span class="linenos"> 769</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 770</span>                <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">)][</span><span class="mi">1</span><span class="p">]</span>
-<span class="linenos"> 771</span>                <span class="n">opJ</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">jacobian</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">])</span>
-<span class="linenos"> 772</span>
-<span class="linenos"> 773</span>                <span class="n">i</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
-<span class="linenos"> 774</span>                <span class="n">j</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
-<span class="linenos"> 775</span>                <span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">opJ</span><span class="p">)</span>
-<span class="linenos"> 776</span>
-<span class="linenos"> 777</span>            <span class="n">out</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
-<span class="linenos"> 778</span>                <span class="n">ops</span><span class="o">=</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)),</span>
-<span class="linenos"> 779</span>                <span class="n">grid_shape</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">,</span>
-<span class="linenos"> 780</span>                <span class="n">parallel</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span><span class="p">,</span>
-<span class="linenos"> 781</span>            <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
-<span class="linenos"> 782</span>        <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 783</span>
-<span class="linenos"> 784</span>    <span class="k">def</span> <span class="nf">estimate_diff_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
-<span class="linenos"> 785</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">DIFFERENTIABLE</span><span class="p">):</span>
-<span class="linenos"> 786</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 787</span>
-<span class="linenos"> 788</span>        <span class="n">dLs_all</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">)</span>  <span class="c1"># squared diff-Lipschitz constant of each block.</span>
-<span class="linenos"> 789</span>
-<span class="linenos"> 790</span>        <span class="n">no_eval</span> <span class="o">=</span> <span class="s2">&quot;__rule&quot;</span> <span class="ow">in</span> <span class="n">kwargs</span>
-<span class="linenos"> 791</span>        <span class="k">if</span> <span class="n">no_eval</span><span class="p">:</span>
-<span class="linenos"> 792</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 793</span>                <span class="n">dLs_all</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">diff_lipschitz</span><span class="o">**</span><span class="mi">2</span>
-<span class="linenos"> 794</span>        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">):</span>
-<span class="linenos"> 795</span>            <span class="n">dL</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">QuadraticFunc</span><span class="o">.</span><span class="n">estimate_diff_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 796</span>            <span class="k">return</span> <span class="n">dL</span>
-<span class="linenos"> 797</span>        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
-<span class="linenos"> 798</span>            <span class="n">dL</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="linenos"> 720</span>        <span class="c1"># head = coo_block[grid_shape]</span>
+<span class="linenos"> 721</span>        <span class="n">head</span> <span class="o">=</span> <span class="s2">&quot;coo_block[&quot;</span> <span class="o">+</span> <span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">))</span> <span class="o">+</span> <span class="s2">&quot;]&quot;</span>
+<span class="linenos"> 722</span>
+<span class="linenos"> 723</span>        <span class="c1"># tail = sequence of sub-blocks, encapsulated in _Block to obtain hierarchical view.</span>
+<span class="linenos"> 724</span>        <span class="n">tail</span> <span class="o">=</span> <span class="p">[</span><span class="n">_Block</span><span class="p">(</span><span class="n">idx</span><span class="o">=</span><span class="n">k</span><span class="p">,</span> <span class="n">op</span><span class="o">=</span><span class="n">op</span><span class="p">)</span> <span class="k">for</span> <span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">op</span><span class="p">)</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">()]</span>
+<span class="linenos"> 725</span>        <span class="k">return</span> <span class="p">(</span><span class="n">head</span><span class="p">,</span> <span class="o">*</span><span class="n">tail</span><span class="p">)</span>
+<span class="linenos"> 726</span>
+<span class="linenos"> 727</span>    <span class="nd">@_parallelize</span>
+<span class="linenos"> 728</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">))</span>
+<span class="linenos"> 729</span>    <span class="k">def</span> <span class="nf">prox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">tau</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 730</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">PROXIMABLE</span><span class="p">):</span>
+<span class="linenos"> 731</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 732</span>
+<span class="linenos"> 733</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+<span class="linenos"> 734</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 735</span>            <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
+<span class="linenos"> 736</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">prox</span><span class="p">(</span><span class="n">arr</span><span class="o">=</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">],</span> <span class="n">tau</span><span class="o">=</span><span class="n">tau</span><span class="p">)</span>
+<span class="linenos"> 737</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
+<span class="linenos"> 738</span>
+<span class="linenos"> 739</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+<span class="linenos"> 740</span>        <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">parts</span><span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">parts</span><span class="p">))]</span>  <span class="c1"># re-ordering</span>
+<span class="linenos"> 741</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">parts</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
+<span class="linenos"> 742</span>        <span class="k">return</span> <span class="n">out</span>
+<span class="linenos"> 743</span>
+<span class="linenos"> 744</span>    <span class="k">def</span> <span class="nf">_quad_spec</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 745</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">):</span>
+<span class="linenos"> 746</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 747</span>
+<span class="linenos"> 748</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+<span class="linenos"> 749</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 750</span>            <span class="k">if</span> <span class="n">op</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">):</span>
+<span class="linenos"> 751</span>                <span class="n">_Q</span><span class="p">,</span> <span class="n">_c</span><span class="p">,</span> <span class="n">_t</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">_quad_spec</span><span class="p">()</span>
+<span class="linenos"> 752</span>            <span class="k">else</span><span class="p">:</span>  <span class="c1"># op is necessarily LINEAR</span>
+<span class="linenos"> 753</span>                <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">NullOp</span>
+<span class="linenos"> 754</span>
+<span class="linenos"> 755</span>                <span class="n">_Q</span> <span class="o">=</span> <span class="n">NullOp</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">,</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">))</span><span class="o">.</span><span class="n">asop</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">PosDefOp</span><span class="p">)</span>
+<span class="linenos"> 756</span>                <span class="n">_c</span> <span class="o">=</span> <span class="n">op</span>
+<span class="linenos"> 757</span>                <span class="n">_t</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="linenos"> 758</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">_Q</span><span class="p">,</span> <span class="n">_c</span><span class="p">,</span> <span class="n">_t</span>
+<span class="linenos"> 759</span>
+<span class="linenos"> 760</span>        <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">parts</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">parts</span><span class="o">.</span><span class="n">keys</span><span class="p">())]</span>  <span class="c1"># re-ordering</span>
+<span class="linenos"> 761</span>        <span class="n">Q</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">t</span> <span class="o">=</span> <span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="n">parts</span><span class="p">)</span>
+<span class="linenos"> 762</span>        <span class="k">return</span> <span class="p">(</span><span class="n">block_diag</span><span class="p">(</span><span class="n">Q</span><span class="p">),</span> <span class="n">hstack</span><span class="p">(</span><span class="n">c</span><span class="p">),</span> <span class="nb">sum</span><span class="p">(</span><span class="n">t</span><span class="p">))</span>
+<span class="linenos"> 763</span>
+<span class="linenos"> 764</span>    <span class="k">def</span> <span class="nf">jacobian</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos"> 765</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">DIFFERENTIABLE</span><span class="p">):</span>
+<span class="linenos"> 766</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 767</span>
+<span class="linenos"> 768</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
+<span class="linenos"> 769</span>            <span class="n">out</span> <span class="o">=</span> <span class="bp">self</span>
+<span class="linenos"> 770</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 771</span>            <span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
+<span class="linenos"> 772</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 773</span>                <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">)][</span><span class="mi">1</span><span class="p">]</span>
+<span class="linenos"> 774</span>                <span class="n">opJ</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">jacobian</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">])</span>
+<span class="linenos"> 775</span>
+<span class="linenos"> 776</span>                <span class="n">i</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
+<span class="linenos"> 777</span>                <span class="n">j</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+<span class="linenos"> 778</span>                <span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">opJ</span><span class="p">)</span>
+<span class="linenos"> 779</span>
+<span class="linenos"> 780</span>            <span class="n">out</span> <span class="o">=</span> <span class="n">_COOBlock</span><span class="p">(</span>
+<span class="linenos"> 781</span>                <span class="n">ops</span><span class="o">=</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)),</span>
+<span class="linenos"> 782</span>                <span class="n">grid_shape</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">,</span>
+<span class="linenos"> 783</span>                <span class="n">parallel</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span><span class="p">,</span>
+<span class="linenos"> 784</span>            <span class="p">)</span><span class="o">.</span><span class="n">op</span><span class="p">()</span>
+<span class="linenos"> 785</span>        <span class="k">return</span> <span class="n">out</span>
+<span class="linenos"> 786</span>
+<span class="linenos"> 787</span>    <span class="k">def</span> <span class="nf">estimate_diff_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
+<span class="linenos"> 788</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">DIFFERENTIABLE</span><span class="p">):</span>
+<span class="linenos"> 789</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 790</span>
+<span class="linenos"> 791</span>        <span class="n">dLs_all</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span><span class="p">)</span>  <span class="c1"># squared diff-Lipschitz constant of each block.</span>
+<span class="linenos"> 792</span>
+<span class="linenos"> 793</span>        <span class="n">no_eval</span> <span class="o">=</span> <span class="s2">&quot;__rule&quot;</span> <span class="ow">in</span> <span class="n">kwargs</span>
+<span class="linenos"> 794</span>        <span class="k">if</span> <span class="n">no_eval</span><span class="p">:</span>
+<span class="linenos"> 795</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 796</span>                <span class="n">dLs_all</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">diff_lipschitz</span><span class="o">**</span><span class="mi">2</span>
+<span class="linenos"> 797</span>        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">QUADRATIC</span><span class="p">):</span>
+<span class="linenos"> 798</span>            <span class="n">dL</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">QuadraticFunc</span><span class="o">.</span><span class="n">estimate_diff_lipschitz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
 <span class="linenos"> 799</span>            <span class="k">return</span> <span class="n">dL</span>
-<span class="linenos"> 800</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 801</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 802</span>                <span class="n">dLs_all</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">estimate_diff_lipschitz</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
-<span class="linenos"> 803</span>
-<span class="linenos"> 804</span>        <span class="c1"># Various upper bounds apply depending on how the blocks are organized:</span>
-<span class="linenos"> 805</span>        <span class="c1">#   * vertical alignment: dL**2 = sum(dL_k**2)</span>
-<span class="linenos"> 806</span>        <span class="c1">#   * horizontal alignment: dL**2 = sum(dL_k**2)</span>
-<span class="linenos"> 807</span>        <span class="c1">#   * block-diagonal alignment: dL**2 = max(dL_k**2)</span>
-<span class="linenos"> 808</span>        <span class="c1">#   * arbitrary 2D alignment: dL**2 = sum(dL_k**2)</span>
-<span class="linenos"> 809</span>        <span class="c1">#     [obtained via vertical+horizontal composition (or vice-versa)]</span>
-<span class="linenos"> 810</span>        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">dLs_all</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span> <span class="n">dLs_all</span><span class="o">.</span><span class="n">diagonal</span><span class="p">()</span><span class="o">.</span><span class="n">sum</span><span class="p">()):</span>  <span class="c1"># block-diag case</span>
-<span class="linenos"> 811</span>            <span class="n">dL</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">dLs_all</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
-<span class="linenos"> 812</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 813</span>            <span class="n">dL</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">dLs_all</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span>
-<span class="linenos"> 814</span>        <span class="k">return</span> <span class="n">dL</span>
-<span class="linenos"> 815</span>
-<span class="linenos"> 816</span>    <span class="nd">@_parallelize</span>
-<span class="linenos"> 817</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
-<span class="linenos"> 818</span>    <span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 819</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">DIFFERENTIABLE_FUNCTION</span><span class="p">):</span>
-<span class="linenos"> 820</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 821</span>
-<span class="linenos"> 822</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
-<span class="linenos"> 823</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 824</span>            <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
-<span class="linenos"> 825</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">])</span>
-<span class="linenos"> 826</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
-<span class="linenos"> 827</span>
-<span class="linenos"> 828</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
-<span class="linenos"> 829</span>        <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">parts</span><span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">parts</span><span class="p">))]</span>  <span class="c1"># re-ordering</span>
-<span class="linenos"> 830</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">parts</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
-<span class="linenos"> 831</span>        <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 832</span>
-<span class="linenos"> 833</span>    <span class="nd">@_parallelize</span>
-<span class="linenos"> 834</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
-<span class="linenos"> 835</span>    <span class="k">def</span> <span class="nf">adjoint</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 836</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
-<span class="linenos"> 837</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 838</span>
-<span class="linenos"> 839</span>        <span class="c1"># compute blocks</span>
-<span class="linenos"> 840</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
-<span class="linenos"> 841</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 842</span>            <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
-<span class="linenos"> 843</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">codim</span><span class="p">])</span>
-<span class="linenos"> 844</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span> <span class="o">=</span> <span class="n">p</span>
-<span class="linenos"> 845</span>
-<span class="linenos"> 846</span>        <span class="c1"># row-oriented reduction (via +)</span>
-<span class="linenos"> 847</span>        <span class="n">rows</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
-<span class="linenos"> 848</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parts</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 849</span>            <span class="n">rows</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
-<span class="linenos"> 850</span>        <span class="n">cols</span> <span class="o">=</span> <span class="p">[</span><span class="nb">sum</span><span class="p">(</span><span class="n">rows</span><span class="p">[</span><span class="n">r</span><span class="p">])</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">rows</span><span class="p">))]</span>
-<span class="linenos"> 851</span>
-<span class="linenos"> 852</span>        <span class="c1"># concatenate to super-column</span>
-<span class="linenos"> 853</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
-<span class="linenos"> 854</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">cols</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
-<span class="linenos"> 855</span>        <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 856</span>
-<span class="linenos"> 857</span>    <span class="k">def</span> <span class="nf">asarray</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 858</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
-<span class="linenos"> 859</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 860</span>
-<span class="linenos"> 861</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
-<span class="linenos"> 862</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 863</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 864</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
-<span class="linenos"> 865</span>
-<span class="linenos"> 866</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;xp&quot;</span><span class="p">,</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">default</span><span class="p">()</span><span class="o">.</span><span class="n">module</span><span class="p">())</span>
-<span class="linenos"> 867</span>        <span class="n">dtype</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;dtype&quot;</span><span class="p">,</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">getPrecision</span><span class="p">()</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
-<span class="linenos"> 868</span>        <span class="n">A</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">)</span>
-<span class="linenos"> 869</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parts</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 870</span>            <span class="n">r_o</span><span class="p">,</span> <span class="n">c_o</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>  <span class="c1"># offsets</span>
-<span class="linenos"> 871</span>            <span class="n">r_s</span><span class="p">,</span> <span class="n">c_s</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># spans</span>
-<span class="linenos"> 872</span>            <span class="n">A</span><span class="p">[</span><span class="n">r_o</span> <span class="p">:</span> <span class="n">r_o</span> <span class="o">+</span> <span class="n">r_s</span><span class="p">,</span> <span class="n">c_o</span> <span class="p">:</span> <span class="n">c_o</span> <span class="o">+</span> <span class="n">c_s</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
-<span class="linenos"> 873</span>        <span class="k">return</span> <span class="n">A</span>
-<span class="linenos"> 874</span>
-<span class="linenos"> 875</span>    <span class="k">def</span> <span class="nf">svdvals</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 876</span>        <span class="n">D</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">svdvals</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 877</span>        <span class="k">return</span> <span class="n">D</span>
-<span class="linenos"> 878</span>
-<span class="linenos"> 879</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;damp&quot;</span><span class="p">))</span>
-<span class="linenos"> 880</span>    <span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">damp</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 881</span>        <span class="n">out</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="o">=</span><span class="n">arr</span><span class="p">,</span> <span class="n">damp</span><span class="o">=</span><span class="n">damp</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 882</span>        <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 883</span>
-<span class="linenos"> 884</span>    <span class="k">def</span> <span class="nf">gram</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos"> 885</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
-<span class="linenos"> 886</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 887</span>
-<span class="linenos"> 888</span>        <span class="n">blk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>  <span class="c1"># shorthand</span>
-<span class="linenos"> 889</span>        <span class="n">N_row</span><span class="p">,</span> <span class="n">N_col</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span>
+<span class="linenos"> 800</span>        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
+<span class="linenos"> 801</span>            <span class="n">dL</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="linenos"> 802</span>            <span class="k">return</span> <span class="n">dL</span>
+<span class="linenos"> 803</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 804</span>            <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 805</span>                <span class="n">dLs_all</span><span class="p">[</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">estimate_diff_lipschitz</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
+<span class="linenos"> 806</span>
+<span class="linenos"> 807</span>        <span class="c1"># Various upper bounds apply depending on how the blocks are organized:</span>
+<span class="linenos"> 808</span>        <span class="c1">#   * vertical alignment: dL**2 = sum(dL_k**2)</span>
+<span class="linenos"> 809</span>        <span class="c1">#   * horizontal alignment: dL**2 = sum(dL_k**2)</span>
+<span class="linenos"> 810</span>        <span class="c1">#   * block-diagonal alignment: dL**2 = max(dL_k**2)</span>
+<span class="linenos"> 811</span>        <span class="c1">#   * arbitrary 2D alignment: dL**2 = sum(dL_k**2)</span>
+<span class="linenos"> 812</span>        <span class="c1">#     [obtained via vertical+horizontal composition (or vice-versa)]</span>
+<span class="linenos"> 813</span>        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">dLs_all</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span> <span class="n">dLs_all</span><span class="o">.</span><span class="n">diagonal</span><span class="p">()</span><span class="o">.</span><span class="n">sum</span><span class="p">()):</span>  <span class="c1"># block-diag case</span>
+<span class="linenos"> 814</span>            <span class="n">dL</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">dLs_all</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
+<span class="linenos"> 815</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 816</span>            <span class="n">dL</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">dLs_all</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span>
+<span class="linenos"> 817</span>        <span class="k">return</span> <span class="n">dL</span>
+<span class="linenos"> 818</span>
+<span class="linenos"> 819</span>    <span class="nd">@_parallelize</span>
+<span class="linenos"> 820</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
+<span class="linenos"> 821</span>    <span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 822</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">DIFFERENTIABLE_FUNCTION</span><span class="p">):</span>
+<span class="linenos"> 823</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 824</span>
+<span class="linenos"> 825</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+<span class="linenos"> 826</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 827</span>            <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
+<span class="linenos"> 828</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">dim</span><span class="p">])</span>
+<span class="linenos"> 829</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
+<span class="linenos"> 830</span>
+<span class="linenos"> 831</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+<span class="linenos"> 832</span>        <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">parts</span><span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">parts</span><span class="p">))]</span>  <span class="c1"># re-ordering</span>
+<span class="linenos"> 833</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">parts</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
+<span class="linenos"> 834</span>        <span class="k">return</span> <span class="n">out</span>
+<span class="linenos"> 835</span>
+<span class="linenos"> 836</span>    <span class="nd">@_parallelize</span>
+<span class="linenos"> 837</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
+<span class="linenos"> 838</span>    <span class="k">def</span> <span class="nf">adjoint</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 839</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
+<span class="linenos"> 840</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 841</span>
+<span class="linenos"> 842</span>        <span class="c1"># compute blocks</span>
+<span class="linenos"> 843</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+<span class="linenos"> 844</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 845</span>            <span class="n">offset</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<span class="linenos"> 846</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">offset</span> <span class="p">:</span> <span class="n">offset</span> <span class="o">+</span> <span class="n">op</span><span class="o">.</span><span class="n">codim</span><span class="p">])</span>
+<span class="linenos"> 847</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]]</span> <span class="o">=</span> <span class="n">p</span>
+<span class="linenos"> 848</span>
+<span class="linenos"> 849</span>        <span class="c1"># row-oriented reduction (via +)</span>
+<span class="linenos"> 850</span>        <span class="n">rows</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
+<span class="linenos"> 851</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parts</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 852</span>            <span class="n">rows</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
+<span class="linenos"> 853</span>        <span class="n">cols</span> <span class="o">=</span> <span class="p">[</span><span class="nb">sum</span><span class="p">(</span><span class="n">rows</span><span class="p">[</span><span class="n">r</span><span class="p">])</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">rows</span><span class="p">))]</span>
+<span class="linenos"> 854</span>
+<span class="linenos"> 855</span>        <span class="c1"># concatenate to super-column</span>
+<span class="linenos"> 856</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+<span class="linenos"> 857</span>        <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span><span class="n">cols</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
+<span class="linenos"> 858</span>        <span class="k">return</span> <span class="n">out</span>
+<span class="linenos"> 859</span>
+<span class="linenos"> 860</span>    <span class="k">def</span> <span class="nf">asarray</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 861</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
+<span class="linenos"> 862</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+<span class="linenos"> 863</span>
+<span class="linenos"> 864</span>        <span class="n">parts</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+<span class="linenos"> 865</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">op</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 866</span>            <span class="n">p</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos"> 867</span>            <span class="n">parts</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
+<span class="linenos"> 868</span>
+<span class="linenos"> 869</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;xp&quot;</span><span class="p">,</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">default</span><span class="p">()</span><span class="o">.</span><span class="n">module</span><span class="p">())</span>
+<span class="linenos"> 870</span>        <span class="n">dtype</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;dtype&quot;</span><span class="p">,</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">getPrecision</span><span class="p">()</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
+<span class="linenos"> 871</span>        <span class="n">A</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dtype</span><span class="p">)</span>
+<span class="linenos"> 872</span>        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parts</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 873</span>            <span class="n">r_o</span><span class="p">,</span> <span class="n">c_o</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block_offset</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>  <span class="c1"># offsets</span>
+<span class="linenos"> 874</span>            <span class="n">r_s</span><span class="p">,</span> <span class="n">c_s</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># spans</span>
+<span class="linenos"> 875</span>            <span class="n">A</span><span class="p">[</span><span class="n">r_o</span> <span class="p">:</span> <span class="n">r_o</span> <span class="o">+</span> <span class="n">r_s</span><span class="p">,</span> <span class="n">c_o</span> <span class="p">:</span> <span class="n">c_o</span> <span class="o">+</span> <span class="n">c_s</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
+<span class="linenos"> 876</span>        <span class="k">return</span> <span class="n">A</span>
+<span class="linenos"> 877</span>
+<span class="linenos"> 878</span>    <span class="k">def</span> <span class="nf">svdvals</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 879</span>        <span class="n">D</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">svdvals</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos"> 880</span>        <span class="k">return</span> <span class="n">D</span>
+<span class="linenos"> 881</span>
+<span class="linenos"> 882</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;damp&quot;</span><span class="p">))</span>
+<span class="linenos"> 883</span>    <span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">damp</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 884</span>        <span class="n">out</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="o">=</span><span class="n">arr</span><span class="p">,</span> <span class="n">damp</span><span class="o">=</span><span class="n">damp</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos"> 885</span>        <span class="k">return</span> <span class="n">out</span>
+<span class="linenos"> 886</span>
+<span class="linenos"> 887</span>    <span class="k">def</span> <span class="nf">gram</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos"> 888</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
+<span class="linenos"> 889</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
 <span class="linenos"> 890</span>
-<span class="linenos"> 891</span>        <span class="c1"># Determine operator(s) which will occupy position (r,c) on coarse grid.</span>
-<span class="linenos"> 892</span>        <span class="n">ops</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>  <span class="c1"># coarse_grid(int, int) -&gt; [pxt.OpT]</span>
-<span class="linenos"> 893</span>        <span class="k">for</span> <span class="n">r</span><span class="p">,</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">itertools</span><span class="o">.</span><span class="n">product</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">),</span> <span class="n">repeat</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
-<span class="linenos"> 894</span>            <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">):</span>
-<span class="linenos"> 895</span>                <span class="k">if</span> <span class="p">((</span><span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span><span class="p">)</span> <span class="ow">and</span> <span class="p">((</span><span class="n">k</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span><span class="p">):</span>
-<span class="linenos"> 896</span>                    <span class="k">if</span> <span class="n">r</span> <span class="o">==</span> <span class="n">c</span><span class="p">:</span>
-<span class="linenos"> 897</span>                        <span class="n">_op</span> <span class="o">=</span> <span class="n">blk</span><span class="p">[(</span><span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">)]</span><span class="o">.</span><span class="n">gram</span><span class="p">()</span>
-<span class="linenos"> 898</span>                    <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 899</span>                        <span class="n">_op</span> <span class="o">=</span> <span class="n">blk</span><span class="p">[(</span><span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">)]</span><span class="o">.</span><span class="n">T</span> <span class="o">*</span> <span class="n">blk</span><span class="p">[(</span><span class="n">k</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span>
-<span class="linenos"> 900</span>                    <span class="n">ops</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_op</span><span class="p">)</span>
-<span class="linenos"> 901</span>
-<span class="linenos"> 902</span>        <span class="c1"># ops[(r,c)] should be reduced (via +) to form a single operator per (r,c)-entry.</span>
-<span class="linenos"> 903</span>        <span class="c1"># It is inefficient however to chain so many operators together via AddRule().</span>
-<span class="linenos"> 904</span>        <span class="c1"># G.[apply,adjoint]() are thus redefined to improve performance.</span>
-<span class="linenos"> 905</span>        <span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
-<span class="linenos"> 906</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">_ops</span> <span class="ow">in</span> <span class="n">ops</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 907</span>            <span class="n">klass</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">SelfAdjointOp</span> <span class="k">if</span> <span class="p">(</span><span class="n">r</span> <span class="o">==</span> <span class="n">c</span><span class="p">)</span> <span class="k">else</span> <span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span>
-<span class="linenos"> 908</span>            <span class="n">_op</span> <span class="o">=</span> <span class="n">klass</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">_ops</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>  <span class="c1"># .[apply|adjoint]() overridden below.</span>
-<span class="linenos"> 909</span>            <span class="n">_op</span><span class="o">.</span><span class="n">_ops</span> <span class="o">=</span> <span class="n">_ops</span>  <span class="c1"># embed for introspection</span>
-<span class="linenos"> 910</span>
-<span class="linenos"> 911</span>            <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
-<span class="linenos"> 912</span>            <span class="k">def</span> <span class="nf">op_apply</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 913</span>                <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_ops</span><span class="p">]</span>
-<span class="linenos"> 914</span>                <span class="n">out</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
-<span class="linenos"> 915</span>                <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 916</span>
-<span class="linenos"> 917</span>            <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
-<span class="linenos"> 918</span>            <span class="k">def</span> <span class="nf">op_adjoint</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 919</span>                <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_ops</span><span class="p">]</span>
-<span class="linenos"> 920</span>                <span class="n">out</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
-<span class="linenos"> 921</span>                <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 922</span>
-<span class="linenos"> 923</span>            <span class="n">_op</span><span class="o">.</span><span class="n">apply</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_apply</span><span class="p">,</span> <span class="n">_op</span><span class="p">)</span>
-<span class="linenos"> 924</span>            <span class="n">_op</span><span class="o">.</span><span class="n">adjoint</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_adjoint</span><span class="p">,</span> <span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 891</span>        <span class="n">blk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>  <span class="c1"># shorthand</span>
+<span class="linenos"> 892</span>        <span class="n">N_row</span><span class="p">,</span> <span class="n">N_col</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span>
+<span class="linenos"> 893</span>
+<span class="linenos"> 894</span>        <span class="c1"># Determine operator(s) which will occupy position (r,c) on coarse grid.</span>
+<span class="linenos"> 895</span>        <span class="n">ops</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>  <span class="c1"># coarse_grid(int, int) -&gt; [pxt.OpT]</span>
+<span class="linenos"> 896</span>        <span class="k">for</span> <span class="n">r</span><span class="p">,</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">itertools</span><span class="o">.</span><span class="n">product</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">),</span> <span class="n">repeat</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
+<span class="linenos"> 897</span>            <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">):</span>
+<span class="linenos"> 898</span>                <span class="k">if</span> <span class="p">((</span><span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span><span class="p">)</span> <span class="ow">and</span> <span class="p">((</span><span class="n">k</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span><span class="p">):</span>
+<span class="linenos"> 899</span>                    <span class="k">if</span> <span class="n">r</span> <span class="o">==</span> <span class="n">c</span><span class="p">:</span>
+<span class="linenos"> 900</span>                        <span class="n">_op</span> <span class="o">=</span> <span class="n">blk</span><span class="p">[(</span><span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">)]</span><span class="o">.</span><span class="n">gram</span><span class="p">()</span>
+<span class="linenos"> 901</span>                    <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 902</span>                        <span class="n">_op</span> <span class="o">=</span> <span class="n">blk</span><span class="p">[(</span><span class="n">k</span><span class="p">,</span> <span class="n">r</span><span class="p">)]</span><span class="o">.</span><span class="n">T</span> <span class="o">*</span> <span class="n">blk</span><span class="p">[(</span><span class="n">k</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span>
+<span class="linenos"> 903</span>                    <span class="n">ops</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 904</span>
+<span class="linenos"> 905</span>        <span class="c1"># ops[(r,c)] should be reduced (via +) to form a single operator per (r,c)-entry.</span>
+<span class="linenos"> 906</span>        <span class="c1"># It is inefficient however to chain so many operators together via AddRule().</span>
+<span class="linenos"> 907</span>        <span class="c1"># G.[apply,adjoint]() are thus redefined to improve performance.</span>
+<span class="linenos"> 908</span>        <span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
+<span class="linenos"> 909</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">_ops</span> <span class="ow">in</span> <span class="n">ops</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 910</span>            <span class="n">klass</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">SelfAdjointOp</span> <span class="k">if</span> <span class="p">(</span><span class="n">r</span> <span class="o">==</span> <span class="n">c</span><span class="p">)</span> <span class="k">else</span> <span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span>
+<span class="linenos"> 911</span>            <span class="n">_op</span> <span class="o">=</span> <span class="n">klass</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">_ops</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>  <span class="c1"># .[apply|adjoint]() overridden below.</span>
+<span class="linenos"> 912</span>            <span class="n">_op</span><span class="o">.</span><span class="n">_ops</span> <span class="o">=</span> <span class="n">_ops</span>  <span class="c1"># embed for introspection</span>
+<span class="linenos"> 913</span>
+<span class="linenos"> 914</span>            <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
+<span class="linenos"> 915</span>            <span class="k">def</span> <span class="nf">op_apply</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 916</span>                <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_ops</span><span class="p">]</span>
+<span class="linenos"> 917</span>                <span class="n">out</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
+<span class="linenos"> 918</span>                <span class="k">return</span> <span class="n">out</span>
+<span class="linenos"> 919</span>
+<span class="linenos"> 920</span>            <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
+<span class="linenos"> 921</span>            <span class="k">def</span> <span class="nf">op_adjoint</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 922</span>                <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_ops</span><span class="p">]</span>
+<span class="linenos"> 923</span>                <span class="n">out</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
+<span class="linenos"> 924</span>                <span class="k">return</span> <span class="n">out</span>
 <span class="linenos"> 925</span>
-<span class="linenos"> 926</span>            <span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_op</span><span class="p">)</span>
-<span class="linenos"> 927</span>            <span class="n">i</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
-<span class="linenos"> 928</span>            <span class="n">j</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
-<span class="linenos"> 929</span>        <span class="n">G</span> <span class="o">=</span> <span class="p">(</span>
-<span class="linenos"> 930</span>            <span class="n">_COOBlock</span><span class="p">(</span>
-<span class="linenos"> 931</span>                <span class="n">ops</span><span class="o">=</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)),</span>
-<span class="linenos"> 932</span>                <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_col</span><span class="p">,</span> <span class="n">N_col</span><span class="p">),</span>
-<span class="linenos"> 933</span>                <span class="n">parallel</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span><span class="p">,</span>
-<span class="linenos"> 934</span>            <span class="p">)</span>
-<span class="linenos"> 935</span>            <span class="o">.</span><span class="n">op</span><span class="p">()</span>
-<span class="linenos"> 936</span>            <span class="o">.</span><span class="n">asop</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">SelfAdjointOp</span><span class="p">)</span>
-<span class="linenos"> 937</span>        <span class="p">)</span>
-<span class="linenos"> 938</span>        <span class="k">return</span> <span class="n">G</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
-<span class="linenos"> 939</span>
-<span class="linenos"> 940</span>    <span class="k">def</span> <span class="nf">cogram</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos"> 941</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
-<span class="linenos"> 942</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
-<span class="linenos"> 943</span>
-<span class="linenos"> 944</span>        <span class="n">blk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>  <span class="c1"># shorthand</span>
-<span class="linenos"> 945</span>        <span class="n">N_row</span><span class="p">,</span> <span class="n">N_col</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span>
+<span class="linenos"> 926</span>            <span class="n">_op</span><span class="o">.</span><span class="n">apply</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_apply</span><span class="p">,</span> <span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 927</span>            <span class="n">_op</span><span class="o">.</span><span class="n">adjoint</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_adjoint</span><span class="p">,</span> <span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 928</span>
+<span class="linenos"> 929</span>            <span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 930</span>            <span class="n">i</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
+<span class="linenos"> 931</span>            <span class="n">j</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+<span class="linenos"> 932</span>        <span class="n">G</span> <span class="o">=</span> <span class="p">(</span>
+<span class="linenos"> 933</span>            <span class="n">_COOBlock</span><span class="p">(</span>
+<span class="linenos"> 934</span>                <span class="n">ops</span><span class="o">=</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)),</span>
+<span class="linenos"> 935</span>                <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_col</span><span class="p">,</span> <span class="n">N_col</span><span class="p">),</span>
+<span class="linenos"> 936</span>                <span class="n">parallel</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span><span class="p">,</span>
+<span class="linenos"> 937</span>            <span class="p">)</span>
+<span class="linenos"> 938</span>            <span class="o">.</span><span class="n">op</span><span class="p">()</span>
+<span class="linenos"> 939</span>            <span class="o">.</span><span class="n">asop</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">SelfAdjointOp</span><span class="p">)</span>
+<span class="linenos"> 940</span>        <span class="p">)</span>
+<span class="linenos"> 941</span>        <span class="k">return</span> <span class="n">G</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
+<span class="linenos"> 942</span>
+<span class="linenos"> 943</span>    <span class="k">def</span> <span class="nf">cogram</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos"> 944</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">has</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Property</span><span class="o">.</span><span class="n">LINEAR</span><span class="p">):</span>
+<span class="linenos"> 945</span>            <span class="k">raise</span> <span class="ne">NotImplementedError</span>
 <span class="linenos"> 946</span>
-<span class="linenos"> 947</span>        <span class="c1"># Determine operator(s) which will occupy position (r,c) on coarse grid.</span>
-<span class="linenos"> 948</span>        <span class="n">ops</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>  <span class="c1"># coarse_grid(int, int) -&gt; [pxt.OpT]</span>
-<span class="linenos"> 949</span>        <span class="k">for</span> <span class="n">r</span><span class="p">,</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">itertools</span><span class="o">.</span><span class="n">product</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">),</span> <span class="n">repeat</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
-<span class="linenos"> 950</span>            <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">):</span>
-<span class="linenos"> 951</span>                <span class="k">if</span> <span class="p">((</span><span class="n">r</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span><span class="p">)</span> <span class="ow">and</span> <span class="p">((</span><span class="n">c</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span><span class="p">):</span>
-<span class="linenos"> 952</span>                    <span class="k">if</span> <span class="n">r</span> <span class="o">==</span> <span class="n">c</span><span class="p">:</span>
-<span class="linenos"> 953</span>                        <span class="n">_op</span> <span class="o">=</span> <span class="n">blk</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">k</span><span class="p">)]</span><span class="o">.</span><span class="n">cogram</span><span class="p">()</span>
-<span class="linenos"> 954</span>                    <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 955</span>                        <span class="n">_op</span> <span class="o">=</span> <span class="n">blk</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">k</span><span class="p">)]</span> <span class="o">*</span> <span class="n">blk</span><span class="p">[(</span><span class="n">c</span><span class="p">,</span> <span class="n">k</span><span class="p">)]</span><span class="o">.</span><span class="n">T</span>
-<span class="linenos"> 956</span>                    <span class="n">ops</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_op</span><span class="p">)</span>
-<span class="linenos"> 957</span>
-<span class="linenos"> 958</span>        <span class="c1"># ops[(r,c)] should be reduced (via +) to form a single operator per (r,c)-entry.</span>
-<span class="linenos"> 959</span>        <span class="c1"># It is inefficient however to chain so many operators together via AddRule().</span>
-<span class="linenos"> 960</span>        <span class="c1"># CG.[apply,adjoint]() are thus redefined to improve performance.</span>
-<span class="linenos"> 961</span>        <span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
-<span class="linenos"> 962</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">_ops</span> <span class="ow">in</span> <span class="n">ops</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos"> 963</span>            <span class="n">klass</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">SelfAdjointOp</span> <span class="k">if</span> <span class="p">(</span><span class="n">r</span> <span class="o">==</span> <span class="n">c</span><span class="p">)</span> <span class="k">else</span> <span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span>
-<span class="linenos"> 964</span>            <span class="n">_op</span> <span class="o">=</span> <span class="n">klass</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">_ops</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>  <span class="c1"># .[apply|adjoint]() overridden below.</span>
-<span class="linenos"> 965</span>            <span class="n">_op</span><span class="o">.</span><span class="n">_ops</span> <span class="o">=</span> <span class="n">_ops</span>  <span class="c1"># embed for introspection</span>
-<span class="linenos"> 966</span>
-<span class="linenos"> 967</span>            <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
-<span class="linenos"> 968</span>            <span class="k">def</span> <span class="nf">op_apply</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 969</span>                <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_ops</span><span class="p">]</span>
-<span class="linenos"> 970</span>                <span class="n">out</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
-<span class="linenos"> 971</span>                <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 972</span>
-<span class="linenos"> 973</span>            <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
-<span class="linenos"> 974</span>            <span class="k">def</span> <span class="nf">op_adjoint</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 975</span>                <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_ops</span><span class="p">]</span>
-<span class="linenos"> 976</span>                <span class="n">out</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
-<span class="linenos"> 977</span>                <span class="k">return</span> <span class="n">out</span>
-<span class="linenos"> 978</span>
-<span class="linenos"> 979</span>            <span class="n">_op</span><span class="o">.</span><span class="n">apply</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_apply</span><span class="p">,</span> <span class="n">_op</span><span class="p">)</span>
-<span class="linenos"> 980</span>            <span class="n">_op</span><span class="o">.</span><span class="n">adjoint</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_adjoint</span><span class="p">,</span> <span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 947</span>        <span class="n">blk</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_block</span>  <span class="c1"># shorthand</span>
+<span class="linenos"> 948</span>        <span class="n">N_row</span><span class="p">,</span> <span class="n">N_col</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_grid_shape</span>
+<span class="linenos"> 949</span>
+<span class="linenos"> 950</span>        <span class="c1"># Determine operator(s) which will occupy position (r,c) on coarse grid.</span>
+<span class="linenos"> 951</span>        <span class="n">ops</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>  <span class="c1"># coarse_grid(int, int) -&gt; [pxt.OpT]</span>
+<span class="linenos"> 952</span>        <span class="k">for</span> <span class="n">r</span><span class="p">,</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">itertools</span><span class="o">.</span><span class="n">product</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N_row</span><span class="p">),</span> <span class="n">repeat</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
+<span class="linenos"> 953</span>            <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_col</span><span class="p">):</span>
+<span class="linenos"> 954</span>                <span class="k">if</span> <span class="p">((</span><span class="n">r</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span><span class="p">)</span> <span class="ow">and</span> <span class="p">((</span><span class="n">c</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span> <span class="ow">in</span> <span class="n">blk</span><span class="p">):</span>
+<span class="linenos"> 955</span>                    <span class="k">if</span> <span class="n">r</span> <span class="o">==</span> <span class="n">c</span><span class="p">:</span>
+<span class="linenos"> 956</span>                        <span class="n">_op</span> <span class="o">=</span> <span class="n">blk</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">k</span><span class="p">)]</span><span class="o">.</span><span class="n">cogram</span><span class="p">()</span>
+<span class="linenos"> 957</span>                    <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 958</span>                        <span class="n">_op</span> <span class="o">=</span> <span class="n">blk</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">k</span><span class="p">)]</span> <span class="o">*</span> <span class="n">blk</span><span class="p">[(</span><span class="n">c</span><span class="p">,</span> <span class="n">k</span><span class="p">)]</span><span class="o">.</span><span class="n">T</span>
+<span class="linenos"> 959</span>                    <span class="n">ops</span><span class="p">[(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">)]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 960</span>
+<span class="linenos"> 961</span>        <span class="c1"># ops[(r,c)] should be reduced (via +) to form a single operator per (r,c)-entry.</span>
+<span class="linenos"> 962</span>        <span class="c1"># It is inefficient however to chain so many operators together via AddRule().</span>
+<span class="linenos"> 963</span>        <span class="c1"># CG.[apply,adjoint]() are thus redefined to improve performance.</span>
+<span class="linenos"> 964</span>        <span class="n">data</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
+<span class="linenos"> 965</span>        <span class="k">for</span> <span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">c</span><span class="p">),</span> <span class="n">_ops</span> <span class="ow">in</span> <span class="n">ops</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos"> 966</span>            <span class="n">klass</span> <span class="o">=</span> <span class="n">pxa</span><span class="o">.</span><span class="n">SelfAdjointOp</span> <span class="k">if</span> <span class="p">(</span><span class="n">r</span> <span class="o">==</span> <span class="n">c</span><span class="p">)</span> <span class="k">else</span> <span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span>
+<span class="linenos"> 967</span>            <span class="n">_op</span> <span class="o">=</span> <span class="n">klass</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="n">_ops</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>  <span class="c1"># .[apply|adjoint]() overridden below.</span>
+<span class="linenos"> 968</span>            <span class="n">_op</span><span class="o">.</span><span class="n">_ops</span> <span class="o">=</span> <span class="n">_ops</span>  <span class="c1"># embed for introspection</span>
+<span class="linenos"> 969</span>
+<span class="linenos"> 970</span>            <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
+<span class="linenos"> 971</span>            <span class="k">def</span> <span class="nf">op_apply</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 972</span>                <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_ops</span><span class="p">]</span>
+<span class="linenos"> 973</span>                <span class="n">out</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
+<span class="linenos"> 974</span>                <span class="k">return</span> <span class="n">out</span>
+<span class="linenos"> 975</span>
+<span class="linenos"> 976</span>            <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
+<span class="linenos"> 977</span>            <span class="k">def</span> <span class="nf">op_adjoint</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 978</span>                <span class="n">parts</span> <span class="o">=</span> <span class="p">[</span><span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">_</span><span class="o">.</span><span class="n">_ops</span><span class="p">]</span>
+<span class="linenos"> 979</span>                <span class="n">out</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">parts</span><span class="p">)</span>
+<span class="linenos"> 980</span>                <span class="k">return</span> <span class="n">out</span>
 <span class="linenos"> 981</span>
-<span class="linenos"> 982</span>            <span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_op</span><span class="p">)</span>
-<span class="linenos"> 983</span>            <span class="n">i</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
-<span class="linenos"> 984</span>            <span class="n">j</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
-<span class="linenos"> 985</span>        <span class="n">CG</span> <span class="o">=</span> <span class="p">(</span>
-<span class="linenos"> 986</span>            <span class="n">_COOBlock</span><span class="p">(</span>
-<span class="linenos"> 987</span>                <span class="n">ops</span><span class="o">=</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)),</span>
-<span class="linenos"> 988</span>                <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_row</span><span class="p">,</span> <span class="n">N_row</span><span class="p">),</span>
-<span class="linenos"> 989</span>                <span class="n">parallel</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span><span class="p">,</span>
-<span class="linenos"> 990</span>            <span class="p">)</span>
-<span class="linenos"> 991</span>            <span class="o">.</span><span class="n">op</span><span class="p">()</span>
-<span class="linenos"> 992</span>            <span class="o">.</span><span class="n">asop</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">SelfAdjointOp</span><span class="p">)</span>
-<span class="linenos"> 993</span>        <span class="p">)</span>
-<span class="linenos"> 994</span>        <span class="k">return</span> <span class="n">CG</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
-<span class="linenos"> 995</span>
-<span class="linenos"> 996</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">()</span>
-<span class="linenos"> 997</span>    <span class="k">def</span> <span class="nf">trace</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
-<span class="linenos"> 998</span>        <span class="n">tr</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">trace</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 999</span>        <span class="k">return</span> <span class="n">tr</span>
-<span class="linenos">1000</span>
-<span class="linenos">1001</span>    <span class="k">def</span> <span class="nf">asloss</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
-<span class="linenos">1002</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;asloss() is ambiguous for block-defined operators.&quot;</span>
-<span class="linenos">1003</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
+<span class="linenos"> 982</span>            <span class="n">_op</span><span class="o">.</span><span class="n">apply</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_apply</span><span class="p">,</span> <span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 983</span>            <span class="n">_op</span><span class="o">.</span><span class="n">adjoint</span> <span class="o">=</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">(</span><span class="n">op_adjoint</span><span class="p">,</span> <span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 984</span>
+<span class="linenos"> 985</span>            <span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">_op</span><span class="p">)</span>
+<span class="linenos"> 986</span>            <span class="n">i</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">r</span><span class="p">)</span>
+<span class="linenos"> 987</span>            <span class="n">j</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+<span class="linenos"> 988</span>        <span class="n">CG</span> <span class="o">=</span> <span class="p">(</span>
+<span class="linenos"> 989</span>            <span class="n">_COOBlock</span><span class="p">(</span>
+<span class="linenos"> 990</span>                <span class="n">ops</span><span class="o">=</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">)),</span>
+<span class="linenos"> 991</span>                <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_row</span><span class="p">,</span> <span class="n">N_row</span><span class="p">),</span>
+<span class="linenos"> 992</span>                <span class="n">parallel</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_parallel</span><span class="p">,</span>
+<span class="linenos"> 993</span>            <span class="p">)</span>
+<span class="linenos"> 994</span>            <span class="o">.</span><span class="n">op</span><span class="p">()</span>
+<span class="linenos"> 995</span>            <span class="o">.</span><span class="n">asop</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">SelfAdjointOp</span><span class="p">)</span>
+<span class="linenos"> 996</span>        <span class="p">)</span>
+<span class="linenos"> 997</span>        <span class="k">return</span> <span class="n">CG</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
+<span class="linenos"> 998</span>
+<span class="linenos"> 999</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">()</span>
+<span class="linenos">1000</span>    <span class="k">def</span> <span class="nf">trace</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">:</span>
+<span class="linenos">1001</span>        <span class="n">tr</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="o">.</span><span class="n">trace</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos">1002</span>        <span class="k">return</span> <span class="n">tr</span>
+<span class="linenos">1003</span>
+<span class="linenos">1004</span>    <span class="k">def</span> <span class="nf">asloss</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">data</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
+<span class="linenos">1005</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;asloss() is ambiguous for block-defined operators.&quot;</span>
+<span class="linenos">1006</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
 </pre></div>
 
                 </article>
diff --git a/_modules/pyxu/operator/func/indicator.html b/_modules/pyxu/operator/func/indicator.html
index e2bc2b76..fcc73a47 100644
--- a/_modules/pyxu/operator/func/indicator.html
+++ b/_modules/pyxu/operator/func/indicator.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/copybutton.css?v=76b2166b" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
     <link rel="stylesheet" type="text/css" href="../../../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -523,7 +523,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos"> 70</span>
 <span class="linenos"> 71</span>
 <div class="viewcode-block" id="L1Ball">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.L1Ball">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.L1Ball">[docs]</a>
 <span class="linenos"> 72</span><span class="k">def</span> <span class="nf">L1Ball</span><span class="p">(</span><span class="n">dim</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span> <span class="n">radius</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 73</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 74</span><span class="sd">    Indicator function of the :math:`\ell_{1}`-ball.</span>
@@ -560,7 +560,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">104</span>
 <span class="linenos">105</span>
 <div class="viewcode-block" id="L2Ball">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.L2Ball">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.L2Ball">[docs]</a>
 <span class="linenos">106</span><span class="k">def</span> <span class="nf">L2Ball</span><span class="p">(</span><span class="n">dim</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span> <span class="n">radius</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos">107</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">108</span><span class="sd">    Indicator function of the :math:`\ell_{2}`-ball.</span>
@@ -597,7 +597,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">138</span>
 <span class="linenos">139</span>
 <div class="viewcode-block" id="LInfinityBall">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.LInfinityBall">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.LInfinityBall">[docs]</a>
 <span class="linenos">140</span><span class="k">def</span> <span class="nf">LInfinityBall</span><span class="p">(</span><span class="n">dim</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span> <span class="n">radius</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos">141</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">142</span><span class="sd">    Indicator function of the :math:`\ell_{\infty}`-ball.</span>
@@ -634,7 +634,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">172</span>
 <span class="linenos">173</span>
 <div class="viewcode-block" id="PositiveOrthant">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.PositiveOrthant">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.PositiveOrthant">[docs]</a>
 <span class="linenos">174</span><span class="k">class</span> <span class="nc">PositiveOrthant</span><span class="p">(</span><span class="n">_IndicatorFunction</span><span class="p">):</span>
 <span class="linenos">175</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">176</span><span class="sd">    Indicator function of the positive orthant.</span>
@@ -672,7 +672,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">207</span>
 <span class="linenos">208</span>
 <div class="viewcode-block" id="HyperSlab">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.HyperSlab">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.HyperSlab">[docs]</a>
 <span class="linenos">209</span><span class="k">class</span> <span class="nc">HyperSlab</span><span class="p">(</span><span class="n">_IndicatorFunction</span><span class="p">):</span>
 <span class="linenos">210</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">211</span><span class="sd">    Indicator function of a hyperslab.</span>
@@ -698,7 +698,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">231</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">232</span>
 <div class="viewcode-block" id="HyperSlab.__init__">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.HyperSlab.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.HyperSlab.__init__">[docs]</a>
 <span class="linenos">233</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;lb&quot;</span><span class="p">,</span> <span class="s2">&quot;ub&quot;</span><span class="p">))</span>
 <span class="linenos">234</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">a</span><span class="p">:</span> <span class="n">pxa</span><span class="o">.</span><span class="n">LinFunc</span><span class="p">,</span> <span class="n">lb</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="n">ub</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">):</span>
 <span class="linenos">235</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
@@ -749,7 +749,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">278</span>
 <span class="linenos">279</span>
 <div class="viewcode-block" id="RangeSet">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.RangeSet">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.RangeSet">[docs]</a>
 <span class="linenos">280</span><span class="k">class</span> <span class="nc">RangeSet</span><span class="p">(</span><span class="n">_IndicatorFunction</span><span class="p">):</span>
 <span class="linenos">281</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">282</span><span class="sd">    Indicator function of a range set.</span>
@@ -771,7 +771,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">298</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">299</span>
 <div class="viewcode-block" id="RangeSet.__init__">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.RangeSet.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.RangeSet.__init__">[docs]</a>
 <span class="linenos">300</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">A</span><span class="p">:</span> <span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span><span class="p">):</span>
 <span class="linenos">301</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">302</span><span class="sd">        Parameters</span>
@@ -811,7 +811,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">334</span>
 <span class="linenos">335</span>
 <div class="viewcode-block" id="AffineSet">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.AffineSet">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.AffineSet">[docs]</a>
 <span class="linenos">336</span><span class="k">class</span> <span class="nc">AffineSet</span><span class="p">(</span><span class="n">_IndicatorFunction</span><span class="p">):</span>
 <span class="linenos">337</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">338</span><span class="sd">    Indicator function of an affine set.</span>
@@ -843,7 +843,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">364</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">365</span>
 <div class="viewcode-block" id="AffineSet.__init__">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.AffineSet.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.AffineSet.__init__">[docs]</a>
 <span class="linenos">366</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;b&quot;</span><span class="p">)</span>
 <span class="linenos">367</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">A</span><span class="p">:</span> <span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span><span class="p">,</span> <span class="n">b</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">):</span>
 <span class="linenos">368</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
@@ -883,7 +883,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">400</span>
 <span class="linenos">401</span>
 <div class="viewcode-block" id="ConvexSetIntersection">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.ConvexSetIntersection">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.ConvexSetIntersection">[docs]</a>
 <span class="linenos">402</span><span class="k">class</span> <span class="nc">ConvexSetIntersection</span><span class="p">(</span><span class="n">_IndicatorFunction</span><span class="p">):</span>
 <span class="linenos">403</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">404</span><span class="sd">    Indicator function of an intersection of convex domains :math:`\mathcal{C}_{1} \cap \cdots \cap \mathcal{C}_{K}`.</span>
@@ -924,7 +924,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">439</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">440</span>
 <div class="viewcode-block" id="ConvexSetIntersection.__init__">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.ConvexSetIntersection.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.ConvexSetIntersection.__init__">[docs]</a>
 <span class="linenos">441</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxa</span><span class="o">.</span><span class="n">ProxFunc</span><span class="p">]):</span>
 <span class="linenos">442</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">443</span><span class="sd">        Parameters</span>
@@ -959,7 +959,7 @@ <h1>Source code for pyxu.operator.func.indicator</h1><div class="highlight"><pre
 <span class="linenos">471</span>        <span class="k">return</span> <span class="n">out</span>
 <span class="linenos">472</span>
 <div class="viewcode-block" id="ConvexSetIntersection.prox">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.ConvexSetIntersection.prox">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.ConvexSetIntersection.prox">[docs]</a>
 <span class="linenos">473</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">))</span>
 <span class="linenos">474</span>    <span class="k">def</span> <span class="nf">prox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">tau</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos">475</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_f</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
diff --git a/_modules/pyxu/operator/func/loss.html b/_modules/pyxu/operator/func/loss.html
index 42f33837..a6a0c91f 100644
--- a/_modules/pyxu/operator/func/loss.html
+++ b/_modules/pyxu/operator/func/loss.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css" />
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@@ -37,13 +37,13 @@
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+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
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-    <script src="../../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
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     <script src="../../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -463,7 +463,7 @@ <h1>Source code for pyxu.operator.func.loss</h1><div class="highlight"><pre>
 <span class="linenos"> 10</span>
 <span class="linenos"> 11</span>
 <div class="viewcode-block" id="shift_loss">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.shift_loss">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.shift_loss">[docs]</a>
 <span class="linenos"> 12</span><span class="k">def</span> <span class="nf">shift_loss</span><span class="p">(</span>
 <span class="linenos"> 13</span>    <span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">,</span>
 <span class="linenos"> 14</span>    <span class="n">data</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
@@ -493,7 +493,7 @@ <h1>Source code for pyxu.operator.func.loss</h1><div class="highlight"><pre>
 <span class="linenos"> 37</span>
 <span class="linenos"> 38</span>
 <div class="viewcode-block" id="KLDivergence">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.KLDivergence">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.KLDivergence">[docs]</a>
 <span class="linenos"> 39</span><span class="k">class</span> <span class="nc">KLDivergence</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">ProxFunc</span><span class="p">):</span>
 <span class="linenos"> 40</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 41</span><span class="sd">    Generalised Kullback-Leibler divergence :math:`D_{KL}(\mathbf{y}||\mathbf{x}):=\sum_{i=1}^N y_i\log(y_i/x_i) -y_i</span>
@@ -501,7 +501,7 @@ <h1>Source code for pyxu.operator.func.loss</h1><div class="highlight"><pre>
 <span class="linenos"> 43</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos"> 44</span>
 <div class="viewcode-block" id="KLDivergence.__init__">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.KLDivergence.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.KLDivergence.__init__">[docs]</a>
 <span class="linenos"> 45</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
 <span class="linenos"> 46</span>        <span class="bp">self</span><span class="p">,</span>
 <span class="linenos"> 47</span>        <span class="n">dim</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
diff --git a/_modules/pyxu/operator/func/norm.html b/_modules/pyxu/operator/func/norm.html
index 3ce1d57e..491a85a0 100644
--- a/_modules/pyxu/operator/func/norm.html
+++ b/_modules/pyxu/operator/func/norm.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css" />
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     <link rel="stylesheet" type="text/css" href="../../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
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-    <script src="../../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -484,7 +484,7 @@ <h1>Source code for pyxu.operator.func.norm</h1><div class="highlight"><pre>
 <span class="linenos"> 31</span>
 <span class="linenos"> 32</span>
 <div class="viewcode-block" id="L1Norm">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.L1Norm">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.L1Norm">[docs]</a>
 <span class="linenos"> 33</span><span class="k">class</span> <span class="nc">L1Norm</span><span class="p">(</span><span class="n">_ShiftLossMixin</span><span class="p">,</span> <span class="n">pxa</span><span class="o">.</span><span class="n">ProxFunc</span><span class="p">):</span>
 <span class="linenos"> 34</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 35</span><span class="sd">    :math:`\ell_{1}`-norm, :math:`\Vert\mathbf{x}\Vert_{1} := \sum_{i=1}^{N} |x_{i}|`.</span>
@@ -509,7 +509,7 @@ <h1>Source code for pyxu.operator.func.norm</h1><div class="highlight"><pre>
 <span class="linenos"> 53</span>
 <span class="linenos"> 54</span>
 <div class="viewcode-block" id="L2Norm">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.L2Norm">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.L2Norm">[docs]</a>
 <span class="linenos"> 55</span><span class="k">class</span> <span class="nc">L2Norm</span><span class="p">(</span><span class="n">_ShiftLossMixin</span><span class="p">,</span> <span class="n">pxa</span><span class="o">.</span><span class="n">ProxFunc</span><span class="p">):</span>
 <span class="linenos"> 56</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 57</span><span class="sd">    :math:`\ell_{2}`-norm, :math:`\Vert\mathbf{x}\Vert_{2} := \sqrt{\sum_{i=1}^{N} |x_{i}|^{2}}`.</span>
@@ -537,7 +537,7 @@ <h1>Source code for pyxu.operator.func.norm</h1><div class="highlight"><pre>
 <span class="linenos"> 78</span>
 <span class="linenos"> 79</span>
 <div class="viewcode-block" id="SquaredL2Norm">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.SquaredL2Norm">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.SquaredL2Norm">[docs]</a>
 <span class="linenos"> 80</span><span class="k">class</span> <span class="nc">SquaredL2Norm</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">QuadraticFunc</span><span class="p">):</span>
 <span class="linenos"> 81</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 82</span><span class="sd">    :math:`\ell^{2}_{2}`-norm, :math:`\Vert\mathbf{x}\Vert^{2}_{2} := \sum_{i=1}^{N} |x_{i}|^{2}`.</span>
@@ -575,14 +575,14 @@ <h1>Source code for pyxu.operator.func.norm</h1><div class="highlight"><pre>
 <span class="linenos">113</span>
 <span class="linenos">114</span>
 <div class="viewcode-block" id="SquaredL1Norm">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.SquaredL1Norm">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.SquaredL1Norm">[docs]</a>
 <span class="linenos">115</span><span class="k">class</span> <span class="nc">SquaredL1Norm</span><span class="p">(</span><span class="n">_ShiftLossMixin</span><span class="p">,</span> <span class="n">pxa</span><span class="o">.</span><span class="n">ProxFunc</span><span class="p">):</span>
 <span class="linenos">116</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">117</span><span class="sd">    :math:`\ell^{2}_{1}`-norm, :math:`\Vert\mathbf{x}\Vert^{2}_{1} := (\sum_{i=1}^{N} |x_{i}|)^{2}`.</span>
 <span class="linenos">118</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">119</span>
 <div class="viewcode-block" id="SquaredL1Norm.__init__">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.SquaredL1Norm.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.SquaredL1Norm.__init__">[docs]</a>
 <span class="linenos">120</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">dim</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span> <span class="n">prox_algo</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;sort&quot;</span><span class="p">):</span>
 <span class="linenos">121</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">122</span><span class="sd">        Parameters</span>
@@ -678,7 +678,7 @@ <h1>Source code for pyxu.operator.func.norm</h1><div class="highlight"><pre>
 <span class="linenos">211</span>        <span class="k">return</span> <span class="n">out</span>
 <span class="linenos">212</span>
 <div class="viewcode-block" id="SquaredL1Norm.prox">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.SquaredL1Norm.prox">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.SquaredL1Norm.prox">[docs]</a>
 <span class="linenos">213</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;arr&quot;</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">))</span>
 <span class="linenos">214</span>    <span class="k">def</span> <span class="nf">prox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">tau</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos">215</span>        <span class="n">N</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span>
@@ -709,7 +709,7 @@ <h1>Source code for pyxu.operator.func.norm</h1><div class="highlight"><pre>
 <span class="linenos">238</span>
 <span class="linenos">239</span>
 <div class="viewcode-block" id="LInfinityNorm">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.LInfinityNorm">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.LInfinityNorm">[docs]</a>
 <span class="linenos">240</span><span class="k">class</span> <span class="nc">LInfinityNorm</span><span class="p">(</span><span class="n">_ShiftLossMixin</span><span class="p">,</span> <span class="n">pxa</span><span class="o">.</span><span class="n">ProxFunc</span><span class="p">):</span>
 <span class="linenos">241</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">242</span><span class="sd">    :math:`\ell_{\infty}`-norm, :math:`\Vert\mathbf{x}\Vert_{\infty} := \max_{i=1,\ldots,N} |x_{i}|`.</span>
@@ -767,7 +767,7 @@ <h1>Source code for pyxu.operator.func.norm</h1><div class="highlight"><pre>
 <span class="linenos">293</span>
 <span class="linenos">294</span>
 <div class="viewcode-block" id="L21Norm">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.L21Norm">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.L21Norm">[docs]</a>
 <span class="linenos">295</span><span class="k">class</span> <span class="nc">L21Norm</span><span class="p">(</span><span class="n">_ShiftLossMixin</span><span class="p">,</span> <span class="n">pxa</span><span class="o">.</span><span class="n">ProxFunc</span><span class="p">):</span>
 <span class="linenos">296</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">297</span><span class="sd">    Mixed :math:`\ell_{2}-\ell_{1}` norm, :math:`\Vert\mathbf{x}\Vert_{2, 1} := \sum_{i=1}^{N} \sqrt{\sum_{j=1}^{M}</span>
@@ -780,7 +780,7 @@ <h1>Source code for pyxu.operator.func.norm</h1><div class="highlight"><pre>
 <span class="linenos">304</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">305</span>
 <div class="viewcode-block" id="L21Norm.__init__">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.L21Norm.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.L21Norm.__init__">[docs]</a>
 <span class="linenos">306</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
 <span class="linenos">307</span>        <span class="bp">self</span><span class="p">,</span>
 <span class="linenos">308</span>        <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
@@ -842,7 +842,7 @@ <h1>Source code for pyxu.operator.func.norm</h1><div class="highlight"><pre>
 <span class="linenos">362</span>
 <span class="linenos">363</span>
 <div class="viewcode-block" id="PositiveL1Norm">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.PositiveL1Norm">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/func.html#pyxu.operator.PositiveL1Norm">[docs]</a>
 <span class="linenos">364</span><span class="k">class</span> <span class="nc">PositiveL1Norm</span><span class="p">(</span><span class="n">_ShiftLossMixin</span><span class="p">,</span> <span class="n">pxa</span><span class="o">.</span><span class="n">ProxFunc</span><span class="p">):</span>
 <span class="linenos">365</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">366</span><span class="sd">    :math:`\ell_{1}`-norm, with a positivity constraint.</span>
diff --git a/_modules/pyxu/operator/interop/jax.html b/_modules/pyxu/operator/interop/jax.html
index 98e28b3f..647aed3f 100644
--- a/_modules/pyxu/operator/interop/jax.html
+++ b/_modules/pyxu/operator/interop/jax.html
@@ -27,8 +27,8 @@
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
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+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
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-    <script src="../../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
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@@ -236,7 +236,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
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         <li class="nav-item">
diff --git a/_modules/pyxu/operator/interop/sciop.html b/_modules/pyxu/operator/interop/sciop.html
index f09713cf..a5b43f2d 100644
--- a/_modules/pyxu/operator/interop/sciop.html
+++ b/_modules/pyxu/operator/interop/sciop.html
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
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+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
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-    <script src="../../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
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@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
diff --git a/_modules/pyxu/operator/interop/source.html b/_modules/pyxu/operator/interop/source.html
index 4ca83b72..05675977 100644
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@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
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diff --git a/_modules/pyxu/operator/interop/torch.html b/_modules/pyxu/operator/interop/torch.html
index be71ddd2..eb79d55a 100644
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
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@@ -236,7 +236,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
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@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
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         <li class="nav-item">
diff --git a/_modules/pyxu/operator/linop/base.html b/_modules/pyxu/operator/linop/base.html
index 47c0c2ff..eadc85c4 100644
--- a/_modules/pyxu/operator/linop/base.html
+++ b/_modules/pyxu/operator/linop/base.html
@@ -27,8 +27,8 @@
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
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+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
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diff --git a/_modules/pyxu/operator/linop/diff.html b/_modules/pyxu/operator/linop/diff.html
index cdcbe812..4551b566 100644
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
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@@ -236,7 +236,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
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@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
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@@ -896,7 +896,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos"> 443</span>
 <span class="linenos"> 444</span>
 <div class="viewcode-block" id="PartialDerivative">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.PartialDerivative">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.PartialDerivative">[docs]</a>
 <span class="linenos"> 445</span><span class="k">class</span> <span class="nc">PartialDerivative</span><span class="p">:</span>
 <span class="linenos"> 446</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 447</span><span class="sd">    Partial derivative operator based on `Numba stencils</span>
@@ -953,7 +953,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos"> 498</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos"> 499</span>
 <div class="viewcode-block" id="PartialDerivative.finite_difference">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.PartialDerivative.finite_difference">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.PartialDerivative.finite_difference">[docs]</a>
 <span class="linenos"> 500</span>    <span class="nd">@staticmethod</span>
 <span class="linenos"> 501</span>    <span class="k">def</span> <span class="nf">finite_difference</span><span class="p">(</span>
 <span class="linenos"> 502</span>        <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
@@ -1151,9 +1151,9 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos"> 694</span><span class="sd">           axs[2].set_title(r&quot;$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$&quot;)</span>
 <span class="linenos"> 695</span><span class="sd">           plt.colorbar(im, ax=axs[2])</span>
 <span class="linenos"> 696</span>
-<span class="linenos"> 697</span><span class="sd">           # Test approximation error</span>
+<span class="linenos"> 697</span><span class="sd">           # Check approximation error</span>
 <span class="linenos"> 698</span><span class="sd">           plt.figure()</span>
-<span class="linenos"> 699</span><span class="sd">           plt.imshow(abs(out1 - out2) / abs(out2)), plt.colorbar()</span>
+<span class="linenos"> 699</span><span class="sd">           plt.imshow(abs(out1 - out2)), plt.colorbar()</span>
 <span class="linenos"> 700</span>
 <span class="linenos"> 701</span><span class="sd">        &quot;&quot;&quot;</span>
 <span class="linenos"> 702</span>        <span class="k">assert</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">order</span><span class="p">,</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">),</span> <span class="s2">&quot;`order` should be a tuple / list&quot;</span>
@@ -1197,7 +1197,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 
 <span class="linenos"> 740</span>
 <div class="viewcode-block" id="PartialDerivative.gaussian_derivative">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.PartialDerivative.gaussian_derivative">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.PartialDerivative.gaussian_derivative">[docs]</a>
 <span class="linenos"> 741</span>    <span class="nd">@staticmethod</span>
 <span class="linenos"> 742</span>    <span class="k">def</span> <span class="nf">gaussian_derivative</span><span class="p">(</span>
 <span class="linenos"> 743</span>        <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
@@ -1573,7 +1573,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos">1111</span>
 <span class="linenos">1112</span>
 <div class="viewcode-block" id="Gradient">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.Gradient">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Gradient">[docs]</a>
 <span class="linenos">1113</span><span class="k">def</span> <span class="nf">Gradient</span><span class="p">(</span>
 <span class="linenos">1114</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">1115</span>    <span class="n">directions</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Optional</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayAxis</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
@@ -1731,7 +1731,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos">1266</span>
 <span class="linenos">1267</span>
 <div class="viewcode-block" id="Jacobian">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.Jacobian">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Jacobian">[docs]</a>
 <span class="linenos">1268</span><span class="k">def</span> <span class="nf">Jacobian</span><span class="p">(</span>
 <span class="linenos">1269</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">1270</span>    <span class="n">n_channels</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
@@ -1884,7 +1884,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos">1416</span>
 <span class="linenos">1417</span>
 <div class="viewcode-block" id="Divergence">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.Divergence">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Divergence">[docs]</a>
 <span class="linenos">1418</span><span class="k">def</span> <span class="nf">Divergence</span><span class="p">(</span>
 <span class="linenos">1419</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">1420</span>    <span class="n">directions</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Optional</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayAxis</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
@@ -2060,7 +2060,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos">1589</span>
 <span class="linenos">1590</span>
 <div class="viewcode-block" id="Hessian">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.Hessian">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Hessian">[docs]</a>
 <span class="linenos">1591</span><span class="k">def</span> <span class="nf">Hessian</span><span class="p">(</span>
 <span class="linenos">1592</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">1593</span>    <span class="n">directions</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Union</span><span class="p">[</span>
@@ -2271,7 +2271,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos">1797</span>
 <span class="linenos">1798</span>
 <div class="viewcode-block" id="Laplacian">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.Laplacian">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Laplacian">[docs]</a>
 <span class="linenos">1799</span><span class="k">def</span> <span class="nf">Laplacian</span><span class="p">(</span>
 <span class="linenos">1800</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">1801</span>    <span class="n">directions</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Optional</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayAxis</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
@@ -2413,7 +2413,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos">1936</span>
 <span class="linenos">1937</span>
 <div class="viewcode-block" id="DirectionalDerivative">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.DirectionalDerivative">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.DirectionalDerivative">[docs]</a>
 <span class="linenos">1938</span><span class="k">def</span> <span class="nf">DirectionalDerivative</span><span class="p">(</span>
 <span class="linenos">1939</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">1940</span>    <span class="n">order</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
@@ -2664,7 +2664,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos">2184</span>
 <span class="linenos">2185</span>
 <div class="viewcode-block" id="DirectionalGradient">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.DirectionalGradient">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.DirectionalGradient">[docs]</a>
 <span class="linenos">2186</span><span class="k">def</span> <span class="nf">DirectionalGradient</span><span class="p">(</span>
 <span class="linenos">2187</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">2188</span>    <span class="n">directions</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">],</span>
@@ -2839,7 +2839,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos">2356</span>
 <span class="linenos">2357</span>
 <div class="viewcode-block" id="DirectionalLaplacian">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.DirectionalLaplacian">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.DirectionalLaplacian">[docs]</a>
 <span class="linenos">2358</span><span class="k">def</span> <span class="nf">DirectionalLaplacian</span><span class="p">(</span>
 <span class="linenos">2359</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">2360</span>    <span class="n">directions</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">],</span>
@@ -3030,7 +3030,7 @@ <h1>Source code for pyxu.operator.linop.diff</h1><div class="highlight"><pre>
 <span class="linenos">2544</span>
 <span class="linenos">2545</span>
 <div class="viewcode-block" id="DirectionalHessian">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.DirectionalHessian">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.DirectionalHessian">[docs]</a>
 <span class="linenos">2546</span><span class="k">def</span> <span class="nf">DirectionalHessian</span><span class="p">(</span>
 <span class="linenos">2547</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">2548</span>    <span class="n">directions</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">],</span>
diff --git a/_modules/pyxu/operator/linop/fft/fft.html b/_modules/pyxu/operator/linop/fft/fft.html
index de72a3bc..0f320b66 100644
--- a/_modules/pyxu/operator/linop/fft/fft.html
+++ b/_modules/pyxu/operator/linop/fft/fft.html
@@ -27,8 +27,8 @@
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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@@ -468,7 +468,7 @@ <h1>Source code for pyxu.operator.linop.fft.fft</h1><div class="highlight"><pre>
 <span class="linenos"> 15</span>
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 <span class="linenos"> 18</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 19</span><span class="sd">    Multi-dimensional Discrete Fourier Transform (DFT) :math:`A: \mathbb{C}^{N_{1} \times \cdots \times N_{D}} \to</span>
@@ -611,7 +611,7 @@ <h1>Source code for pyxu.operator.linop.fft.fft</h1><div class="highlight"><pre>
 <span class="linenos">156</span><span class="sd">    &quot;&quot;&quot;</span>
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 <span class="linenos">158</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
 <span class="linenos">159</span>        <span class="bp">self</span><span class="p">,</span>
 <span class="linenos">160</span>        <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
@@ -760,7 +760,7 @@ <h1>Source code for pyxu.operator.linop.fft.fft</h1><div class="highlight"><pre>
 <span class="linenos">302</span>        <span class="k">return</span> <span class="n">out</span>
 <span class="linenos">303</span>
 <div class="viewcode-block" id="FFT.apply">
-<a class="viewcode-back" href="../../../../../api/operator.html#pyxu.operator.FFT.apply">[docs]</a>
+<a class="viewcode-back" href="../../../../../api/operator/linop.html#pyxu.operator.FFT.apply">[docs]</a>
 <span class="linenos">304</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">&quot;arr&quot;</span><span class="p">)</span>
 <span class="linenos">305</span>    <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos">306</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
@@ -803,7 +803,7 @@ <h1>Source code for pyxu.operator.linop.fft.fft</h1><div class="highlight"><pre>
 
 <span class="linenos">343</span>
 <div class="viewcode-block" id="FFT.adjoint">
-<a class="viewcode-back" href="../../../../../api/operator.html#pyxu.operator.FFT.adjoint">[docs]</a>
+<a class="viewcode-back" href="../../../../../api/operator/linop.html#pyxu.operator.FFT.adjoint">[docs]</a>
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 <span class="linenos">345</span>    <span class="k">def</span> <span class="nf">adjoint</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos">346</span><span class="w">        </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
diff --git a/_modules/pyxu/operator/linop/fft/nufft.html b/_modules/pyxu/operator/linop/fft/nufft.html
index c6b018fa..9e7fc16b 100644
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diff --git a/_modules/pyxu/operator/linop/filter.html b/_modules/pyxu/operator/linop/filter.html
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@@ -236,7 +236,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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@@ -378,7 +378,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
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@@ -525,7 +525,7 @@ <h1>Source code for pyxu.operator.linop.filter</h1><div class="highlight"><pre>
 <span class="linenos">  72</span>
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 <div class="viewcode-block" id="MovingAverage">
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+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.MovingAverage">[docs]</a>
 <span class="linenos">  74</span><span class="k">def</span> <span class="nf">MovingAverage</span><span class="p">(</span>
 <span class="linenos">  75</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos">  76</span>    <span class="n">size</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Union</span><span class="p">[</span><span class="n">typ</span><span class="o">.</span><span class="n">Tuple</span><span class="p">,</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">],</span>
@@ -640,7 +640,7 @@ <h1>Source code for pyxu.operator.linop.filter</h1><div class="highlight"><pre>
 <span class="linenos"> 184</span>
 <span class="linenos"> 185</span>
 <div class="viewcode-block" id="Gaussian">
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+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Gaussian">[docs]</a>
 <span class="linenos"> 186</span><span class="k">def</span> <span class="nf">Gaussian</span><span class="p">(</span>
 <span class="linenos"> 187</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
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@@ -770,7 +770,7 @@ <h1>Source code for pyxu.operator.linop.filter</h1><div class="highlight"><pre>
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 <div class="viewcode-block" id="DifferenceOfGaussians">
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 <span class="linenos"> 313</span><span class="k">def</span> <span class="nf">DifferenceOfGaussians</span><span class="p">(</span>
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 <span class="linenos"> 315</span>    <span class="n">low_sigma</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span>
@@ -902,7 +902,7 @@ <h1>Source code for pyxu.operator.linop.filter</h1><div class="highlight"><pre>
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+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Laplace">[docs]</a>
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 <span class="linenos"> 444</span>    <span class="n">mode</span><span class="p">:</span> <span class="n">ModeSpec</span> <span class="o">=</span> <span class="s2">&quot;constant&quot;</span><span class="p">,</span>
@@ -998,7 +998,7 @@ <h1>Source code for pyxu.operator.linop.filter</h1><div class="highlight"><pre>
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 <div class="viewcode-block" id="Sobel">
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+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Sobel">[docs]</a>
 <span class="linenos"> 535</span><span class="k">def</span> <span class="nf">Sobel</span><span class="p">(</span>
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@@ -1099,7 +1099,7 @@ <h1>Source code for pyxu.operator.linop.filter</h1><div class="highlight"><pre>
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+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Prewitt">[docs]</a>
 <span class="linenos"> 633</span><span class="k">def</span> <span class="nf">Prewitt</span><span class="p">(</span>
 <span class="linenos"> 634</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
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@@ -1200,7 +1200,7 @@ <h1>Source code for pyxu.operator.linop.filter</h1><div class="highlight"><pre>
 <span class="linenos"> 729</span>
 <span class="linenos"> 730</span>
 <div class="viewcode-block" id="Scharr">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.Scharr">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Scharr">[docs]</a>
 <span class="linenos"> 731</span><span class="k">def</span> <span class="nf">Scharr</span><span class="p">(</span>
 <span class="linenos"> 732</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos"> 733</span>    <span class="n">axis</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Optional</span><span class="p">[</span><span class="n">typ</span><span class="o">.</span><span class="n">Tuple</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
@@ -1342,7 +1342,7 @@ <h1>Source code for pyxu.operator.linop.filter</h1><div class="highlight"><pre>
 <span class="linenos"> 868</span>
 <span class="linenos"> 869</span>
 <div class="viewcode-block" id="StructureTensor">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.StructureTensor">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.StructureTensor">[docs]</a>
 <span class="linenos"> 870</span><span class="k">class</span> <span class="nc">StructureTensor</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">DiffMap</span><span class="p">):</span>
 <span class="linenos"> 871</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 872</span><span class="sd">    Structure tensor operator.</span>
@@ -1492,19 +1492,19 @@ <h1>Source code for pyxu.operator.linop.filter</h1><div class="highlight"><pre>
 <span class="linenos">1016</span>            <span class="bp">self</span><span class="o">.</span><span class="n">smooth</span> <span class="o">=</span> <span class="n">pxlb</span><span class="o">.</span><span class="n">IdentityOp</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span><span class="o">.</span><span class="n">item</span><span class="p">())</span>
 <span class="linenos">1017</span>
 <div class="viewcode-block" id="StructureTensor.unravel">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.StructureTensor.unravel">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.StructureTensor.unravel">[docs]</a>
 <span class="linenos">1018</span>    <span class="k">def</span> <span class="nf">unravel</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span>
 <span class="linenos">1019</span>        <span class="k">return</span> <span class="n">arr</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arr</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">arg_shape</span><span class="p">)</span></div>
 
 <span class="linenos">1020</span>
 <div class="viewcode-block" id="StructureTensor.ravel">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.StructureTensor.ravel">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.StructureTensor.ravel">[docs]</a>
 <span class="linenos">1021</span>    <span class="k">def</span> <span class="nf">ravel</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span>
 <span class="linenos">1022</span>        <span class="k">return</span> <span class="n">arr</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arr</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span> <span class="o">-</span><span class="mi">1</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">arg_shape</span><span class="p">)],</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span></div>
 
 <span class="linenos">1023</span>
 <div class="viewcode-block" id="StructureTensor.apply">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.StructureTensor.apply">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.StructureTensor.apply">[docs]</a>
 <span class="linenos">1024</span>    <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span>
 <span class="linenos">1025</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
 <span class="linenos">1026</span>        <span class="n">sh</span> <span class="o">=</span> <span class="n">arr</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
diff --git a/_modules/pyxu/operator/linop/kron.html b/_modules/pyxu/operator/linop/kron.html
index 39af0e49..9c3ec1cf 100644
--- a/_modules/pyxu/operator/linop/kron.html
+++ b/_modules/pyxu/operator/linop/kron.html
@@ -27,8 +27,8 @@
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
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@@ -37,13 +37,13 @@
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
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-    <script src="../../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
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@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -467,7 +467,7 @@ <h1>Source code for pyxu.operator.linop.kron</h1><div class="highlight"><pre>
 <span class="linenos"> 14</span>
 <span class="linenos"> 15</span>
 <div class="viewcode-block" id="kron">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.kron">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.kron">[docs]</a>
 <span class="linenos"> 16</span><span class="k">def</span> <span class="nf">kron</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">,</span> <span class="n">B</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 17</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 18</span><span class="sd">    `Kronecker product &lt;https://en.wikipedia.org/wiki/Kronecker_product#Definition&gt;`_ :math:`A \otimes B` between two</span>
@@ -694,7 +694,7 @@ <h1>Source code for pyxu.operator.linop.kron</h1><div class="highlight"><pre>
 <span class="linenos">238</span>
 <span class="linenos">239</span>
 <div class="viewcode-block" id="khatri_rao">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.khatri_rao">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.khatri_rao">[docs]</a>
 <span class="linenos">240</span><span class="k">def</span> <span class="nf">khatri_rao</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">,</span> <span class="n">B</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos">241</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">242</span><span class="sd">    `Column-wise Khatri-Rao product</span>
diff --git a/_modules/pyxu/operator/linop/pad.html b/_modules/pyxu/operator/linop/pad.html
index bf36f12c..21798428 100644
--- a/_modules/pyxu/operator/linop/pad.html
+++ b/_modules/pyxu/operator/linop/pad.html
@@ -27,8 +27,8 @@
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/css/custom.css?v=14df3d68" />
   
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-    <script src="../../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
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@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -467,7 +467,7 @@ <h1>Source code for pyxu.operator.linop.pad</h1><div class="highlight"><pre>
 <span class="linenos"> 14</span>
 <span class="linenos"> 15</span>
 <div class="viewcode-block" id="Pad">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.Pad">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Pad">[docs]</a>
 <span class="linenos"> 16</span><span class="k">class</span> <span class="nc">Pad</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span><span class="p">):</span>
 <span class="linenos"> 17</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 18</span><span class="sd">    Multi-dimensional padding operator.</span>
@@ -592,7 +592,7 @@ <h1>Source code for pyxu.operator.linop.pad</h1><div class="highlight"><pre>
 <span class="linenos">137</span>    <span class="n">ModeSpec</span> <span class="o">=</span> <span class="n">typ</span><span class="o">.</span><span class="n">Union</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="nb">str</span><span class="p">]]</span>
 <span class="linenos">138</span>
 <div class="viewcode-block" id="Pad.__init__">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.Pad.__init__">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Pad.__init__">[docs]</a>
 <span class="linenos">139</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
 <span class="linenos">140</span>        <span class="bp">self</span><span class="p">,</span>
 <span class="linenos">141</span>        <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
diff --git a/_modules/pyxu/operator/linop/reduce.html b/_modules/pyxu/operator/linop/reduce.html
index e2e1ae01..21278343 100644
--- a/_modules/pyxu/operator/linop/reduce.html
+++ b/_modules/pyxu/operator/linop/reduce.html
@@ -27,8 +27,8 @@
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css" />
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+    <script src="../../../../_static/documentation_options.js?v=a4a8746c"></script>
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@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -467,7 +467,7 @@ <h1>Source code for pyxu.operator.linop.reduce</h1><div class="highlight"><pre>
 <span class="linenos"> 14</span>
 <span class="linenos"> 15</span>
 <div class="viewcode-block" id="Sum">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.Sum">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Sum">[docs]</a>
 <span class="linenos"> 16</span><span class="k">def</span> <span class="nf">Sum</span><span class="p">(</span>
 <span class="linenos"> 17</span>    <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
 <span class="linenos"> 18</span>    <span class="n">axis</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArrayAxis</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
diff --git a/_modules/pyxu/operator/linop/select.html b/_modules/pyxu/operator/linop/select.html
index a4a4bb04..89920bd1 100644
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-    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/plot_directive.css" />
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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@@ -469,7 +469,7 @@ <h1>Source code for pyxu.operator.linop.select</h1><div class="highlight"><pre>
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@@ -575,7 +575,7 @@ <h1>Source code for pyxu.operator.linop.select</h1><div class="highlight"><pre>
 
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 <span class="linenos">121</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
@@ -602,7 +602,7 @@ <h1>Source code for pyxu.operator.linop.select</h1><div class="highlight"><pre>
 
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@@ -668,7 +668,7 @@ <h1>Source code for pyxu.operator.linop.select</h1><div class="highlight"><pre>
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+<a class="viewcode-back" href="../../../../api/operator/linop.html#pyxu.operator.Trim">[docs]</a>
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
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@@ -513,7 +513,7 @@ <h1>Source code for pyxu.operator.linop.stencil._stencil</h1><div class="highlig
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-<a class="viewcode-back" href="../../../../../api/operator.html#pyxu.operator._Stencil">[docs]</a>
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+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
       
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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@@ -341,7 +341,7 @@
     
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+          <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
         
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@@ -378,7 +378,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -465,7 +465,7 @@ <h1>Source code for pyxu.operator.map.base</h1><div class="highlight"><pre>
 <span class="linenos">12</span>
 <span class="linenos">13</span>
 <div class="viewcode-block" id="ConstantValued">
-<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.map.base.ConstantValued">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.ConstantValued">[docs]</a>
 <span class="linenos">14</span><span class="k">def</span> <span class="nf">ConstantValued</span><span class="p">(</span>
 <span class="linenos">15</span>    <span class="n">shape</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span>
 <span class="linenos">16</span>    <span class="n">cst</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span>
@@ -578,15 +578,11 @@ <h1>Source code for pyxu.operator.map.base</h1><div class="highlight"><pre>
       
         <div class="footer-item">
   <p class="sphinx-version">
-    Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5.
+     Created with <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5, with some help from <a href="https://chat.openai.com/"> ChatGPT</a> (GPT 4).
     <br/>
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-  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
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diff --git a/_modules/pyxu/operator/map/ufunc.html b/_modules/pyxu/operator/map/ufunc.html
index 8755f342..06a1f4a9 100644
--- a/_modules/pyxu/operator/map/ufunc.html
+++ b/_modules/pyxu/operator/map/ufunc.html
@@ -27,8 +27,8 @@
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@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
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@@ -378,7 +378,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
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@@ -534,7 +534,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos">  81</span>
 <span class="linenos">  82</span>
 <div class="viewcode-block" id="sin">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.sin">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.sin">[docs]</a>
 <span class="linenos">  83</span><span class="k">def</span> <span class="nf">sin</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos">  84</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">  85</span><span class="sd">    Trigonometric sine, element-wise.</span>
@@ -574,7 +574,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 118</span>
 <span class="linenos"> 119</span>
 <div class="viewcode-block" id="cos">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.cos">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.cos">[docs]</a>
 <span class="linenos"> 120</span><span class="k">def</span> <span class="nf">cos</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 121</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 122</span><span class="sd">    Trigonometric cosine, element-wise.</span>
@@ -616,7 +616,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 157</span>
 <span class="linenos"> 158</span>
 <div class="viewcode-block" id="tan">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.tan">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.tan">[docs]</a>
 <span class="linenos"> 159</span><span class="k">def</span> <span class="nf">tan</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 160</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 161</span><span class="sd">    Trigonometric tangent, element-wise.</span>
@@ -659,7 +659,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 197</span>
 <span class="linenos"> 198</span>
 <div class="viewcode-block" id="arcsin">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.arcsin">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.arcsin">[docs]</a>
 <span class="linenos"> 199</span><span class="k">def</span> <span class="nf">arcsin</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 200</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 201</span><span class="sd">    Inverse sine, element-wise.</span>
@@ -700,7 +700,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 235</span>
 <span class="linenos"> 236</span>
 <div class="viewcode-block" id="arccos">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.arccos">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.arccos">[docs]</a>
 <span class="linenos"> 237</span><span class="k">def</span> <span class="nf">arccos</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 238</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 239</span><span class="sd">    Inverse cosine, element-wise.</span>
@@ -743,7 +743,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 275</span>
 <span class="linenos"> 276</span>
 <div class="viewcode-block" id="arctan">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.arctan">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.arctan">[docs]</a>
 <span class="linenos"> 277</span><span class="k">def</span> <span class="nf">arctan</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 278</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 279</span><span class="sd">    Inverse tangent, element-wise.</span>
@@ -783,7 +783,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 312</span>
 <span class="linenos"> 313</span>
 <div class="viewcode-block" id="sinh">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.sinh">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.sinh">[docs]</a>
 <span class="linenos"> 314</span><span class="k">def</span> <span class="nf">sinh</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 315</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 316</span><span class="sd">    Hyperbolic sine, element-wise.</span>
@@ -822,7 +822,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 348</span>
 <span class="linenos"> 349</span>
 <div class="viewcode-block" id="cosh">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.cosh">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.cosh">[docs]</a>
 <span class="linenos"> 350</span><span class="k">def</span> <span class="nf">cosh</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 351</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 352</span><span class="sd">    Hyperbolic cosine, element-wise.</span>
@@ -867,7 +867,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 390</span>
 <span class="linenos"> 391</span>
 <div class="viewcode-block" id="tanh">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.tanh">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.tanh">[docs]</a>
 <span class="linenos"> 392</span><span class="k">def</span> <span class="nf">tanh</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 393</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 394</span><span class="sd">    Hyperbolic tangent, element-wise.</span>
@@ -913,7 +913,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 433</span>
 <span class="linenos"> 434</span>
 <div class="viewcode-block" id="arcsinh">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.arcsinh">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.arcsinh">[docs]</a>
 <span class="linenos"> 435</span><span class="k">def</span> <span class="nf">arcsinh</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 436</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 437</span><span class="sd">    Inverse hyperbolic sine, element-wise.</span>
@@ -955,7 +955,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 472</span>
 <span class="linenos"> 473</span>
 <div class="viewcode-block" id="arccosh">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.arccosh">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.arccosh">[docs]</a>
 <span class="linenos"> 474</span><span class="k">def</span> <span class="nf">arccosh</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 475</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 476</span><span class="sd">    Inverse hyperbolic cosine, element-wise.</span>
@@ -996,7 +996,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 510</span>
 <span class="linenos"> 511</span>
 <div class="viewcode-block" id="arctanh">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.arctanh">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.arctanh">[docs]</a>
 <span class="linenos"> 512</span><span class="k">def</span> <span class="nf">arctanh</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 513</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 514</span><span class="sd">    Inverse hyperbolic tangent, element-wise.</span>
@@ -1044,7 +1044,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 555</span>
 <span class="linenos"> 556</span>
 <div class="viewcode-block" id="exp">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.exp">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.exp">[docs]</a>
 <span class="linenos"> 557</span><span class="k">def</span> <span class="nf">exp</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">,</span> <span class="n">base</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 558</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 559</span><span class="sd">    Exponential, element-wise. (Default: base-E exponential.)</span>
@@ -1089,7 +1089,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 597</span>
 <span class="linenos"> 598</span>
 <div class="viewcode-block" id="log">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.log">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.log">[docs]</a>
 <span class="linenos"> 599</span><span class="k">def</span> <span class="nf">log</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">,</span> <span class="n">base</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 600</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 601</span><span class="sd">    Logarithm, element-wise. (Default: base-E logarithm.)</span>
@@ -1134,7 +1134,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 639</span>
 <span class="linenos"> 640</span>
 <div class="viewcode-block" id="clip">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.clip">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.clip">[docs]</a>
 <span class="linenos"> 641</span><span class="k">def</span> <span class="nf">clip</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">,</span> <span class="n">a_min</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">a_max</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="kc">None</span><span class="p">):</span>
 <span class="linenos"> 642</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 643</span><span class="sd">    Clip (limit) values in an array, element-wise.</span>
@@ -1174,7 +1174,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 676</span>
 <span class="linenos"> 677</span>
 <div class="viewcode-block" id="sqrt">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.sqrt">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.sqrt">[docs]</a>
 <span class="linenos"> 678</span><span class="k">def</span> <span class="nf">sqrt</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 679</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 680</span><span class="sd">    Non-negative square-root, element-wise.</span>
@@ -1215,7 +1215,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 714</span>
 <span class="linenos"> 715</span>
 <div class="viewcode-block" id="cbrt">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.cbrt">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.cbrt">[docs]</a>
 <span class="linenos"> 716</span><span class="k">def</span> <span class="nf">cbrt</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 717</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 718</span><span class="sd">    Cube-root, element-wise.</span>
@@ -1256,7 +1256,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 752</span>
 <span class="linenos"> 753</span>
 <div class="viewcode-block" id="square">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.square">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.square">[docs]</a>
 <span class="linenos"> 754</span><span class="k">def</span> <span class="nf">square</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 755</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 756</span><span class="sd">    Square, element-wise.</span>
@@ -1289,7 +1289,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 782</span>
 <span class="linenos"> 783</span>
 <div class="viewcode-block" id="abs">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.abs">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.abs">[docs]</a>
 <span class="linenos"> 784</span><span class="k">def</span> <span class="nf">abs</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 785</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 786</span><span class="sd">    Absolute value, element-wise.</span>
@@ -1315,7 +1315,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 805</span>
 <span class="linenos"> 806</span>
 <div class="viewcode-block" id="sign">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.sign">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.sign">[docs]</a>
 <span class="linenos"> 807</span><span class="k">def</span> <span class="nf">sign</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 808</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 809</span><span class="sd">    Number sign indicator, element-wise.</span>
@@ -1354,7 +1354,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 841</span>
 <span class="linenos"> 842</span>
 <div class="viewcode-block" id="gaussian">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.gaussian">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.gaussian">[docs]</a>
 <span class="linenos"> 843</span><span class="k">def</span> <span class="nf">gaussian</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 844</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 845</span><span class="sd">    Gaussian, element-wise.</span>
@@ -1399,7 +1399,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 883</span>
 <span class="linenos"> 884</span>
 <div class="viewcode-block" id="sigmoid">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.sigmoid">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.sigmoid">[docs]</a>
 <span class="linenos"> 885</span><span class="k">def</span> <span class="nf">sigmoid</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 886</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 887</span><span class="sd">    Sigmoid, element-wise.</span>
@@ -1439,7 +1439,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 920</span>
 <span class="linenos"> 921</span>
 <div class="viewcode-block" id="softplus">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.softplus">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.softplus">[docs]</a>
 <span class="linenos"> 922</span><span class="k">def</span> <span class="nf">softplus</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 923</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 924</span><span class="sd">    Softplus operator.</span>
@@ -1474,7 +1474,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 952</span>
 <span class="linenos"> 953</span>
 <div class="viewcode-block" id="leakyrelu">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.leakyrelu">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.leakyrelu">[docs]</a>
 <span class="linenos"> 954</span><span class="k">def</span> <span class="nf">leakyrelu</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">,</span> <span class="n">alpha</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 955</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 956</span><span class="sd">    Leaky rectified linear unit, element-wise.</span>
@@ -1494,7 +1494,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos"> 969</span>
 <span class="linenos"> 970</span>
 <div class="viewcode-block" id="relu">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.relu">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.relu">[docs]</a>
 <span class="linenos"> 971</span><span class="k">def</span> <span class="nf">relu</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos"> 972</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 973</span><span class="sd">    Rectified linear unit, element-wise.</span>
@@ -1534,7 +1534,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos">1006</span>
 <span class="linenos">1007</span>
 <div class="viewcode-block" id="silu">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.silu">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.silu">[docs]</a>
 <span class="linenos">1008</span><span class="k">def</span> <span class="nf">silu</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos">1009</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1010</span><span class="sd">    Sigmoid linear unit, element-wise.</span>
@@ -1578,7 +1578,7 @@ <h1>Source code for pyxu.operator.map.ufunc</h1><div class="highlight"><pre>
 <span class="linenos">1047</span>
 <span class="linenos">1048</span>
 <div class="viewcode-block" id="softmax">
-<a class="viewcode-back" href="../../../../api/operator.html#pyxu.operator.softmax">[docs]</a>
+<a class="viewcode-back" href="../../../../api/operator/map.html#pyxu.operator.softmax">[docs]</a>
 <span class="linenos">1049</span><span class="k">def</span> <span class="nf">softmax</span><span class="p">(</span><span class="n">op</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 <span class="linenos">1050</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">1051</span><span class="sd">    Softmax operator.</span>
diff --git a/_modules/pyxu/opt/solver/adam.html b/_modules/pyxu/opt/solver/adam.html
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--- a/_modules/pyxu/opt/solver/adam.html
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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diff --git a/_modules/pyxu/opt/solver/cg.html b/_modules/pyxu/opt/solver/cg.html
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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@@ -378,7 +378,7 @@
           
           
           
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
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-  <h1>Source code for pyxu.opt.solver.prox_adam</h1><div class="highlight"><pre>
-<span></span><span class="linenos">  1</span><span class="kn">import</span> <span class="nn">math</span>
-<span class="linenos">  2</span><span class="kn">import</span> <span class="nn">warnings</span>
-<span class="linenos">  3</span>
-<span class="linenos">  4</span><span class="kn">import</span> <span class="nn">pyxu.abc</span> <span class="k">as</span> <span class="nn">pxa</span>
-<span class="linenos">  5</span><span class="kn">import</span> <span class="nn">pyxu.info.ptype</span> <span class="k">as</span> <span class="nn">pxt</span>
-<span class="linenos">  6</span><span class="kn">import</span> <span class="nn">pyxu.info.warning</span> <span class="k">as</span> <span class="nn">pxw</span>
-<span class="linenos">  7</span><span class="kn">import</span> <span class="nn">pyxu.operator.func</span> <span class="k">as</span> <span class="nn">pxf</span>
-<span class="linenos">  8</span><span class="kn">import</span> <span class="nn">pyxu.operator.linop</span> <span class="k">as</span> <span class="nn">pxl</span>
-<span class="linenos">  9</span><span class="kn">import</span> <span class="nn">pyxu.opt.solver</span> <span class="k">as</span> <span class="nn">pxs</span>
-<span class="linenos"> 10</span><span class="kn">import</span> <span class="nn">pyxu.runtime</span> <span class="k">as</span> <span class="nn">pxrt</span>
-<span class="linenos"> 11</span><span class="kn">import</span> <span class="nn">pyxu.util</span> <span class="k">as</span> <span class="nn">pxu</span>
-<span class="linenos"> 12</span>
-<span class="linenos"> 13</span><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
-<span class="linenos"> 14</span>    <span class="s2">&quot;ProxAdam&quot;</span><span class="p">,</span>
-<span class="linenos"> 15</span><span class="p">]</span>
-<span class="linenos"> 16</span>
-<span class="linenos"> 17</span>
-<div class="viewcode-block" id="ProxAdam">
-<a class="viewcode-back" href="../../../../api/opt.html#pyxu.opt.solver.prox_adam.ProxAdam">[docs]</a>
-<span class="linenos"> 18</span><span class="k">class</span> <span class="nc">ProxAdam</span><span class="p">(</span><span class="n">pxa</span><span class="o">.</span><span class="n">Solver</span><span class="p">):</span>
-<span class="linenos"> 19</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 20</span><span class="sd">    Proximal Adam solver [ProxAdam]_.</span>
-<span class="linenos"> 21</span>
-<span class="linenos"> 22</span><span class="sd">    ProxAdam minimizes</span>
-<span class="linenos"> 23</span>
-<span class="linenos"> 24</span><span class="sd">    .. math::</span>
-<span class="linenos"> 25</span>
-<span class="linenos"> 26</span><span class="sd">       {\min_{\mathbf{x}\in\mathbb{R}^N} \;\mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{G}(\mathbf{x})},</span>
-<span class="linenos"> 27</span>
-<span class="linenos"> 28</span><span class="sd">    where:</span>
-<span class="linenos"> 29</span>
-<span class="linenos"> 30</span><span class="sd">    * :math:`\mathcal{F}:\mathbb{R}^N\rightarrow \mathbb{R}` is *convex* and *differentiable*, with</span>
-<span class="linenos"> 31</span><span class="sd">      :math:`\beta`-*Lipschitz continuous* gradient, for some :math:`\beta\in[0,+\infty[`.</span>
-<span class="linenos"> 32</span><span class="sd">    * :math:`\mathcal{G}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}` is a *proper*, *lower</span>
-<span class="linenos"> 33</span><span class="sd">      semicontinuous* and *convex function* with a *simple proximal operator*.</span>
-<span class="linenos"> 34</span>
-<span class="linenos"> 35</span><span class="sd">    ProxAdam is a suitable alternative to Proximal Gradient Descent</span>
-<span class="linenos"> 36</span><span class="sd">    (:py:class:`~pyxu.opt.solver.pgd.PGD`) when:</span>
-<span class="linenos"> 37</span>
-<span class="linenos"> 38</span><span class="sd">    * computing :math:`\beta` to optimally choose the step size is infeasible, and</span>
-<span class="linenos"> 39</span><span class="sd">    * line-search methods to estimate step sizes are too expensive.</span>
-<span class="linenos"> 40</span>
-<span class="linenos"> 41</span><span class="sd">    Compared to PGD, ProxAdam:</span>
-<span class="linenos"> 42</span>
-<span class="linenos"> 43</span><span class="sd">    * auto-tunes gradient updates based on stochastic estimates of</span>
-<span class="linenos"> 44</span><span class="sd">      :math:`\phi_{t} = \mathbb{E}[\nabla\mathcal{F}]` and :math:`\psi_{t} =</span>
-<span class="linenos"> 45</span><span class="sd">      \mathbb{E}[\nabla\mathcal{F}^{2}]` respectively;</span>
-<span class="linenos"> 46</span><span class="sd">    * uses a modified proximity operator at each iteration to update coordinates at varying scales:</span>
-<span class="linenos"> 47</span>
-<span class="linenos"> 48</span><span class="sd">      .. math::</span>
-<span class="linenos"> 49</span>
-<span class="linenos"> 50</span><span class="sd">         \text{prox}_{\alpha\mathcal{G}}(\mathbf{x}_{t})</span>
-<span class="linenos"> 51</span><span class="sd">         =</span>
-<span class="linenos"> 52</span><span class="sd">         \min_{\mathbf{z}\in\mathbb{R}^N} \;\mathcal{G}(\mathbf{z})\;\;+\;\;\frac{1}{2\alpha}||\mathbf{z}-\mathbf{x}_t||_H^2,</span>
-<span class="linenos"> 53</span>
-<span class="linenos"> 54</span><span class="sd">      where :math:`H=\text{diag}(\psi_t)`.</span>
-<span class="linenos"> 55</span><span class="sd">      The modified proximity operator is computed by solving a PGD sub-problem.</span>
-<span class="linenos"> 56</span>
-<span class="linenos"> 57</span><span class="sd">    ProxAdam has many named variants for particular choices of :math:`\phi` and :math:`\psi`:</span>
-<span class="linenos"> 58</span>
-<span class="linenos"> 59</span><span class="sd">    * Adam:</span>
-<span class="linenos"> 60</span>
-<span class="linenos"> 61</span><span class="sd">      .. math::</span>
-<span class="linenos"> 62</span>
-<span class="linenos"> 63</span><span class="sd">         \phi_t</span>
-<span class="linenos"> 64</span><span class="sd">         =</span>
-<span class="linenos"> 65</span><span class="sd">         \frac{</span>
-<span class="linenos"> 66</span><span class="sd">           \mathbf{m}_t</span>
-<span class="linenos"> 67</span><span class="sd">         }{</span>
-<span class="linenos"> 68</span><span class="sd">           1-\beta_1^t</span>
-<span class="linenos"> 69</span><span class="sd">         }</span>
-<span class="linenos"> 70</span><span class="sd">         \qquad</span>
-<span class="linenos"> 71</span><span class="sd">         \psi_t</span>
-<span class="linenos"> 72</span><span class="sd">         =</span>
-<span class="linenos"> 73</span><span class="sd">         \sqrt{</span>
-<span class="linenos"> 74</span><span class="sd">           \frac{</span>
-<span class="linenos"> 75</span><span class="sd">             \mathbf{v}_t</span>
-<span class="linenos"> 76</span><span class="sd">           }{</span>
-<span class="linenos"> 77</span><span class="sd">             1-\beta_2^t</span>
-<span class="linenos"> 78</span><span class="sd">           }</span>
-<span class="linenos"> 79</span><span class="sd">         } + \epsilon,</span>
-<span class="linenos"> 80</span>
-<span class="linenos"> 81</span><span class="sd">    * AMSGrad:</span>
-<span class="linenos"> 82</span>
-<span class="linenos"> 83</span><span class="sd">      .. math::</span>
-<span class="linenos"> 84</span>
-<span class="linenos"> 85</span><span class="sd">         \phi_t = \mathbf{m}_t</span>
-<span class="linenos"> 86</span><span class="sd">         \qquad</span>
-<span class="linenos"> 87</span><span class="sd">         \psi_t = \sqrt{\hat{\mathbf{v}}_t},</span>
-<span class="linenos"> 88</span>
-<span class="linenos"> 89</span><span class="sd">    * PAdam:</span>
-<span class="linenos"> 90</span>
-<span class="linenos"> 91</span><span class="sd">      .. math::</span>
-<span class="linenos"> 92</span>
-<span class="linenos"> 93</span><span class="sd">         \phi_t = \mathbf{m}_t</span>
-<span class="linenos"> 94</span><span class="sd">         \qquad</span>
-<span class="linenos"> 95</span><span class="sd">         \psi_t = \hat{\mathbf{v}}_t^p,</span>
-<span class="linenos"> 96</span>
-<span class="linenos"> 97</span><span class="sd">    where in all cases:</span>
-<span class="linenos"> 98</span>
-<span class="linenos"> 99</span><span class="sd">    .. math::</span>
-<span class="linenos">100</span>
-<span class="linenos">101</span><span class="sd">       \mathbf{m}_t</span>
-<span class="linenos">102</span><span class="sd">       =</span>
-<span class="linenos">103</span><span class="sd">       \beta_1\mathbf{m}_{t-1}</span>
-<span class="linenos">104</span><span class="sd">       +</span>
-<span class="linenos">105</span><span class="sd">       (1-\beta_1)\mathbf{g}_t \\</span>
-<span class="linenos">106</span><span class="sd">       \mathbf{v}_t</span>
-<span class="linenos">107</span><span class="sd">       =</span>
-<span class="linenos">108</span><span class="sd">       \beta_2\mathbf{v}_{t-1}</span>
-<span class="linenos">109</span><span class="sd">       +</span>
-<span class="linenos">110</span><span class="sd">       (1-\beta_2)\mathbf{g}_t^2\\</span>
-<span class="linenos">111</span><span class="sd">       \hat{\mathbf{v}}_t</span>
-<span class="linenos">112</span><span class="sd">       =</span>
-<span class="linenos">113</span><span class="sd">       \max(\hat{\mathbf{v}}_{t-1}, \mathbf{v}_t),</span>
-<span class="linenos">114</span>
-<span class="linenos">115</span><span class="sd">    with :math:`\mathbf{m}_0 = \mathbf{v}_0 = \mathbf{0}`.</span>
-<span class="linenos">116</span>
-<span class="linenos">117</span><span class="sd">    Remarks</span>
-<span class="linenos">118</span><span class="sd">    -------</span>
-<span class="linenos">119</span><span class="sd">    * The algorithm is still valid if :math:`\mathcal{G}` is zero.</span>
-<span class="linenos">120</span>
-<span class="linenos">121</span><span class="sd">    * The convergence is guaranteed for step sizes :math:`\alpha\leq 2/\beta`.</span>
-<span class="linenos">122</span>
-<span class="linenos">123</span><span class="sd">    * The default stopping criterion is the relative norm change of the primal variable.</span>
-<span class="linenos">124</span><span class="sd">      By default, the algorithm stops when the norm of the difference between two consecutive iterates</span>
-<span class="linenos">125</span><span class="sd">      :math:`\{\mathbf{x}_n\}_{n\in\mathbb{N}}` is smaller than 1e-4.</span>
-<span class="linenos">126</span><span class="sd">      Different stopping criteria can be used.</span>
-<span class="linenos">127</span><span class="sd">      It is recommended to change the stopping criterion when using the PAdam and AMSGrad variants to</span>
-<span class="linenos">128</span><span class="sd">      avoid premature stops.</span>
-<span class="linenos">129</span><span class="sd">      By default, the same stopping criterion is used for the proximal sub-problem.</span>
-<span class="linenos">130</span>
-<span class="linenos">131</span><span class="sd">    Parameters (``__init__()``)</span>
-<span class="linenos">132</span><span class="sd">    ---------------------------</span>
-<span class="linenos">133</span><span class="sd">    * **f** (:py:class:`~pyxu.abc.operator.DiffFunc`)</span>
-<span class="linenos">134</span><span class="sd">      --</span>
-<span class="linenos">135</span><span class="sd">      Differentiable function :math:`\mathcal{F}`.</span>
-<span class="linenos">136</span><span class="sd">    * **g** (:py:class:`~pyxu.abc.operator.ProxFunc`, :py:obj:`None`)</span>
-<span class="linenos">137</span><span class="sd">      --</span>
-<span class="linenos">138</span><span class="sd">      Proximable function :math:`\mathcal{G}`.</span>
-<span class="linenos">139</span><span class="sd">    * **\*\*kwargs** (:py:class:`~collections.abc.Mapping`)</span>
-<span class="linenos">140</span><span class="sd">      --</span>
-<span class="linenos">141</span><span class="sd">      Other keyword parameters passed on to :py:meth:`pyxu.abc.solver.Solver.__init__`.</span>
-<span class="linenos">142</span>
-<span class="linenos">143</span><span class="sd">    Parameters (``fit()``)</span>
-<span class="linenos">144</span><span class="sd">    ----------------------</span>
-<span class="linenos">145</span><span class="sd">    * **x0** (:py:attr:`~pyxu.info.ptype.NDArray`)</span>
-<span class="linenos">146</span><span class="sd">      --</span>
-<span class="linenos">147</span><span class="sd">      (..., N) initial point(s).</span>
-<span class="linenos">148</span><span class="sd">    * **variant** (&quot;adam&quot;, &quot;amsgrad&quot;, &quot;padam&quot;)</span>
-<span class="linenos">149</span><span class="sd">      --</span>
-<span class="linenos">150</span><span class="sd">      Name of the ProxAdam variant to use.</span>
-<span class="linenos">151</span><span class="sd">      Defaults to &quot;adam&quot;.</span>
-<span class="linenos">152</span><span class="sd">    * **a** (:py:attr:`~pyxu.info.ptype.Real`, :py:obj:`None`)</span>
-<span class="linenos">153</span><span class="sd">      --</span>
-<span class="linenos">154</span><span class="sd">      Max normalized gradient step size.</span>
-<span class="linenos">155</span><span class="sd">      Defaults to :math:`1 / \beta` if unspecified.</span>
-<span class="linenos">156</span><span class="sd">    * **b1** (:py:attr:`~pyxu.info.ptype.Real`)</span>
-<span class="linenos">157</span><span class="sd">      --</span>
-<span class="linenos">158</span><span class="sd">      1st-order gradient exponential decay :math:`\beta_{1} \in [0, 1)`.</span>
-<span class="linenos">159</span><span class="sd">    * **b2** (:py:attr:`~pyxu.info.ptype.Real`)</span>
-<span class="linenos">160</span><span class="sd">      --</span>
-<span class="linenos">161</span><span class="sd">      2nd-order gradient exponential decay :math:`\beta_{2} \in [0, 1)`.</span>
-<span class="linenos">162</span><span class="sd">    * **m0** (:py:attr:`~pyxu.info.ptype.NDArray`, :py:obj:`None`)</span>
-<span class="linenos">163</span><span class="sd">      --</span>
-<span class="linenos">164</span><span class="sd">      (..., N) initial 1st-order gradient estimate corresponding to each initial point.</span>
-<span class="linenos">165</span><span class="sd">      Defaults to the null vector if unspecified.</span>
-<span class="linenos">166</span><span class="sd">    * **v0** (:py:attr:`~pyxu.info.ptype.NDArray`, :py:obj:`None`)</span>
-<span class="linenos">167</span><span class="sd">      --</span>
-<span class="linenos">168</span><span class="sd">      (..., N) initial 2nd-order gradient estimate corresponding to each initial point.</span>
-<span class="linenos">169</span><span class="sd">      Defaults to the null vector if unspecified.</span>
-<span class="linenos">170</span><span class="sd">    * **kwargs_sub** (:py:class:`~collections.abc.Mapping`, :py:obj:`None`)</span>
-<span class="linenos">171</span><span class="sd">      --</span>
-<span class="linenos">172</span><span class="sd">      Keyword parameters used to initialize :py:meth:`~pyxu.opt.solver.pgd.PGD`&#39;s ``__init__()`` in</span>
-<span class="linenos">173</span><span class="sd">      sub-problems.</span>
-<span class="linenos">174</span><span class="sd">      This is an advanced option: use it with care.</span>
-<span class="linenos">175</span><span class="sd">    * **stop_crit_sub** (:py:class:`~pyxu.abc.solver.StoppingCriterion`, :py:obj:`None`)</span>
-<span class="linenos">176</span><span class="sd">      --</span>
-<span class="linenos">177</span><span class="sd">      Sub-problem stopping criterion.</span>
-<span class="linenos">178</span><span class="sd">      Default: use same stopping criterion as main problem.</span>
-<span class="linenos">179</span><span class="sd">    * **p** (:py:attr:`~pyxu.info.ptype.Real`)</span>
-<span class="linenos">180</span><span class="sd">      --</span>
-<span class="linenos">181</span><span class="sd">      PAdam power parameter :math:`p \in (0, 0.5]`.</span>
-<span class="linenos">182</span><span class="sd">      Must be specified for PAdam, unused otherwise.</span>
-<span class="linenos">183</span><span class="sd">    * **eps_adam** (:py:attr:`~pyxu.info.ptype.Real`)</span>
-<span class="linenos">184</span><span class="sd">      --</span>
-<span class="linenos">185</span><span class="sd">      Adam noise parameter :math:`\epsilon`.</span>
-<span class="linenos">186</span><span class="sd">      This term is used exclusively if `variant=&quot;adam&quot;`.</span>
-<span class="linenos">187</span><span class="sd">      Defaults to 1e-6.</span>
-<span class="linenos">188</span><span class="sd">    * **eps_var** (:py:attr:`~pyxu.info.ptype.Real`)</span>
-<span class="linenos">189</span><span class="sd">      --</span>
-<span class="linenos">190</span><span class="sd">      Avoids division by zero if estimated gradient variance is too small.</span>
-<span class="linenos">191</span><span class="sd">      Defaults to 1e-6.</span>
-<span class="linenos">192</span><span class="sd">    * **\*\*kwargs** (:py:class:`~collections.abc.Mapping`)</span>
-<span class="linenos">193</span><span class="sd">      --</span>
-<span class="linenos">194</span><span class="sd">      Other keyword parameters passed on to :py:meth:`pyxu.abc.solver.Solver.fit`.</span>
-<span class="linenos">195</span>
-<span class="linenos">196</span><span class="sd">    Note</span>
-<span class="linenos">197</span><span class="sd">    ----</span>
-<span class="linenos">198</span><span class="sd">    If provided, `m0` and `v0` must be broadcastable with `x0`.</span>
-<span class="linenos">199</span>
-<span class="linenos">200</span><span class="sd">    Example</span>
-<span class="linenos">201</span><span class="sd">    -------</span>
-<span class="linenos">202</span><span class="sd">    Consider the following optimization problem:</span>
-<span class="linenos">203</span>
-<span class="linenos">204</span><span class="sd">    .. math::</span>
-<span class="linenos">205</span>
-<span class="linenos">206</span><span class="sd">       \min_{\mathbf{x}\in\mathbb{R}^N} \Vert{\mathbf{x}-\mathbf{1}}\Vert_2^2 + \Vert{\mathbf{x}-\mathbf{1}}\Vert_1</span>
-<span class="linenos">207</span>
-<span class="linenos">208</span><span class="sd">    .. code-block:: python3</span>
-<span class="linenos">209</span>
-<span class="linenos">210</span><span class="sd">       import numpy as np</span>
-<span class="linenos">211</span>
-<span class="linenos">212</span><span class="sd">       from pyxu.operator.func import L1Norm, SquaredL2Norm</span>
-<span class="linenos">213</span><span class="sd">       from pyxu.opt.solver import ProxAdam</span>
-<span class="linenos">214</span>
-<span class="linenos">215</span><span class="sd">       N = 3</span>
-<span class="linenos">216</span><span class="sd">       f = SquaredL2Norm(dim=N).asloss(1)</span>
-<span class="linenos">217</span><span class="sd">       g = L1Norm(dim=N).asloss(1)</span>
-<span class="linenos">218</span>
-<span class="linenos">219</span><span class="sd">       prox_adam = ProxAdam(f, g)</span>
-<span class="linenos">220</span><span class="sd">       prox_adam.fit(</span>
-<span class="linenos">221</span><span class="sd">           x0=np.zeros((N,)),</span>
-<span class="linenos">222</span><span class="sd">           variant=&quot;padam&quot;,</span>
-<span class="linenos">223</span><span class="sd">           p=0.25,</span>
-<span class="linenos">224</span><span class="sd">       )</span>
-<span class="linenos">225</span><span class="sd">       x_opt = prox_adam.solution()</span>
-<span class="linenos">226</span><span class="sd">       np.allclose(x_opt, 1)  # True</span>
-<span class="linenos">227</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">228</span>
-<span class="linenos">229</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
-<span class="linenos">230</span>        <span class="bp">self</span><span class="p">,</span>
-<span class="linenos">231</span>        <span class="n">f</span><span class="p">:</span> <span class="n">pxa</span><span class="o">.</span><span class="n">DiffFunc</span><span class="p">,</span>
-<span class="linenos">232</span>        <span class="n">g</span><span class="p">:</span> <span class="n">pxa</span><span class="o">.</span><span class="n">ProxFunc</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-<span class="linenos">233</span>        <span class="o">**</span><span class="n">kwargs</span><span class="p">,</span>
-<span class="linenos">234</span>    <span class="p">):</span>
-<span class="linenos">235</span>        <span class="n">kwargs</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
-<span class="linenos">236</span>            <span class="n">log_var</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;log_var&quot;</span><span class="p">,</span> <span class="p">(</span><span class="s2">&quot;x&quot;</span><span class="p">,)),</span>
-<span class="linenos">237</span>        <span class="p">)</span>
-<span class="linenos">238</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos">239</span>
-<span class="linenos">240</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_f</span> <span class="o">=</span> <span class="n">f</span>
-<span class="linenos">241</span>        <span class="c1"># If f is domain-agnostic and g is unspecified, cannot auto-infer NullFunc dimension.</span>
-<span class="linenos">242</span>        <span class="c1"># Solution: delay initialization of g to m_init(), where x0&#39;s shape can be used.</span>
-<span class="linenos">243</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_prox_required</span> <span class="o">=</span> <span class="n">g</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span>
-<span class="linenos">244</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_g</span> <span class="o">=</span> <span class="n">g</span>
-<span class="linenos">245</span>
-<span class="linenos">246</span>    <span class="nd">@pxrt</span><span class="o">.</span><span class="n">enforce_precision</span><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="p">(</span><span class="s2">&quot;x0&quot;</span><span class="p">,</span> <span class="s2">&quot;a&quot;</span><span class="p">,</span> <span class="s2">&quot;b1&quot;</span><span class="p">,</span> <span class="s2">&quot;b2&quot;</span><span class="p">,</span> <span class="s2">&quot;m0&quot;</span><span class="p">,</span> <span class="s2">&quot;v0&quot;</span><span class="p">,</span> <span class="s2">&quot;p&quot;</span><span class="p">,</span> <span class="s2">&quot;eps_adam&quot;</span><span class="p">,</span> <span class="s2">&quot;eps_var&quot;</span><span class="p">))</span>
-<span class="linenos">247</span>    <span class="k">def</span> <span class="nf">m_init</span><span class="p">(</span>  <span class="c1"># default values from https://github.com/pmelchior/proxmin/blob/master/proxmin/algorithms.py</span>
-<span class="linenos">248</span>        <span class="bp">self</span><span class="p">,</span>
-<span class="linenos">249</span>        <span class="n">x0</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span>
-<span class="linenos">250</span>        <span class="n">variant</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;adam&quot;</span><span class="p">,</span>
-<span class="linenos">251</span>        <span class="n">a</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-<span class="linenos">252</span>        <span class="n">b1</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="mf">0.9</span><span class="p">,</span>
-<span class="linenos">253</span>        <span class="n">b2</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="mf">0.999</span><span class="p">,</span>
-<span class="linenos">254</span>        <span class="n">m0</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-<span class="linenos">255</span>        <span class="n">v0</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-<span class="linenos">256</span>        <span class="n">kwargs_sub</span><span class="p">:</span> <span class="nb">dict</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-<span class="linenos">257</span>        <span class="n">stop_crit_sub</span><span class="p">:</span> <span class="n">pxa</span><span class="o">.</span><span class="n">solver</span><span class="o">.</span><span class="n">StoppingCriterion</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
-<span class="linenos">258</span>        <span class="n">p</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">,</span>
-<span class="linenos">259</span>        <span class="n">eps_adam</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="mf">1e-6</span><span class="p">,</span>
-<span class="linenos">260</span>        <span class="n">eps_var</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span> <span class="o">=</span> <span class="mf">1e-6</span><span class="p">,</span>
-<span class="linenos">261</span>    <span class="p">):</span>
-<span class="linenos">262</span>        <span class="n">mst</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_mstate</span>  <span class="c1"># shorthand</span>
-<span class="linenos">263</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">x0</span>
-<span class="linenos">264</span>
-<span class="linenos">265</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_g</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">266</span>            <span class="bp">self</span><span class="o">.</span><span class="n">_g</span> <span class="o">=</span> <span class="n">pxf</span><span class="o">.</span><span class="n">NullFunc</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="n">x0</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
-<span class="linenos">267</span>
-<span class="linenos">268</span>        <span class="k">if</span> <span class="n">a</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">269</span>            <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;a&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">coerce</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">_f</span><span class="o">.</span><span class="n">diff_lipschitz</span><span class="p">)</span>
-<span class="linenos">270</span>            <span class="k">if</span> <span class="n">math</span><span class="o">.</span><span class="n">isinf</span><span class="p">(</span><span class="n">mst</span><span class="p">[</span><span class="s2">&quot;a&quot;</span><span class="p">]):</span>
-<span class="linenos">271</span>                <span class="c1"># _f is constant-valued: a is a free parameter.</span>
-<span class="linenos">272</span>                <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;a&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">coerce</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-<span class="linenos">273</span>                <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;</span><span class="se">\n</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span>
-<span class="linenos">274</span>                    <span class="p">[</span>
-<span class="linenos">275</span>                        <span class="sa">rf</span><span class="s2">&quot;The gradient step size `a` is auto-set to </span><span class="si">{</span><span class="n">mst</span><span class="p">[</span><span class="s1">&#39;a&#39;</span><span class="p">]</span><span class="si">}</span><span class="s2">.&quot;</span><span class="p">,</span>
-<span class="linenos">276</span>                        <span class="sa">r</span><span class="s2">&quot;Choosing a manually may lead to faster convergence.&quot;</span><span class="p">,</span>
-<span class="linenos">277</span>                    <span class="p">]</span>
-<span class="linenos">278</span>                <span class="p">)</span>
-<span class="linenos">279</span>                <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="n">msg</span><span class="p">,</span> <span class="n">pxw</span><span class="o">.</span><span class="n">AutoInferenceWarning</span><span class="p">)</span>
-<span class="linenos">280</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">281</span>            <span class="k">try</span><span class="p">:</span>
-<span class="linenos">282</span>                <span class="k">assert</span> <span class="n">a</span> <span class="o">&gt;</span> <span class="mi">0</span>
-<span class="linenos">283</span>                <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;a&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">a</span>
-<span class="linenos">284</span>            <span class="k">except</span> <span class="ne">Exception</span><span class="p">:</span>
-<span class="linenos">285</span>                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;`a` must be positive, got </span><span class="si">{</span><span class="n">a</span><span class="si">}</span><span class="s2">.&quot;</span><span class="p">)</span>
-<span class="linenos">286</span>
-<span class="linenos">287</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variant&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__parse_variant</span><span class="p">(</span><span class="n">variant</span><span class="p">)</span>
-<span class="linenos">288</span>
-<span class="linenos">289</span>        <span class="k">assert</span> <span class="mi">0</span> <span class="o">&lt;</span> <span class="n">p</span> <span class="o">&lt;=</span> <span class="mf">0.5</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;p: expected value in (0, 0.5], got </span><span class="si">{</span><span class="n">p</span><span class="si">}</span><span class="s2">.&quot;</span>
-<span class="linenos">290</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;padam_p&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span>
-<span class="linenos">291</span>
-<span class="linenos">292</span>        <span class="k">assert</span> <span class="n">eps_adam</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;eps_adam: expected positive value, got </span><span class="si">{</span><span class="n">eps_adam</span><span class="si">}</span><span class="s2">.&quot;</span>
-<span class="linenos">293</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;eps_adam&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">eps_adam</span>
-<span class="linenos">294</span>
-<span class="linenos">295</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span>
-<span class="linenos">296</span>
-<span class="linenos">297</span>        <span class="k">if</span> <span class="n">m0</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">298</span>            <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;mean&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span>
-<span class="linenos">299</span>        <span class="k">elif</span> <span class="n">m0</span><span class="o">.</span><span class="n">shape</span> <span class="o">==</span> <span class="n">x0</span><span class="o">.</span><span class="n">shape</span><span class="p">:</span>
-<span class="linenos">300</span>            <span class="c1"># No broadcasting involved</span>
-<span class="linenos">301</span>            <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;mean&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">m0</span>
-<span class="linenos">302</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">303</span>            <span class="n">x0</span><span class="p">,</span> <span class="n">m0</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">broadcast_arrays</span><span class="p">(</span><span class="n">x0</span><span class="p">,</span> <span class="n">m0</span><span class="p">)</span>
-<span class="linenos">304</span>            <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;mean&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">m0</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
-<span class="linenos">305</span>
-<span class="linenos">306</span>        <span class="k">if</span> <span class="n">v0</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">307</span>            <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span>
-<span class="linenos">308</span>        <span class="k">elif</span> <span class="n">v0</span><span class="o">.</span><span class="n">shape</span> <span class="o">==</span> <span class="n">x0</span><span class="o">.</span><span class="n">shape</span><span class="p">:</span>
-<span class="linenos">309</span>            <span class="c1"># No broadcasting involved</span>
-<span class="linenos">310</span>            <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">v0</span>
-<span class="linenos">311</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">312</span>            <span class="n">x0</span><span class="p">,</span> <span class="n">v0</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">broadcast_arrays</span><span class="p">(</span><span class="n">x0</span><span class="p">,</span> <span class="n">v0</span><span class="p">)</span>
-<span class="linenos">313</span>            <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">v0</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
-<span class="linenos">314</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance_hat&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance&quot;</span><span class="p">]</span>
-<span class="linenos">315</span>
-<span class="linenos">316</span>        <span class="k">if</span> <span class="n">kwargs_sub</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">317</span>            <span class="n">kwargs_sub</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
-<span class="linenos">318</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;subproblem_init_kwargs&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">kwargs_sub</span>
-<span class="linenos">319</span>        <span class="k">if</span> <span class="n">stop_crit_sub</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">320</span>            <span class="n">stop_crit_sub</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">default_stop_crit</span><span class="p">()</span>
-<span class="linenos">321</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;subproblem_stop_crit&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">stop_crit_sub</span>
-<span class="linenos">322</span>
-<span class="linenos">323</span>        <span class="k">assert</span> <span class="mi">0</span> <span class="o">&lt;=</span> <span class="n">b1</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;b1: expected value in [0, 1), got </span><span class="si">{</span><span class="n">b1</span><span class="si">}</span><span class="s2">.&quot;</span>
-<span class="linenos">324</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;b1&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">b1</span>
-<span class="linenos">325</span>
-<span class="linenos">326</span>        <span class="k">assert</span> <span class="mi">0</span> <span class="o">&lt;=</span> <span class="n">b2</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;b2: expected value in [0, 1), got </span><span class="si">{</span><span class="n">b2</span><span class="si">}</span><span class="s2">.&quot;</span>
-<span class="linenos">327</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;b2&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">b2</span>
-<span class="linenos">328</span>
-<span class="linenos">329</span>        <span class="k">assert</span> <span class="n">eps_var</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;eps_var: expected positive value, got </span><span class="si">{</span><span class="n">eps_var</span><span class="si">}</span><span class="s2">.&quot;</span>
-<span class="linenos">330</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;eps_variance&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">eps_var</span>
-<span class="linenos">331</span>
-<span class="linenos">332</span>    <span class="k">def</span> <span class="nf">m_step</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">333</span>        <span class="n">mst</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_mstate</span>  <span class="c1"># shorthand</span>
-<span class="linenos">334</span>
-<span class="linenos">335</span>        <span class="n">x</span><span class="p">,</span> <span class="n">a</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">],</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;a&quot;</span><span class="p">]</span>
-<span class="linenos">336</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="linenos">337</span>        <span class="n">gm</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">copy_if_unsafe</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_f</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
-<span class="linenos">338</span>        <span class="n">gv</span> <span class="o">=</span> <span class="n">gm</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
-<span class="linenos">339</span>
-<span class="linenos">340</span>        <span class="c1">## Part 1: evaluate phi/psi ============================</span>
-<span class="linenos">341</span>        <span class="n">m</span><span class="p">,</span> <span class="n">b1</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;mean&quot;</span><span class="p">],</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;b1&quot;</span><span class="p">]</span>
-<span class="linenos">342</span>        <span class="c1"># In-place implementation of -----------------</span>
-<span class="linenos">343</span>        <span class="c1">#   m = b1 * m + (1 - b1) * g</span>
-<span class="linenos">344</span>        <span class="n">m</span> <span class="o">*=</span> <span class="n">b1</span>
-<span class="linenos">345</span>        <span class="n">gm</span> <span class="o">*=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">b1</span>
-<span class="linenos">346</span>        <span class="n">m</span> <span class="o">+=</span> <span class="n">gm</span>
-<span class="linenos">347</span>        <span class="c1"># --------------------------------------------</span>
-<span class="linenos">348</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;mean&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">m</span>
-<span class="linenos">349</span>
-<span class="linenos">350</span>        <span class="n">v</span><span class="p">,</span> <span class="n">b2</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance&quot;</span><span class="p">],</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;b2&quot;</span><span class="p">]</span>
-<span class="linenos">351</span>        <span class="c1"># In-place implementation of -----------------</span>
-<span class="linenos">352</span>        <span class="c1">#   v = b2 * v + (1 - b2) * (g ** 2)</span>
-<span class="linenos">353</span>        <span class="n">v</span> <span class="o">*=</span> <span class="n">b2</span>
-<span class="linenos">354</span>        <span class="n">gv</span> <span class="o">**=</span> <span class="mi">2</span>
-<span class="linenos">355</span>        <span class="n">gv</span> <span class="o">*=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">b2</span>
-<span class="linenos">356</span>        <span class="n">v</span> <span class="o">+=</span> <span class="n">gv</span>
-<span class="linenos">357</span>        <span class="c1"># --------------------------------------------</span>
-<span class="linenos">358</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="n">mst</span><span class="p">[</span><span class="s2">&quot;eps_variance&quot;</span><span class="p">],</span> <span class="kc">None</span><span class="p">)</span>  <span class="c1"># avoid division-by-zero</span>
-<span class="linenos">359</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance_hat&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance_hat&quot;</span><span class="p">],</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance&quot;</span><span class="p">])</span>
-<span class="linenos">360</span>
-<span class="linenos">361</span>        <span class="n">phi</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__phi</span><span class="p">(</span><span class="n">t</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_astate</span><span class="p">[</span><span class="s2">&quot;idx&quot;</span><span class="p">])</span>
-<span class="linenos">362</span>        <span class="n">psi</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__psi</span><span class="p">(</span><span class="n">t</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_astate</span><span class="p">[</span><span class="s2">&quot;idx&quot;</span><span class="p">])</span>
-<span class="linenos">363</span>        <span class="c1">## =====================================================</span>
-<span class="linenos">364</span>
-<span class="linenos">365</span>        <span class="c1">## Part 2: take a step in the gradient&#39;s direction =====</span>
-<span class="linenos">366</span>        <span class="c1"># In-place implementation of -----------------</span>
-<span class="linenos">367</span>        <span class="c1">#   x = x - a * (phi / psi)</span>
-<span class="linenos">368</span>        <span class="n">phi</span> <span class="o">/=</span> <span class="n">psi</span>
-<span class="linenos">369</span>        <span class="n">phi</span> <span class="o">*=</span> <span class="n">a</span>
-<span class="linenos">370</span>        <span class="n">x</span> <span class="o">-=</span> <span class="n">phi</span>
-<span class="linenos">371</span>        <span class="c1">## =====================================================</span>
-<span class="linenos">372</span>
-<span class="linenos">373</span>        <span class="c1">## Part 3: eval PGD sub-problems =======================</span>
-<span class="linenos">374</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_prox_required</span><span class="p">:</span>
-<span class="linenos">375</span>            <span class="c1"># Assume N initial points were provided in fit().</span>
-<span class="linenos">376</span>            <span class="c1"># We need to solve a PGD sub-problem for each of them.</span>
-<span class="linenos">377</span>            <span class="c1">#</span>
-<span class="linenos">378</span>            <span class="c1"># Option 1: solve one large PGD(f, g) sub-problem, with</span>
-<span class="linenos">379</span>            <span class="c1">#    f = hstack(f1, ..., fN)</span>
-<span class="linenos">380</span>            <span class="c1">#    g = hstack(g, ..., g)</span>
-<span class="linenos">381</span>            <span class="c1"># Option 2: solve N small PGD(f, g) sub-problems, with</span>
-<span class="linenos">382</span>            <span class="c1">#    f = fn</span>
-<span class="linenos">383</span>            <span class="c1">#    g = g</span>
-<span class="linenos">384</span>            <span class="c1">#</span>
-<span class="linenos">385</span>            <span class="c1"># The former (1) is more convenient since all sub-problems are solved in parallel, but:</span>
-<span class="linenos">386</span>            <span class="c1"># * convergence will be slower since diff-Lipschitz constant of hstack(f1, ..., fN) is</span>
-<span class="linenos">387</span>            <span class="c1">#   larger than those of fn. (Moreover the diff-Lipschitz constants of the fn may be</span>
-<span class="linenos">388</span>            <span class="c1">#   spread out.)</span>
-<span class="linenos">389</span>            <span class="c1"># * in the event `stop_crit_sub` is provided, we cannot always intercept/adapt it to</span>
-<span class="linenos">390</span>            <span class="c1">#   apply block-wise on `_mstate`.</span>
-<span class="linenos">391</span>            <span class="c1">#</span>
-<span class="linenos">392</span>            <span class="c1"># Each sub-problem in the latter (2) converges fast, but sub-problems may execute in</span>
-<span class="linenos">393</span>            <span class="c1"># sequence depending on the array backend used.</span>
-<span class="linenos">394</span>            <span class="c1">#</span>
-<span class="linenos">395</span>            <span class="c1"># In light of the above, we opt for Option 2.</span>
-<span class="linenos">396</span>            <span class="o">*</span><span class="n">x_sh</span><span class="p">,</span> <span class="n">N</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span>
-<span class="linenos">397</span>            <span class="n">x_sub</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># sub-problem solutions</span>
-<span class="linenos">398</span>            <span class="n">scale</span> <span class="o">=</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">coerce</span><span class="p">(</span><span class="mf">0.5</span> <span class="o">/</span> <span class="n">a</span><span class="p">)</span>
-<span class="linenos">399</span>            <span class="k">for</span> <span class="n">_x</span><span class="p">,</span> <span class="n">_psi</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span> <span class="n">psi</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">)):</span>
-<span class="linenos">400</span>                <span class="n">gamma</span> <span class="o">=</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">coerce</span><span class="p">(</span><span class="n">a</span> <span class="o">/</span> <span class="n">xp</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">_psi</span><span class="p">))</span>
-<span class="linenos">401</span>                <span class="n">h_half</span> <span class="o">=</span> <span class="n">pxl</span><span class="o">.</span><span class="n">DiagonalOp</span><span class="p">(</span><span class="n">xp</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">_psi</span><span class="p">))</span>
-<span class="linenos">402</span>
-<span class="linenos">403</span>                <span class="n">f1</span> <span class="o">=</span> <span class="n">pxf</span><span class="o">.</span><span class="n">SquaredL2Norm</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="n">N</span><span class="p">)</span><span class="o">.</span><span class="n">asloss</span><span class="p">(</span><span class="n">h_half</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">_x</span><span class="p">))</span> <span class="o">*</span> <span class="n">h_half</span>
-<span class="linenos">404</span>                <span class="n">f</span> <span class="o">=</span> <span class="n">f1</span> <span class="o">*</span> <span class="n">scale</span>
-<span class="linenos">405</span>
-<span class="linenos">406</span>                <span class="n">kwargs</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;subproblem_init_kwargs&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
-<span class="linenos">407</span>                <span class="n">kwargs</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">show_progress</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
-<span class="linenos">408</span>                <span class="n">slvr</span> <span class="o">=</span> <span class="n">pxs</span><span class="o">.</span><span class="n">PGD</span><span class="p">(</span><span class="n">f</span><span class="o">=</span><span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_g</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos">409</span>
-<span class="linenos">410</span>                <span class="n">slvr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span>
-<span class="linenos">411</span>                    <span class="n">x0</span><span class="o">=</span><span class="n">_x</span><span class="p">,</span>
-<span class="linenos">412</span>                    <span class="n">tau</span><span class="o">=</span><span class="n">gamma</span><span class="p">,</span>
-<span class="linenos">413</span>                    <span class="n">stop_crit</span><span class="o">=</span><span class="n">mst</span><span class="p">[</span><span class="s2">&quot;subproblem_stop_crit&quot;</span><span class="p">],</span>
-<span class="linenos">414</span>                <span class="p">)</span>
-<span class="linenos">415</span>                <span class="n">x_sub</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">slvr</span><span class="o">.</span><span class="n">solution</span><span class="p">())</span>
-<span class="linenos">416</span>            <span class="n">x</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">x_sub</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">x_sh</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>  <span class="c1"># (..., N) original shape</span>
-<span class="linenos">417</span>        <span class="c1">## =====================================================</span>
-<span class="linenos">418</span>
-<span class="linenos">419</span>        <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span>
-<span class="linenos">420</span>
-<span class="linenos">421</span>    <span class="k">def</span> <span class="nf">default_stop_crit</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxa</span><span class="o">.</span><span class="n">StoppingCriterion</span><span class="p">:</span>
-<span class="linenos">422</span>        <span class="kn">from</span> <span class="nn">pyxu.opt.stop</span> <span class="kn">import</span> <span class="n">RelError</span>
-<span class="linenos">423</span>
-<span class="linenos">424</span>        <span class="c1"># Described in [ProxAdam]_ and used in their implementation:</span>
-<span class="linenos">425</span>        <span class="c1"># https://github.com/pmelchior/proxmin/blob/master/proxmin/algorithms.py</span>
-<span class="linenos">426</span>        <span class="n">rel_error</span> <span class="o">=</span> <span class="n">RelError</span><span class="p">(</span>
-<span class="linenos">427</span>            <span class="n">eps</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">,</span>
-<span class="linenos">428</span>            <span class="n">var</span><span class="o">=</span><span class="s2">&quot;x&quot;</span><span class="p">,</span>
-<span class="linenos">429</span>            <span class="n">f</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
-<span class="linenos">430</span>            <span class="n">norm</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
-<span class="linenos">431</span>            <span class="n">satisfy_all</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
-<span class="linenos">432</span>        <span class="p">)</span>
-<span class="linenos">433</span>        <span class="k">return</span> <span class="n">rel_error</span>
-<span class="linenos">434</span>
-<span class="linenos">435</span>    <span class="k">def</span> <span class="nf">objective_func</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos">436</span>        <span class="n">func</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">_f</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_g</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="linenos">437</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_mstate</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">])</span>
-<span class="linenos">438</span>        <span class="k">return</span> <span class="n">y</span>
-<span class="linenos">439</span>
-<span class="linenos">440</span>    <span class="k">def</span> <span class="nf">solution</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos">441</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">442</span><span class="sd">        Returns</span>
-<span class="linenos">443</span><span class="sd">        -------</span>
-<span class="linenos">444</span><span class="sd">        x: NDArray</span>
-<span class="linenos">445</span><span class="sd">            (..., N) solution.</span>
-<span class="linenos">446</span><span class="sd">        &quot;&quot;&quot;</span>
-<span class="linenos">447</span>        <span class="n">data</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">stats</span><span class="p">()</span>
-<span class="linenos">448</span>        <span class="k">return</span> <span class="n">data</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;x&quot;</span><span class="p">)</span>
-<span class="linenos">449</span>
-<span class="linenos">450</span>    <span class="k">def</span> <span class="nf">__phi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<span class="linenos">451</span>        <span class="n">mst</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_mstate</span>
-<span class="linenos">452</span>        <span class="n">var</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variant&quot;</span><span class="p">]</span>
-<span class="linenos">453</span>        <span class="k">if</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;adam&quot;</span><span class="p">:</span>
-<span class="linenos">454</span>            <span class="n">out</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;mean&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
-<span class="linenos">455</span>            <span class="n">out</span> <span class="o">/=</span> <span class="mi">1</span> <span class="o">-</span> <span class="p">(</span><span class="n">mst</span><span class="p">[</span><span class="s2">&quot;b1&quot;</span><span class="p">]</span> <span class="o">**</span> <span class="n">t</span><span class="p">)</span>
-<span class="linenos">456</span>        <span class="k">elif</span> <span class="n">var</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;amsgrad&quot;</span><span class="p">,</span> <span class="s2">&quot;padam&quot;</span><span class="p">]:</span>
-<span class="linenos">457</span>            <span class="n">out</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;mean&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>  <span class="c1"># to allow in-place updates outside __compute_phi()</span>
-<span class="linenos">458</span>        <span class="k">return</span> <span class="n">out</span>
-<span class="linenos">459</span>
-<span class="linenos">460</span>    <span class="k">def</span> <span class="nf">__psi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
-<span class="linenos">461</span>        <span class="n">mst</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_mstate</span>
-<span class="linenos">462</span>        <span class="n">xp</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">get_array_module</span><span class="p">(</span><span class="n">mst</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">])</span>
-<span class="linenos">463</span>        <span class="n">var</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variant&quot;</span><span class="p">]</span>
-<span class="linenos">464</span>        <span class="k">if</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;adam&quot;</span><span class="p">:</span>
-<span class="linenos">465</span>            <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance&quot;</span><span class="p">])</span>
-<span class="linenos">466</span>            <span class="n">out</span> <span class="o">/=</span> <span class="n">xp</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;b2&quot;</span><span class="p">]</span> <span class="o">**</span> <span class="n">t</span><span class="p">)</span>
-<span class="linenos">467</span>            <span class="n">out</span> <span class="o">+=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;eps_adam&quot;</span><span class="p">]</span>
-<span class="linenos">468</span>        <span class="k">elif</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;amsgrad&quot;</span><span class="p">:</span>
-<span class="linenos">469</span>            <span class="n">out</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance_hat&quot;</span><span class="p">])</span>
-<span class="linenos">470</span>        <span class="k">elif</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;padam&quot;</span><span class="p">:</span>
-<span class="linenos">471</span>            <span class="n">out</span> <span class="o">=</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;variance_hat&quot;</span><span class="p">]</span> <span class="o">**</span> <span class="n">mst</span><span class="p">[</span><span class="s2">&quot;padam_p&quot;</span><span class="p">]</span>
-<span class="linenos">472</span>        <span class="k">return</span> <span class="n">out</span>
-<span class="linenos">473</span>
-<span class="linenos">474</span>    <span class="k">def</span> <span class="nf">__parse_variant</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variant</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
-<span class="linenos">475</span>        <span class="n">supported_variants</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;adam&quot;</span><span class="p">,</span> <span class="s2">&quot;amsgrad&quot;</span><span class="p">,</span> <span class="s2">&quot;padam&quot;</span><span class="p">}</span>
-<span class="linenos">476</span>        <span class="k">if</span> <span class="p">(</span><span class="n">v</span> <span class="o">:=</span> <span class="n">variant</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span><span class="o">.</span><span class="n">strip</span><span class="p">())</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">supported_variants</span><span class="p">:</span>
-<span class="linenos">477</span>            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Unsupported variant &#39;</span><span class="si">{</span><span class="n">variant</span><span class="si">}</span><span class="s2">&#39;.&quot;</span><span class="p">)</span>
-<span class="linenos">478</span>        <span class="k">return</span> <span class="n">v</span></div>
-
-</pre></div>
-
-                </article>
-              
-              
-              
-                <footer class="bd-footer-article">
-                  
-<div class="footer-article-items footer-article__inner">
-  
-    <div class="footer-article-item"><!-- Previous / next buttons -->
-<div class="prev-next-area">
-</div></div>
-  
-</div>
-
-                </footer>
-              
-            </div>
-            
-            
-              
-                <div class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
-
-  <div class="sidebar-secondary-item">
-<div id="searchbox"></div></div>
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-          <footer class="bd-footer-content">
-            
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-        
-      </main>
-    </div>
-  </div>
-  
-  <!-- Scripts loaded after <body> so the DOM is not blocked -->
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-<script src="../../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52"></script>
-
-  <footer class="bd-footer">
-<div class="bd-footer__inner bd-page-width">
-  
-    <div class="footer-items__start">
-      
-        <div class="footer-item">
-  <p class="copyright">
-    
-      © Copyright 2023, M. Simeoni, S. Kashani, J. Rué-Queralt &amp; Pyxu Developers.
-      <br/>
-    
-  </p>
-</div>
-      
-        <div class="footer-item">
-  <p class="sphinx-version">
-    Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5.
-    <br/>
-  </p>
-</div>
-      
-        <div class="footer-item"><p class="theme-version">
-  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
-</p></div>
-      
-    </div>
-  
-  
-    <div class="footer-items__end">
-      
-        <div class="footer-item"><p class="theme-version">
-  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
-</p></div>
-      
-    </div>
-  
-</div>
-
-  </footer>
-  </body>
-</html>
\ No newline at end of file
diff --git a/_modules/pyxu/opt/stop.html b/_modules/pyxu/opt/stop.html
index fd171b25..95aab75f 100644
--- a/_modules/pyxu/opt/stop.html
+++ b/_modules/pyxu/opt/stop.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
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-    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
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     <link rel="stylesheet" type="text/css" href="../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
diff --git a/_modules/pyxu/runtime/_runtime.html b/_modules/pyxu/runtime/_runtime.html
index b993ecf4..db14b792 100644
--- a/_modules/pyxu/runtime/_runtime.html
+++ b/_modules/pyxu/runtime/_runtime.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
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-    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../../_static/copybutton.css?v=76b2166b" />
     <link rel="stylesheet" type="text/css" href="../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
diff --git a/_modules/pyxu/util/array_module.html b/_modules/pyxu/util/array_module.html
index 9f27061e..40108d46 100644
--- a/_modules/pyxu/util/array_module.html
+++ b/_modules/pyxu/util/array_module.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../../_static/copybutton.css?v=76b2166b" />
     <link rel="stylesheet" type="text/css" href="../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -454,124 +454,197 @@ <h1>Source code for pyxu.util.array_module</h1><div class="highlight"><pre>
 <span></span><span class="linenos">  1</span><span class="kn">import</span> <span class="nn">collections.abc</span> <span class="k">as</span> <span class="nn">cabc</span>
 <span class="linenos">  2</span><span class="kn">import</span> <span class="nn">functools</span>
 <span class="linenos">  3</span>
-<span class="linenos">  4</span><span class="kn">import</span> <span class="nn">pyxu.info.deps</span> <span class="k">as</span> <span class="nn">pxd</span>
-<span class="linenos">  5</span><span class="kn">import</span> <span class="nn">pyxu.info.ptype</span> <span class="k">as</span> <span class="nn">pxt</span>
-<span class="linenos">  6</span><span class="kn">import</span> <span class="nn">pyxu.util.misc</span> <span class="k">as</span> <span class="nn">pxm</span>
-<span class="linenos">  7</span>
-<span class="linenos">  8</span><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
-<span class="linenos">  9</span>    <span class="s2">&quot;get_array_module&quot;</span><span class="p">,</span>
-<span class="linenos"> 10</span>    <span class="s2">&quot;redirect&quot;</span><span class="p">,</span>
-<span class="linenos"> 11</span><span class="p">]</span>
-<span class="linenos"> 12</span>
-<span class="linenos"> 13</span>
+<span class="linenos">  4</span><span class="kn">import</span> <span class="nn">dask</span>
+<span class="linenos">  5</span>
+<span class="linenos">  6</span><span class="kn">import</span> <span class="nn">pyxu.info.deps</span> <span class="k">as</span> <span class="nn">pxd</span>
+<span class="linenos">  7</span><span class="kn">import</span> <span class="nn">pyxu.info.ptype</span> <span class="k">as</span> <span class="nn">pxt</span>
+<span class="linenos">  8</span><span class="kn">import</span> <span class="nn">pyxu.util.misc</span> <span class="k">as</span> <span class="nn">pxm</span>
+<span class="linenos">  9</span>
+<span class="linenos"> 10</span><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
+<span class="linenos"> 11</span>    <span class="s2">&quot;compute&quot;</span><span class="p">,</span>
+<span class="linenos"> 12</span>    <span class="s2">&quot;get_array_module&quot;</span><span class="p">,</span>
+<span class="linenos"> 13</span>    <span class="s2">&quot;redirect&quot;</span><span class="p">,</span>
+<span class="linenos"> 14</span>    <span class="s2">&quot;to_NUMPY&quot;</span><span class="p">,</span>
+<span class="linenos"> 15</span><span class="p">]</span>
+<span class="linenos"> 16</span>
+<span class="linenos"> 17</span>
 <div class="viewcode-block" id="get_array_module">
 <a class="viewcode-back" href="../../../api/util/array_module.html#pyxu.util.get_array_module">[docs]</a>
-<span class="linenos"> 14</span><span class="k">def</span> <span class="nf">get_array_module</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">fallback</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">ArrayModule</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">ArrayModule</span><span class="p">:</span>
-<span class="linenos"> 15</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 16</span><span class="sd">    Get the array namespace corresponding to a given object.</span>
-<span class="linenos"> 17</span>
-<span class="linenos"> 18</span><span class="sd">    Parameters</span>
-<span class="linenos"> 19</span><span class="sd">    ----------</span>
-<span class="linenos"> 20</span><span class="sd">    x: object</span>
-<span class="linenos"> 21</span><span class="sd">        Any object compatible with the interface of NumPy arrays.</span>
-<span class="linenos"> 22</span><span class="sd">    fallback: ArrayModule</span>
-<span class="linenos"> 23</span><span class="sd">        Fallback module if `x` is not a NumPy-like array.  Default behaviour: raise error if fallback used.</span>
-<span class="linenos"> 24</span>
-<span class="linenos"> 25</span><span class="sd">    Returns</span>
-<span class="linenos"> 26</span><span class="sd">    -------</span>
-<span class="linenos"> 27</span><span class="sd">    namespace: ArrayModule</span>
-<span class="linenos"> 28</span><span class="sd">        The namespace to use to manipulate `x`, or `fallback` if provided.</span>
-<span class="linenos"> 29</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 30</span>
-<span class="linenos"> 31</span>    <span class="k">def</span> <span class="nf">infer_api</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
-<span class="linenos"> 32</span>        <span class="k">try</span><span class="p">:</span>
-<span class="linenos"> 33</span>            <span class="k">return</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">module</span><span class="p">()</span>
-<span class="linenos"> 34</span>        <span class="k">except</span> <span class="ne">ValueError</span><span class="p">:</span>
-<span class="linenos"> 35</span>            <span class="k">return</span> <span class="kc">None</span>
-<span class="linenos"> 36</span>
-<span class="linenos"> 37</span>    <span class="k">if</span> <span class="p">(</span><span class="n">xp</span> <span class="o">:=</span> <span class="n">infer_api</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos"> 38</span>        <span class="k">return</span> <span class="n">xp</span>
-<span class="linenos"> 39</span>    <span class="k">elif</span> <span class="n">fallback</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos"> 40</span>        <span class="k">return</span> <span class="n">fallback</span>
-<span class="linenos"> 41</span>    <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 42</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Could not infer array module for </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="si">}</span><span class="s2">.&quot;</span><span class="p">)</span></div>
-
-<span class="linenos"> 43</span>
-<span class="linenos"> 44</span>
+<span class="linenos"> 18</span><span class="k">def</span> <span class="nf">get_array_module</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">fallback</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">ArrayModule</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">ArrayModule</span><span class="p">:</span>
+<span class="linenos"> 19</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 20</span><span class="sd">    Get the array namespace corresponding to a given object.</span>
+<span class="linenos"> 21</span>
+<span class="linenos"> 22</span><span class="sd">    Parameters</span>
+<span class="linenos"> 23</span><span class="sd">    ----------</span>
+<span class="linenos"> 24</span><span class="sd">    x: object</span>
+<span class="linenos"> 25</span><span class="sd">        Any object compatible with the interface of NumPy arrays.</span>
+<span class="linenos"> 26</span><span class="sd">    fallback: ArrayModule</span>
+<span class="linenos"> 27</span><span class="sd">        Fallback module if `x` is not a NumPy-like array.  Default behaviour: raise error if fallback used.</span>
+<span class="linenos"> 28</span>
+<span class="linenos"> 29</span><span class="sd">    Returns</span>
+<span class="linenos"> 30</span><span class="sd">    -------</span>
+<span class="linenos"> 31</span><span class="sd">    namespace: ArrayModule</span>
+<span class="linenos"> 32</span><span class="sd">        The namespace to use to manipulate `x`, or `fallback` if provided.</span>
+<span class="linenos"> 33</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 34</span>
+<span class="linenos"> 35</span>    <span class="k">def</span> <span class="nf">infer_api</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
+<span class="linenos"> 36</span>        <span class="k">try</span><span class="p">:</span>
+<span class="linenos"> 37</span>            <span class="k">return</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">module</span><span class="p">()</span>
+<span class="linenos"> 38</span>        <span class="k">except</span> <span class="ne">ValueError</span><span class="p">:</span>
+<span class="linenos"> 39</span>            <span class="k">return</span> <span class="kc">None</span>
+<span class="linenos"> 40</span>
+<span class="linenos"> 41</span>    <span class="k">if</span> <span class="p">(</span><span class="n">xp</span> <span class="o">:=</span> <span class="n">infer_api</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos"> 42</span>        <span class="k">return</span> <span class="n">xp</span>
+<span class="linenos"> 43</span>    <span class="k">elif</span> <span class="n">fallback</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos"> 44</span>        <span class="k">return</span> <span class="n">fallback</span>
+<span class="linenos"> 45</span>    <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 46</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Could not infer array module for </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="si">}</span><span class="s2">.&quot;</span><span class="p">)</span></div>
+
+<span class="linenos"> 47</span>
+<span class="linenos"> 48</span>
 <div class="viewcode-block" id="redirect">
 <a class="viewcode-back" href="../../../api/util/array_module.html#pyxu.util.redirect">[docs]</a>
-<span class="linenos"> 45</span><span class="k">def</span> <span class="nf">redirect</span><span class="p">(</span>
-<span class="linenos"> 46</span>    <span class="n">i</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">VarName</span><span class="p">,</span>
-<span class="linenos"> 47</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Mapping</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">],</span>
-<span class="linenos"> 48</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">:</span>
-<span class="linenos"> 49</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 50</span><span class="sd">    Change codepath for supplied array backends.</span>
-<span class="linenos"> 51</span>
-<span class="linenos"> 52</span><span class="sd">    Some functions/methods cannot be written in module-agnostic fashion. The action of this decorator is summarized</span>
-<span class="linenos"> 53</span><span class="sd">    below:</span>
-<span class="linenos"> 54</span>
-<span class="linenos"> 55</span><span class="sd">    * Analyze an array-valued parameter (`x`) of the wrapped function/method (`f`).</span>
-<span class="linenos"> 56</span><span class="sd">    * If `x` lies in one of the supplied array namespaces: re-route execution to the specified function.</span>
-<span class="linenos"> 57</span><span class="sd">    * If `x` lies in none of the supplied array namespaces: execute `f`.</span>
+<span class="linenos"> 49</span><span class="k">def</span> <span class="nf">redirect</span><span class="p">(</span>
+<span class="linenos"> 50</span>    <span class="n">i</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">VarName</span><span class="p">,</span>
+<span class="linenos"> 51</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Mapping</span><span class="p">[</span><span class="nb">str</span><span class="p">,</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">],</span>
+<span class="linenos"> 52</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">:</span>
+<span class="linenos"> 53</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 54</span><span class="sd">    Change codepath for supplied array backends.</span>
+<span class="linenos"> 55</span>
+<span class="linenos"> 56</span><span class="sd">    Some functions/methods cannot be written in module-agnostic fashion. The action of this decorator is summarized</span>
+<span class="linenos"> 57</span><span class="sd">    below:</span>
 <span class="linenos"> 58</span>
-<span class="linenos"> 59</span><span class="sd">    Parameters</span>
-<span class="linenos"> 60</span><span class="sd">    ----------</span>
-<span class="linenos"> 61</span><span class="sd">    i: VarName</span>
-<span class="linenos"> 62</span><span class="sd">        name of the array-like variable in `f` to base dispatch on.</span>
-<span class="linenos"> 63</span><span class="sd">    kwargs: ~collections.abc.Mapping</span>
-<span class="linenos"> 64</span>
-<span class="linenos"> 65</span><span class="sd">        * key[:py:class:`str`]: array backend short-name as defined in :py:class:`~pyxu.info.deps.NDArrayInfo`.</span>
-<span class="linenos"> 66</span><span class="sd">        * value[:py:class:`collections.abc.Callable`]: function/method to dispatch to.</span>
-<span class="linenos"> 67</span>
-<span class="linenos"> 68</span><span class="sd">    Notes</span>
-<span class="linenos"> 69</span><span class="sd">    -----</span>
-<span class="linenos"> 70</span><span class="sd">    Auto-dispatch via :py:func:`redirect` assumes the dispatcher/dispatchee have the same parameterization, i.e.:</span>
+<span class="linenos"> 59</span><span class="sd">    * Analyze an array-valued parameter (`x`) of the wrapped function/method (`f`).</span>
+<span class="linenos"> 60</span><span class="sd">    * If `x` lies in one of the supplied array namespaces: re-route execution to the specified function.</span>
+<span class="linenos"> 61</span><span class="sd">    * If `x` lies in none of the supplied array namespaces: execute `f`.</span>
+<span class="linenos"> 62</span>
+<span class="linenos"> 63</span><span class="sd">    Parameters</span>
+<span class="linenos"> 64</span><span class="sd">    ----------</span>
+<span class="linenos"> 65</span><span class="sd">    i: VarName</span>
+<span class="linenos"> 66</span><span class="sd">        name of the array-like variable in `f` to base dispatch on.</span>
+<span class="linenos"> 67</span><span class="sd">    kwargs: ~collections.abc.Mapping</span>
+<span class="linenos"> 68</span>
+<span class="linenos"> 69</span><span class="sd">        * key[:py:class:`str`]: array backend short-name as defined in :py:class:`~pyxu.info.deps.NDArrayInfo`.</span>
+<span class="linenos"> 70</span><span class="sd">        * value[:py:class:`collections.abc.Callable`]: function/method to dispatch to.</span>
 <span class="linenos"> 71</span>
-<span class="linenos"> 72</span><span class="sd">    * if `f` is a function -&gt; dispatch possible to another callable with identical signature (i.e., function or</span>
-<span class="linenos"> 73</span><span class="sd">      staticmethod)</span>
-<span class="linenos"> 74</span><span class="sd">    * if `f` is a staticmethod -&gt; dispatch possible to another callable with identical signature (i.e., function or</span>
-<span class="linenos"> 75</span><span class="sd">      staticmethod)</span>
-<span class="linenos"> 76</span><span class="sd">    * if `f` is an instance-method -&gt; dispatch to another instance-method of the class with identical signature.</span>
-<span class="linenos"> 77</span>
-<span class="linenos"> 78</span><span class="sd">    Example</span>
-<span class="linenos"> 79</span><span class="sd">    -------</span>
-<span class="linenos"> 80</span><span class="sd">    .. code-block:: python3</span>
+<span class="linenos"> 72</span><span class="sd">    Notes</span>
+<span class="linenos"> 73</span><span class="sd">    -----</span>
+<span class="linenos"> 74</span><span class="sd">    Auto-dispatch via :py:func:`redirect` assumes the dispatcher/dispatchee have the same parameterization, i.e.:</span>
+<span class="linenos"> 75</span>
+<span class="linenos"> 76</span><span class="sd">    * if `f` is a function -&gt; dispatch possible to another callable with identical signature (i.e., function or</span>
+<span class="linenos"> 77</span><span class="sd">      staticmethod)</span>
+<span class="linenos"> 78</span><span class="sd">    * if `f` is a staticmethod -&gt; dispatch possible to another callable with identical signature (i.e., function or</span>
+<span class="linenos"> 79</span><span class="sd">      staticmethod)</span>
+<span class="linenos"> 80</span><span class="sd">    * if `f` is an instance-method -&gt; dispatch to another instance-method of the class with identical signature.</span>
 <span class="linenos"> 81</span>
-<span class="linenos"> 82</span><span class="sd">       def f(x, y): return &quot;f&quot;</span>
-<span class="linenos"> 83</span>
-<span class="linenos"> 84</span><span class="sd">       @redirect(&#39;x&#39;, NUMPY=f)    # if &#39;x&#39; is of type NDArrayInfo.NUMPY, i.e. has</span>
-<span class="linenos"> 85</span><span class="sd">       def g(x, y): return &quot;g&quot;    # short-name &#39;NUMPY&#39; -&gt; reroute execution to `f`</span>
-<span class="linenos"> 86</span>
-<span class="linenos"> 87</span><span class="sd">       x1 = np.arange(5)</span>
-<span class="linenos"> 88</span><span class="sd">       x2 = da.array(x1)</span>
-<span class="linenos"> 89</span><span class="sd">       y = 1</span>
-<span class="linenos"> 90</span><span class="sd">       g(x1, y), g(x2, y)  # &#39;f&#39;, &#39;g&#39;</span>
-<span class="linenos"> 91</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 92</span>
-<span class="linenos"> 93</span>    <span class="k">def</span> <span class="nf">decorator</span><span class="p">(</span><span class="n">func</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">:</span>
-<span class="linenos"> 94</span>        <span class="nd">@functools</span><span class="o">.</span><span class="n">wraps</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
-<span class="linenos"> 95</span>        <span class="k">def</span> <span class="nf">wrapper</span><span class="p">(</span><span class="o">*</span><span class="n">ARGS</span><span class="p">,</span> <span class="o">**</span><span class="n">KWARGS</span><span class="p">):</span>
-<span class="linenos"> 96</span>            <span class="k">try</span><span class="p">:</span>
-<span class="linenos"> 97</span>                <span class="n">func_args</span> <span class="o">=</span> <span class="n">pxm</span><span class="o">.</span><span class="n">parse_params</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="o">*</span><span class="n">ARGS</span><span class="p">,</span> <span class="o">**</span><span class="n">KWARGS</span><span class="p">)</span>
-<span class="linenos"> 98</span>            <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
-<span class="linenos"> 99</span>                <span class="n">error_msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Could not parameterize </span><span class="si">{</span><span class="n">func</span><span class="si">}</span><span class="s2">().&quot;</span>
-<span class="linenos">100</span>                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">error_msg</span><span class="p">)</span> <span class="kn">from</span> <span class="nn">e</span>
-<span class="linenos">101</span>
-<span class="linenos">102</span>            <span class="k">if</span> <span class="n">i</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">func_args</span><span class="p">:</span>
-<span class="linenos">103</span>                <span class="n">error_msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Parameter[</span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">] not part of </span><span class="si">{</span><span class="n">func</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s2">() parameter list.&quot;</span>
-<span class="linenos">104</span>                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">error_msg</span><span class="p">)</span>
+<span class="linenos"> 82</span><span class="sd">    Example</span>
+<span class="linenos"> 83</span><span class="sd">    -------</span>
+<span class="linenos"> 84</span><span class="sd">    .. code-block:: python3</span>
+<span class="linenos"> 85</span>
+<span class="linenos"> 86</span><span class="sd">       def f(x, y): return &quot;f&quot;</span>
+<span class="linenos"> 87</span>
+<span class="linenos"> 88</span><span class="sd">       @redirect(&#39;x&#39;, NUMPY=f)    # if &#39;x&#39; is of type NDArrayInfo.NUMPY, i.e. has</span>
+<span class="linenos"> 89</span><span class="sd">       def g(x, y): return &quot;g&quot;    # short-name &#39;NUMPY&#39; -&gt; reroute execution to `f`</span>
+<span class="linenos"> 90</span>
+<span class="linenos"> 91</span><span class="sd">       x1 = np.arange(5)</span>
+<span class="linenos"> 92</span><span class="sd">       x2 = da.array(x1)</span>
+<span class="linenos"> 93</span><span class="sd">       y = 1</span>
+<span class="linenos"> 94</span><span class="sd">       g(x1, y), g(x2, y)  # &#39;f&#39;, &#39;g&#39;</span>
+<span class="linenos"> 95</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 96</span>
+<span class="linenos"> 97</span>    <span class="k">def</span> <span class="nf">decorator</span><span class="p">(</span><span class="n">func</span><span class="p">:</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Callable</span><span class="p">:</span>
+<span class="linenos"> 98</span>        <span class="nd">@functools</span><span class="o">.</span><span class="n">wraps</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
+<span class="linenos"> 99</span>        <span class="k">def</span> <span class="nf">wrapper</span><span class="p">(</span><span class="o">*</span><span class="n">ARGS</span><span class="p">,</span> <span class="o">**</span><span class="n">KWARGS</span><span class="p">):</span>
+<span class="linenos">100</span>            <span class="k">try</span><span class="p">:</span>
+<span class="linenos">101</span>                <span class="n">func_args</span> <span class="o">=</span> <span class="n">pxm</span><span class="o">.</span><span class="n">parse_params</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="o">*</span><span class="n">ARGS</span><span class="p">,</span> <span class="o">**</span><span class="n">KWARGS</span><span class="p">)</span>
+<span class="linenos">102</span>            <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
+<span class="linenos">103</span>                <span class="n">error_msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Could not parameterize </span><span class="si">{</span><span class="n">func</span><span class="si">}</span><span class="s2">().&quot;</span>
+<span class="linenos">104</span>                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">error_msg</span><span class="p">)</span> <span class="kn">from</span> <span class="nn">e</span>
 <span class="linenos">105</span>
-<span class="linenos">106</span>            <span class="n">ndi</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">func_args</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
-<span class="linenos">107</span>            <span class="k">if</span> <span class="p">(</span><span class="n">alt_func</span> <span class="o">:=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">ndi</span><span class="o">.</span><span class="n">name</span><span class="p">))</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">108</span>                <span class="n">out</span> <span class="o">=</span> <span class="n">alt_func</span><span class="p">(</span><span class="o">**</span><span class="n">func_args</span><span class="p">)</span>
-<span class="linenos">109</span>            <span class="k">else</span><span class="p">:</span>
-<span class="linenos">110</span>                <span class="n">out</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="o">**</span><span class="n">func_args</span><span class="p">)</span>
-<span class="linenos">111</span>
-<span class="linenos">112</span>            <span class="k">return</span> <span class="n">out</span>
-<span class="linenos">113</span>
-<span class="linenos">114</span>        <span class="k">return</span> <span class="n">wrapper</span>
+<span class="linenos">106</span>            <span class="k">if</span> <span class="n">i</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">func_args</span><span class="p">:</span>
+<span class="linenos">107</span>                <span class="n">error_msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Parameter[</span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">] not part of </span><span class="si">{</span><span class="n">func</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s2">() parameter list.&quot;</span>
+<span class="linenos">108</span>                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">error_msg</span><span class="p">)</span>
+<span class="linenos">109</span>
+<span class="linenos">110</span>            <span class="n">ndi</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">func_args</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<span class="linenos">111</span>            <span class="k">if</span> <span class="p">(</span><span class="n">alt_func</span> <span class="o">:=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">ndi</span><span class="o">.</span><span class="n">name</span><span class="p">))</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">112</span>                <span class="n">out</span> <span class="o">=</span> <span class="n">alt_func</span><span class="p">(</span><span class="o">**</span><span class="n">func_args</span><span class="p">)</span>
+<span class="linenos">113</span>            <span class="k">else</span><span class="p">:</span>
+<span class="linenos">114</span>                <span class="n">out</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="o">**</span><span class="n">func_args</span><span class="p">)</span>
 <span class="linenos">115</span>
-<span class="linenos">116</span>    <span class="k">return</span> <span class="n">decorator</span></div>
+<span class="linenos">116</span>            <span class="k">return</span> <span class="n">out</span>
+<span class="linenos">117</span>
+<span class="linenos">118</span>        <span class="k">return</span> <span class="n">wrapper</span>
+<span class="linenos">119</span>
+<span class="linenos">120</span>    <span class="k">return</span> <span class="n">decorator</span></div>
+
+<span class="linenos">121</span>
+<span class="linenos">122</span>
+<div class="viewcode-block" id="compute">
+<a class="viewcode-back" href="../../../api/util/array_module.html#pyxu.util.compute">[docs]</a>
+<span class="linenos">123</span><span class="k">def</span> <span class="nf">compute</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="n">mode</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;compute&quot;</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos">124</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">125</span><span class="sd">    Force computation of Dask collections.</span>
+<span class="linenos">126</span>
+<span class="linenos">127</span><span class="sd">    Parameters</span>
+<span class="linenos">128</span><span class="sd">    ----------</span>
+<span class="linenos">129</span><span class="sd">    \*args: object, list</span>
+<span class="linenos">130</span><span class="sd">        Any number of objects.  If it is a dask object, it is evaluated and the result is returned.  Non-dask arguments</span>
+<span class="linenos">131</span><span class="sd">        are passed through unchanged.  Python collections are traversed to find/evaluate dask objects within.  (Use</span>
+<span class="linenos">132</span><span class="sd">        `traverse` =False to disable this behavior.)</span>
+<span class="linenos">133</span><span class="sd">    mode: str</span>
+<span class="linenos">134</span><span class="sd">        Dask evaluation strategy: compute or persist.</span>
+<span class="linenos">135</span><span class="sd">    \*\*kwargs: dict</span>
+<span class="linenos">136</span><span class="sd">        Extra keyword parameters forwarded to :py:func:`dask.compute` or :py:func:`dask.persist`.</span>
+<span class="linenos">137</span>
+<span class="linenos">138</span><span class="sd">    Returns</span>
+<span class="linenos">139</span><span class="sd">    -------</span>
+<span class="linenos">140</span><span class="sd">    \*cargs: object, list</span>
+<span class="linenos">141</span><span class="sd">        Evaluated objects. Non-dask arguments are passed through unchanged.</span>
+<span class="linenos">142</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">143</span>    <span class="k">try</span><span class="p">:</span>
+<span class="linenos">144</span>        <span class="n">func</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">compute</span><span class="o">=</span><span class="n">dask</span><span class="o">.</span><span class="n">compute</span><span class="p">,</span> <span class="n">persist</span><span class="o">=</span><span class="n">dask</span><span class="o">.</span><span class="n">persist</span><span class="p">)[</span><span class="n">mode</span><span class="o">.</span><span class="n">lower</span><span class="p">()]</span>
+<span class="linenos">145</span>    <span class="k">except</span> <span class="ne">Exception</span><span class="p">:</span>
+<span class="linenos">146</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;mode: expected compute/persist, got </span><span class="si">{</span><span class="n">mode</span><span class="si">}</span><span class="s2">.&quot;</span><span class="p">)</span>
+<span class="linenos">147</span>
+<span class="linenos">148</span>    <span class="n">cargs</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos">149</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<span class="linenos">150</span>        <span class="n">cargs</span> <span class="o">=</span> <span class="n">cargs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<span class="linenos">151</span>    <span class="k">return</span> <span class="n">cargs</span></div>
+
+<span class="linenos">152</span>
+<span class="linenos">153</span>
+<div class="viewcode-block" id="to_NUMPY">
+<a class="viewcode-back" href="../../../api/util/array_module.html#pyxu.util.to_NUMPY">[docs]</a>
+<span class="linenos">154</span><span class="k">def</span> <span class="nf">to_NUMPY</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos">155</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">156</span><span class="sd">    Convert an array from a specific backend to NUMPY.</span>
+<span class="linenos">157</span>
+<span class="linenos">158</span><span class="sd">    Parameters</span>
+<span class="linenos">159</span><span class="sd">    ----------</span>
+<span class="linenos">160</span><span class="sd">    x: NDArray</span>
+<span class="linenos">161</span><span class="sd">        Array to be converted.</span>
+<span class="linenos">162</span>
+<span class="linenos">163</span><span class="sd">    Returns</span>
+<span class="linenos">164</span><span class="sd">    -------</span>
+<span class="linenos">165</span><span class="sd">    y: NDArray</span>
+<span class="linenos">166</span><span class="sd">        Array with NumPy backend.</span>
+<span class="linenos">167</span>
+<span class="linenos">168</span><span class="sd">    Notes</span>
+<span class="linenos">169</span><span class="sd">    -----</span>
+<span class="linenos">170</span><span class="sd">    This function is a no-op if the array is already a NumPy array.</span>
+<span class="linenos">171</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">172</span>    <span class="n">N</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span>
+<span class="linenos">173</span>    <span class="n">ndi</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="linenos">174</span>    <span class="k">if</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">:</span>
+<span class="linenos">175</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span>
+<span class="linenos">176</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">DASK</span><span class="p">:</span>
+<span class="linenos">177</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">compute</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="linenos">178</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">CUPY</span><span class="p">:</span>
+<span class="linenos">179</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">get</span><span class="p">()</span>
+<span class="linenos">180</span>    <span class="k">else</span><span class="p">:</span>
+<span class="linenos">181</span>        <span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Dev-action required: define behaviour for </span><span class="si">{</span><span class="n">ndi</span><span class="si">}</span><span class="s2">.&quot;</span>
+<span class="linenos">182</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
+<span class="linenos">183</span>    <span class="k">return</span> <span class="n">y</span></div>
 
 </pre></div>
 
diff --git a/_modules/pyxu/util/complex.html b/_modules/pyxu/util/complex.html
index da7bee8c..776e4064 100644
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+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
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-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
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+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
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-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -464,7 +464,7 @@ <h1>Source code for pyxu.util.complex</h1><div class="highlight"><pre>
 <span class="linenos"> 11</span>
 <span class="linenos"> 12</span>
 <div class="viewcode-block" id="view_as_complex">
-<a class="viewcode-back" href="../../../api/util.html#pyxu.util.view_as_complex">[docs]</a>
+<a class="viewcode-back" href="../../../api/util/complex.html#pyxu.util.view_as_complex">[docs]</a>
 <span class="linenos"> 13</span><span class="k">def</span> <span class="nf">view_as_complex</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos"> 14</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 15</span><span class="sd">    View real-valued array as its complex-valued bijection.  (Inverse of :py:func:`~pyxu.util.view_as_real`.)</span>
@@ -521,7 +521,7 @@ <h1>Source code for pyxu.util.complex</h1><div class="highlight"><pre>
 <span class="linenos"> 65</span>
 <span class="linenos"> 66</span>
 <div class="viewcode-block" id="view_as_real">
-<a class="viewcode-back" href="../../../api/util.html#pyxu.util.view_as_real">[docs]</a>
+<a class="viewcode-back" href="../../../api/util/complex.html#pyxu.util.view_as_real">[docs]</a>
 <span class="linenos"> 67</span><span class="k">def</span> <span class="nf">view_as_real</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
 <span class="linenos"> 68</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos"> 69</span><span class="sd">    View complex-valued array as its real-valued bijection.  (Inverse of :py:func:`~pyxu.util.view_as_complex`.)</span>
@@ -596,7 +596,7 @@ <h1>Source code for pyxu.util.complex</h1><div class="highlight"><pre>
 <span class="linenos">137</span>
 <span class="linenos">138</span>
 <div class="viewcode-block" id="view_as_real_mat">
-<a class="viewcode-back" href="../../../api/util.html#pyxu.util.view_as_real_mat">[docs]</a>
+<a class="viewcode-back" href="../../../api/util/complex.html#pyxu.util.view_as_real_mat">[docs]</a>
 <span class="linenos">139</span><span class="k">def</span> <span class="nf">view_as_real_mat</span><span class="p">(</span>
 <span class="linenos">140</span>    <span class="n">cmat</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span>
 <span class="linenos">141</span>    <span class="n">real_input</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
@@ -688,7 +688,7 @@ <h1>Source code for pyxu.util.complex</h1><div class="highlight"><pre>
 <span class="linenos">226</span>
 <span class="linenos">227</span>
 <div class="viewcode-block" id="view_as_complex_mat">
-<a class="viewcode-back" href="../../../api/util.html#pyxu.util.view_as_complex_mat">[docs]</a>
+<a class="viewcode-back" href="../../../api/util/complex.html#pyxu.util.view_as_complex_mat">[docs]</a>
 <span class="linenos">228</span><span class="k">def</span> <span class="nf">view_as_complex_mat</span><span class="p">(</span>
 <span class="linenos">229</span>    <span class="n">rmat</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span>
 <span class="linenos">230</span>    <span class="n">real_input</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
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-  <h1>Source code for pyxu.util.inspect</h1><div class="highlight"><pre>
-<span></span><span class="linenos"> 1</span><span class="kn">import</span> <span class="nn">collections.abc</span> <span class="k">as</span> <span class="nn">cabc</span>
-<span class="linenos"> 2</span><span class="kn">import</span> <span class="nn">importlib</span>
-<span class="linenos"> 3</span><span class="kn">import</span> <span class="nn">inspect</span>
-<span class="linenos"> 4</span><span class="kn">import</span> <span class="nn">types</span>
-<span class="linenos"> 5</span>
-<span class="linenos"> 6</span><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
-<span class="linenos"> 7</span>    <span class="s2">&quot;import_module&quot;</span><span class="p">,</span>
-<span class="linenos"> 8</span>    <span class="s2">&quot;parse_params&quot;</span><span class="p">,</span>
-<span class="linenos"> 9</span><span class="p">]</span>
-<span class="linenos">10</span>
-<span class="linenos">11</span>
-<div class="viewcode-block" id="parse_params">
-<a class="viewcode-back" href="../../../api/util.html#pyxu.util.inspect.parse_params">[docs]</a>
-<span class="linenos">12</span><span class="k">def</span> <span class="nf">parse_params</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Mapping</span><span class="p">:</span>
-<span class="linenos">13</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">14</span><span class="sd">    Get function parameterization.</span>
-<span class="linenos">15</span>
-<span class="linenos">16</span><span class="sd">    Returns</span>
-<span class="linenos">17</span><span class="sd">    -------</span>
-<span class="linenos">18</span><span class="sd">    params: ~collections.abc.Mapping</span>
-<span class="linenos">19</span><span class="sd">        (key, value) params as seen in body of `func` when called via `func(*args, **kwargs)`.</span>
-<span class="linenos">20</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">21</span>    <span class="n">sig</span> <span class="o">=</span> <span class="n">inspect</span><span class="o">.</span><span class="n">Signature</span><span class="o">.</span><span class="n">from_callable</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
-<span class="linenos">22</span>    <span class="n">f_args</span> <span class="o">=</span> <span class="n">sig</span><span class="o">.</span><span class="n">bind</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos">23</span>    <span class="n">f_args</span><span class="o">.</span><span class="n">apply_defaults</span><span class="p">()</span>
-<span class="linenos">24</span>
-<span class="linenos">25</span>    <span class="n">params</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span>
-<span class="linenos">26</span>        <span class="nb">zip</span><span class="p">(</span><span class="n">f_args</span><span class="o">.</span><span class="n">arguments</span><span class="o">.</span><span class="n">keys</span><span class="p">(),</span> <span class="n">f_args</span><span class="o">.</span><span class="n">args</span><span class="p">),</span>  <span class="c1"># positional arguments</span>
-<span class="linenos">27</span>        <span class="o">**</span><span class="n">f_args</span><span class="o">.</span><span class="n">kwargs</span><span class="p">,</span>
-<span class="linenos">28</span>    <span class="p">)</span>
-<span class="linenos">29</span>    <span class="k">return</span> <span class="n">params</span></div>
-
-<span class="linenos">30</span>
-<span class="linenos">31</span>
-<div class="viewcode-block" id="import_module">
-<a class="viewcode-back" href="../../../api/util.html#pyxu.util.inspect.import_module">[docs]</a>
-<span class="linenos">32</span><span class="k">def</span> <span class="nf">import_module</span><span class="p">(</span><span class="n">name</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">fail_on_error</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">:</span>
-<span class="linenos">33</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">34</span><span class="sd">    Load a Python module dynamically.</span>
-<span class="linenos">35</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">36</span>    <span class="k">try</span><span class="p">:</span>
-<span class="linenos">37</span>        <span class="n">pkg</span> <span class="o">=</span> <span class="n">importlib</span><span class="o">.</span><span class="n">import_module</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
-<span class="linenos">38</span>    <span class="k">except</span> <span class="ne">ModuleNotFoundError</span><span class="p">:</span>
-<span class="linenos">39</span>        <span class="k">if</span> <span class="n">fail_on_error</span><span class="p">:</span>
-<span class="linenos">40</span>            <span class="k">raise</span>
-<span class="linenos">41</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">42</span>            <span class="n">pkg</span> <span class="o">=</span> <span class="kc">None</span>
-<span class="linenos">43</span>    <span class="k">return</span> <span class="n">pkg</span></div>
-
-</pre></div>
-
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diff --git a/_modules/pyxu/util/misc.html b/_modules/pyxu/util/misc.html
index 15d56129..0f4eb4bf 100644
--- a/_modules/pyxu/util/misc.html
+++ b/_modules/pyxu/util/misc.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
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@@ -37,13 +37,13 @@
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     <link rel="stylesheet" type="text/css" href="../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
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     <script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -456,366 +456,294 @@ <h1>Source code for pyxu.util.misc</h1><div class="highlight"><pre>
 <span class="linenos">  3</span><span class="kn">import</span> <span class="nn">inspect</span>
 <span class="linenos">  4</span><span class="kn">import</span> <span class="nn">types</span>
 <span class="linenos">  5</span>
-<span class="linenos">  6</span><span class="kn">import</span> <span class="nn">dask</span>
-<span class="linenos">  7</span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="linenos">  8</span>
-<span class="linenos">  9</span><span class="kn">import</span> <span class="nn">pyxu.info.deps</span> <span class="k">as</span> <span class="nn">pxd</span>
-<span class="linenos"> 10</span><span class="kn">import</span> <span class="nn">pyxu.info.ptype</span> <span class="k">as</span> <span class="nn">pxt</span>
-<span class="linenos"> 11</span>
-<span class="linenos"> 12</span><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
-<span class="linenos"> 13</span>    <span class="s2">&quot;compute&quot;</span><span class="p">,</span>
-<span class="linenos"> 14</span>    <span class="s2">&quot;copy_if_unsafe&quot;</span><span class="p">,</span>
-<span class="linenos"> 15</span>    <span class="s2">&quot;import_module&quot;</span><span class="p">,</span>
-<span class="linenos"> 16</span>    <span class="s2">&quot;infer_composition_shape&quot;</span><span class="p">,</span>
-<span class="linenos"> 17</span>    <span class="s2">&quot;infer_sum_shape&quot;</span><span class="p">,</span>
-<span class="linenos"> 18</span>    <span class="s2">&quot;next_fast_len&quot;</span><span class="p">,</span>
-<span class="linenos"> 19</span>    <span class="s2">&quot;parse_params&quot;</span><span class="p">,</span>
-<span class="linenos"> 20</span>    <span class="s2">&quot;read_only&quot;</span><span class="p">,</span>
-<span class="linenos"> 21</span>    <span class="s2">&quot;to_NUMPY&quot;</span><span class="p">,</span>
-<span class="linenos"> 22</span><span class="p">]</span>
-<span class="linenos"> 23</span>
-<span class="linenos"> 24</span>
+<span class="linenos">  6</span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="linenos">  7</span>
+<span class="linenos">  8</span><span class="kn">import</span> <span class="nn">pyxu.info.deps</span> <span class="k">as</span> <span class="nn">pxd</span>
+<span class="linenos">  9</span><span class="kn">import</span> <span class="nn">pyxu.info.ptype</span> <span class="k">as</span> <span class="nn">pxt</span>
+<span class="linenos"> 10</span>
+<span class="linenos"> 11</span><span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span>
+<span class="linenos"> 12</span>    <span class="s2">&quot;copy_if_unsafe&quot;</span><span class="p">,</span>
+<span class="linenos"> 13</span>    <span class="s2">&quot;import_module&quot;</span><span class="p">,</span>
+<span class="linenos"> 14</span>    <span class="s2">&quot;infer_composition_shape&quot;</span><span class="p">,</span>
+<span class="linenos"> 15</span>    <span class="s2">&quot;infer_sum_shape&quot;</span><span class="p">,</span>
+<span class="linenos"> 16</span>    <span class="s2">&quot;next_fast_len&quot;</span><span class="p">,</span>
+<span class="linenos"> 17</span>    <span class="s2">&quot;parse_params&quot;</span><span class="p">,</span>
+<span class="linenos"> 18</span>    <span class="s2">&quot;read_only&quot;</span><span class="p">,</span>
+<span class="linenos"> 19</span><span class="p">]</span>
+<span class="linenos"> 20</span>
+<span class="linenos"> 21</span>
 <div class="viewcode-block" id="next_fast_len">
 <a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.next_fast_len">[docs]</a>
-<span class="linenos"> 25</span><span class="k">def</span> <span class="nf">next_fast_len</span><span class="p">(</span><span class="n">N</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span> <span class="n">even</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">:</span>
-<span class="linenos"> 26</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 27</span><span class="sd">    Compute the next `5-smooth number &lt;https://en.wikipedia.org/wiki/Smooth_number&gt;`_ greater-or-equal to `N`.</span>
-<span class="linenos"> 28</span>
-<span class="linenos"> 29</span><span class="sd">    If `even=True`, then ensure the next 5-smooth number is even-valued.</span>
-<span class="linenos"> 30</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 31</span>    <span class="c1"># warning: scipy.fftpack.next_fast_len() != scipy.fft.next_fast_len()</span>
-<span class="linenos"> 32</span>    <span class="kn">from</span> <span class="nn">scipy.fftpack</span> <span class="kn">import</span> <span class="n">next_fast_len</span>
-<span class="linenos"> 33</span>
-<span class="linenos"> 34</span>    <span class="n">N5</span> <span class="o">=</span> <span class="n">next_fast_len</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">N</span><span class="p">))</span>
-<span class="linenos"> 35</span>
-<span class="linenos"> 36</span>    <span class="n">is_even</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span>
-<span class="linenos"> 37</span>    <span class="k">if</span> <span class="p">(</span><span class="ow">not</span> <span class="n">is_even</span><span class="p">(</span><span class="n">N5</span><span class="p">))</span> <span class="ow">and</span> <span class="n">even</span><span class="p">:</span>
-<span class="linenos"> 38</span>        <span class="k">while</span> <span class="ow">not</span> <span class="n">is_even</span><span class="p">(</span><span class="n">N5</span> <span class="o">:=</span> <span class="n">next_fast_len</span><span class="p">(</span><span class="n">N5</span><span class="p">)):</span>
-<span class="linenos"> 39</span>            <span class="n">N5</span> <span class="o">+=</span> <span class="mi">1</span>
+<span class="linenos"> 22</span><span class="k">def</span> <span class="nf">next_fast_len</span><span class="p">(</span><span class="n">N</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span> <span class="n">even</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">:</span>
+<span class="linenos"> 23</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 24</span><span class="sd">    Compute the next `5-smooth number &lt;https://en.wikipedia.org/wiki/Smooth_number&gt;`_ greater-or-equal to `N`.</span>
+<span class="linenos"> 25</span>
+<span class="linenos"> 26</span><span class="sd">    If `even=True`, then ensure the next 5-smooth number is even-valued.</span>
+<span class="linenos"> 27</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 28</span>    <span class="c1"># warning: scipy.fftpack.next_fast_len() != scipy.fft.next_fast_len()</span>
+<span class="linenos"> 29</span>    <span class="kn">from</span> <span class="nn">scipy.fftpack</span> <span class="kn">import</span> <span class="n">next_fast_len</span>
+<span class="linenos"> 30</span>
+<span class="linenos"> 31</span>    <span class="n">N5</span> <span class="o">=</span> <span class="n">next_fast_len</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">N</span><span class="p">))</span>
+<span class="linenos"> 32</span>
+<span class="linenos"> 33</span>    <span class="n">is_even</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span>
+<span class="linenos"> 34</span>    <span class="k">if</span> <span class="p">(</span><span class="ow">not</span> <span class="n">is_even</span><span class="p">(</span><span class="n">N5</span><span class="p">))</span> <span class="ow">and</span> <span class="n">even</span><span class="p">:</span>
+<span class="linenos"> 35</span>        <span class="k">while</span> <span class="ow">not</span> <span class="n">is_even</span><span class="p">(</span><span class="n">N5</span> <span class="o">:=</span> <span class="n">next_fast_len</span><span class="p">(</span><span class="n">N5</span><span class="p">)):</span>
+<span class="linenos"> 36</span>            <span class="n">N5</span> <span class="o">+=</span> <span class="mi">1</span>
+<span class="linenos"> 37</span>
+<span class="linenos"> 38</span>    <span class="k">return</span> <span class="n">N5</span></div>
+
+<span class="linenos"> 39</span>
 <span class="linenos"> 40</span>
-<span class="linenos"> 41</span>    <span class="k">return</span> <span class="n">N5</span></div>
-
-<span class="linenos"> 42</span>
-<span class="linenos"> 43</span>
 <div class="viewcode-block" id="peaks">
 <a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.peaks">[docs]</a>
-<span class="linenos"> 44</span><span class="k">def</span> <span class="nf">peaks</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 45</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 46</span><span class="sd">    Matlab 2D peaks function.</span>
+<span class="linenos"> 41</span><span class="k">def</span> <span class="nf">peaks</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 42</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 43</span><span class="sd">    Matlab 2D peaks function.</span>
+<span class="linenos"> 44</span>
+<span class="linenos"> 45</span><span class="sd">    Peaks is a function of two variables, obtained by translating and scaling Gaussian distributions.  (See `Matlab&#39;s</span>
+<span class="linenos"> 46</span><span class="sd">    peaks function &lt;https://www.mathworks.com/help/matlab/ref/peaks.html&gt;`_.)</span>
 <span class="linenos"> 47</span>
-<span class="linenos"> 48</span><span class="sd">    Peaks is a function of two variables, obtained by translating and scaling Gaussian distributions.  (See `Matlab&#39;s</span>
-<span class="linenos"> 49</span><span class="sd">    peaks function &lt;https://www.mathworks.com/help/matlab/ref/peaks.html&gt;`_.)</span>
-<span class="linenos"> 50</span>
-<span class="linenos"> 51</span><span class="sd">    This function is useful for testing purposes.</span>
-<span class="linenos"> 52</span>
-<span class="linenos"> 53</span><span class="sd">    Parameters</span>
-<span class="linenos"> 54</span><span class="sd">    ----------</span>
-<span class="linenos"> 55</span><span class="sd">    x: NDArray</span>
-<span class="linenos"> 56</span><span class="sd">        X coordinates.</span>
-<span class="linenos"> 57</span><span class="sd">    y: NDArray</span>
-<span class="linenos"> 58</span><span class="sd">        Y coordinates.</span>
-<span class="linenos"> 59</span>
-<span class="linenos"> 60</span><span class="sd">    Returns</span>
-<span class="linenos"> 61</span><span class="sd">    -------</span>
-<span class="linenos"> 62</span><span class="sd">    z: NDArray</span>
-<span class="linenos"> 63</span><span class="sd">        Values of the 2D function ``peaks`` at the points specified by the entries of `x` and `y`.</span>
+<span class="linenos"> 48</span><span class="sd">    This function is useful for testing purposes.</span>
+<span class="linenos"> 49</span>
+<span class="linenos"> 50</span><span class="sd">    Parameters</span>
+<span class="linenos"> 51</span><span class="sd">    ----------</span>
+<span class="linenos"> 52</span><span class="sd">    x: NDArray</span>
+<span class="linenos"> 53</span><span class="sd">        X coordinates.</span>
+<span class="linenos"> 54</span><span class="sd">    y: NDArray</span>
+<span class="linenos"> 55</span><span class="sd">        Y coordinates.</span>
+<span class="linenos"> 56</span>
+<span class="linenos"> 57</span><span class="sd">    Returns</span>
+<span class="linenos"> 58</span><span class="sd">    -------</span>
+<span class="linenos"> 59</span><span class="sd">    z: NDArray</span>
+<span class="linenos"> 60</span><span class="sd">        Values of the 2D function ``peaks`` at the points specified by the entries of `x` and `y`.</span>
+<span class="linenos"> 61</span>
+<span class="linenos"> 62</span><span class="sd">    Examples</span>
+<span class="linenos"> 63</span><span class="sd">    --------</span>
 <span class="linenos"> 64</span>
-<span class="linenos"> 65</span><span class="sd">    Examples</span>
-<span class="linenos"> 66</span><span class="sd">    --------</span>
-<span class="linenos"> 67</span>
-<span class="linenos"> 68</span><span class="sd">    .. plot::</span>
-<span class="linenos"> 69</span>
-<span class="linenos"> 70</span><span class="sd">       import numpy as np</span>
-<span class="linenos"> 71</span><span class="sd">       import matplotlib.pyplot as plt</span>
-<span class="linenos"> 72</span><span class="sd">       from pyxu.util.misc import peaks</span>
-<span class="linenos"> 73</span>
-<span class="linenos"> 74</span><span class="sd">       x = np.linspace(-3, 3, 1000)</span>
-<span class="linenos"> 75</span><span class="sd">       xx, yy = np.meshgrid(x, x)</span>
-<span class="linenos"> 76</span><span class="sd">       z = peaks(xx, yy)</span>
-<span class="linenos"> 77</span><span class="sd">       plt.figure()</span>
-<span class="linenos"> 78</span><span class="sd">       plt.imshow(z)</span>
-<span class="linenos"> 79</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 80</span>    <span class="n">ndi</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="linenos"> 81</span>    <span class="n">xp</span> <span class="o">=</span> <span class="n">ndi</span><span class="o">.</span><span class="n">module</span><span class="p">()</span>
-<span class="linenos"> 82</span>
-<span class="linenos"> 83</span>    <span class="n">a</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="p">((</span><span class="mi">1</span> <span class="o">-</span> <span class="n">x</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">xp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
-<span class="linenos"> 84</span>    <span class="n">b</span> <span class="o">=</span> <span class="o">-</span><span class="mi">10</span> <span class="o">*</span> <span class="p">((</span><span class="n">x</span> <span class="o">/</span> <span class="mi">5</span><span class="p">)</span> <span class="o">-</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="n">y</span><span class="o">**</span><span class="mi">5</span><span class="p">)</span> <span class="o">*</span> <span class="n">xp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span>
-<span class="linenos"> 85</span>    <span class="n">c</span> <span class="o">=</span> <span class="o">-</span><span class="n">xp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">((</span><span class="n">x</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span> <span class="o">/</span> <span class="mi">3</span>
-<span class="linenos"> 86</span>    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span> <span class="o">+</span> <span class="n">c</span>
-<span class="linenos"> 87</span>    <span class="k">return</span> <span class="n">z</span></div>
-
-<span class="linenos"> 88</span>
-<span class="linenos"> 89</span>
+<span class="linenos"> 65</span><span class="sd">    .. plot::</span>
+<span class="linenos"> 66</span>
+<span class="linenos"> 67</span><span class="sd">       import numpy as np</span>
+<span class="linenos"> 68</span><span class="sd">       import matplotlib.pyplot as plt</span>
+<span class="linenos"> 69</span><span class="sd">       from pyxu.util.misc import peaks</span>
+<span class="linenos"> 70</span>
+<span class="linenos"> 71</span><span class="sd">       x = np.linspace(-3, 3, 1000)</span>
+<span class="linenos"> 72</span><span class="sd">       xx, yy = np.meshgrid(x, x)</span>
+<span class="linenos"> 73</span><span class="sd">       z = peaks(xx, yy)</span>
+<span class="linenos"> 74</span><span class="sd">       plt.figure()</span>
+<span class="linenos"> 75</span><span class="sd">       plt.imshow(z)</span>
+<span class="linenos"> 76</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 77</span>    <span class="n">ndi</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="linenos"> 78</span>    <span class="n">xp</span> <span class="o">=</span> <span class="n">ndi</span><span class="o">.</span><span class="n">module</span><span class="p">()</span>
+<span class="linenos"> 79</span>
+<span class="linenos"> 80</span>    <span class="n">a</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="p">((</span><span class="mi">1</span> <span class="o">-</span> <span class="n">x</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">xp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
+<span class="linenos"> 81</span>    <span class="n">b</span> <span class="o">=</span> <span class="o">-</span><span class="mi">10</span> <span class="o">*</span> <span class="p">((</span><span class="n">x</span> <span class="o">/</span> <span class="mi">5</span><span class="p">)</span> <span class="o">-</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span> <span class="o">-</span> <span class="n">y</span><span class="o">**</span><span class="mi">5</span><span class="p">)</span> <span class="o">*</span> <span class="n">xp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span>
+<span class="linenos"> 82</span>    <span class="n">c</span> <span class="o">=</span> <span class="o">-</span><span class="n">xp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">((</span><span class="n">x</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="n">y</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span> <span class="o">/</span> <span class="mi">3</span>
+<span class="linenos"> 83</span>    <span class="n">z</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span> <span class="o">+</span> <span class="n">c</span>
+<span class="linenos"> 84</span>    <span class="k">return</span> <span class="n">z</span></div>
+
+<span class="linenos"> 85</span>
+<span class="linenos"> 86</span>
 <div class="viewcode-block" id="star_like_sample">
 <a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.star_like_sample">[docs]</a>
-<span class="linenos"> 90</span><span class="k">def</span> <span class="nf">star_like_sample</span><span class="p">(</span>
-<span class="linenos"> 91</span>    <span class="n">N</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
-<span class="linenos"> 92</span>    <span class="n">w</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
-<span class="linenos"> 93</span>    <span class="n">s</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span>
-<span class="linenos"> 94</span>    <span class="n">po</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
-<span class="linenos"> 95</span>    <span class="n">x0</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span>
-<span class="linenos"> 96</span>    <span class="n">ndi</span><span class="p">:</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">,</span>
-<span class="linenos"> 97</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos"> 98</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos"> 99</span><span class="sd">    Star-like test image.</span>
-<span class="linenos">100</span>
-<span class="linenos">101</span><span class="sd">    Generates a (N, N) square image of a star-like object normalized between 0 and 1.  Based on `GlobalBioIm&#39;s</span>
-<span class="linenos">102</span><span class="sd">    StarLikeSample function</span>
-<span class="linenos">103</span><span class="sd">    &lt;https://github.com/Biomedical-Imaging-Group/GlobalBioIm/blob/master/Util/StarLikeSample.m&gt;`_.  This function is</span>
-<span class="linenos">104</span><span class="sd">    useful for testing purposes as it contains high-frequency information.</span>
-<span class="linenos">105</span>
-<span class="linenos">106</span><span class="sd">    Parameters</span>
-<span class="linenos">107</span><span class="sd">    ----------</span>
-<span class="linenos">108</span><span class="sd">    N: Integer</span>
-<span class="linenos">109</span><span class="sd">        Size of the image (must be an even number).</span>
-<span class="linenos">110</span><span class="sd">    w: Integer</span>
-<span class="linenos">111</span><span class="sd">        The number of branches of the sample will be 4*w.</span>
-<span class="linenos">112</span><span class="sd">    s: Real</span>
-<span class="linenos">113</span><span class="sd">        Slope of the sigmoid function :math:`\frac1{1+\exp[s (x-x_{0})]}` attenuating the boundaries.</span>
-<span class="linenos">114</span><span class="sd">    po: Integer</span>
-<span class="linenos">115</span><span class="sd">        Power-raising factor for the final image (to have smoother edges).</span>
-<span class="linenos">116</span><span class="sd">    x0: Real</span>
-<span class="linenos">117</span><span class="sd">        Radial shift of the sigmoid function :math:`\frac1{1+\exp[s (x-x_{0})]}`.</span>
-<span class="linenos">118</span><span class="sd">    ndi: NDArrayInfo</span>
-<span class="linenos">119</span><span class="sd">        Desired array module for the output.</span>
-<span class="linenos">120</span>
-<span class="linenos">121</span><span class="sd">    Returns</span>
-<span class="linenos">122</span><span class="sd">    -------</span>
-<span class="linenos">123</span><span class="sd">    image: NDArray</span>
-<span class="linenos">124</span><span class="sd">        (N, N) image of star-like sample.</span>
-<span class="linenos">125</span>
-<span class="linenos">126</span><span class="sd">    Examples</span>
-<span class="linenos">127</span><span class="sd">    --------</span>
-<span class="linenos">128</span><span class="sd">    .. plot::</span>
-<span class="linenos">129</span>
-<span class="linenos">130</span><span class="sd">       import numpy as np</span>
-<span class="linenos">131</span><span class="sd">       import matplotlib.pyplot as plt</span>
-<span class="linenos">132</span><span class="sd">       from pyxu.util.misc import star_like_sample</span>
-<span class="linenos">133</span>
-<span class="linenos">134</span><span class="sd">       star = star_like_sample(N=256, w=8, s=20, po=3, x0=0.7)</span>
-<span class="linenos">135</span><span class="sd">       plt.figure()</span>
-<span class="linenos">136</span><span class="sd">       plt.imshow(star)</span>
-<span class="linenos">137</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">138</span>    <span class="k">assert</span> <span class="n">N</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span>
-<span class="linenos">139</span>    <span class="n">xp</span> <span class="o">=</span> <span class="n">ndi</span><span class="o">.</span><span class="n">module</span><span class="p">()</span>
-<span class="linenos">140</span>
-<span class="linenos">141</span>    <span class="n">grid</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
-<span class="linenos">142</span>    <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">grid</span><span class="p">)</span>
-<span class="linenos">143</span>    <span class="n">theta</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="linenos">144</span>    <span class="n">image</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">xp</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">w</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
-<span class="linenos">145</span>    <span class="n">image</span> <span class="o">/=</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">xp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">s</span> <span class="o">*</span> <span class="p">(</span><span class="n">xp</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">y</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="n">x0</span><span class="p">))</span>
-<span class="linenos">146</span>    <span class="n">image</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
-<span class="linenos">147</span>    <span class="n">image</span> <span class="o">**=</span> <span class="n">po</span>
-<span class="linenos">148</span>    <span class="n">image</span> <span class="o">/=</span> <span class="n">xp</span><span class="o">.</span><span class="n">amax</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<span class="linenos">149</span>    <span class="k">return</span> <span class="n">image</span></div>
-
-<span class="linenos">150</span>
-<span class="linenos">151</span>
+<span class="linenos"> 87</span><span class="k">def</span> <span class="nf">star_like_sample</span><span class="p">(</span>
+<span class="linenos"> 88</span>    <span class="n">N</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
+<span class="linenos"> 89</span>    <span class="n">w</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
+<span class="linenos"> 90</span>    <span class="n">s</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span>
+<span class="linenos"> 91</span>    <span class="n">po</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Integer</span><span class="p">,</span>
+<span class="linenos"> 92</span>    <span class="n">x0</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span>
+<span class="linenos"> 93</span>    <span class="n">ndi</span><span class="p">:</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">,</span>
+<span class="linenos"> 94</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos"> 95</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos"> 96</span><span class="sd">    Star-like test image.</span>
+<span class="linenos"> 97</span>
+<span class="linenos"> 98</span><span class="sd">    Generates a (N, N) square image of a star-like object normalized between 0 and 1.  Based on `GlobalBioIm&#39;s</span>
+<span class="linenos"> 99</span><span class="sd">    StarLikeSample function</span>
+<span class="linenos">100</span><span class="sd">    &lt;https://github.com/Biomedical-Imaging-Group/GlobalBioIm/blob/master/Util/StarLikeSample.m&gt;`_.  This function is</span>
+<span class="linenos">101</span><span class="sd">    useful for testing purposes as it contains high-frequency information.</span>
+<span class="linenos">102</span>
+<span class="linenos">103</span><span class="sd">    Parameters</span>
+<span class="linenos">104</span><span class="sd">    ----------</span>
+<span class="linenos">105</span><span class="sd">    N: Integer</span>
+<span class="linenos">106</span><span class="sd">        Size of the image (must be an even number).</span>
+<span class="linenos">107</span><span class="sd">    w: Integer</span>
+<span class="linenos">108</span><span class="sd">        The number of branches of the sample will be 4*w.</span>
+<span class="linenos">109</span><span class="sd">    s: Real</span>
+<span class="linenos">110</span><span class="sd">        Slope of the sigmoid function :math:`\frac1{1+\exp[s (x-x_{0})]}` attenuating the boundaries.</span>
+<span class="linenos">111</span><span class="sd">    po: Integer</span>
+<span class="linenos">112</span><span class="sd">        Power-raising factor for the final image (to have smoother edges).</span>
+<span class="linenos">113</span><span class="sd">    x0: Real</span>
+<span class="linenos">114</span><span class="sd">        Radial shift of the sigmoid function :math:`\frac1{1+\exp[s (x-x_{0})]}`.</span>
+<span class="linenos">115</span><span class="sd">    ndi: NDArrayInfo</span>
+<span class="linenos">116</span><span class="sd">        Desired array module for the output.</span>
+<span class="linenos">117</span>
+<span class="linenos">118</span><span class="sd">    Returns</span>
+<span class="linenos">119</span><span class="sd">    -------</span>
+<span class="linenos">120</span><span class="sd">    image: NDArray</span>
+<span class="linenos">121</span><span class="sd">        (N, N) image of star-like sample.</span>
+<span class="linenos">122</span>
+<span class="linenos">123</span><span class="sd">    Examples</span>
+<span class="linenos">124</span><span class="sd">    --------</span>
+<span class="linenos">125</span><span class="sd">    .. plot::</span>
+<span class="linenos">126</span>
+<span class="linenos">127</span><span class="sd">       import numpy as np</span>
+<span class="linenos">128</span><span class="sd">       import matplotlib.pyplot as plt</span>
+<span class="linenos">129</span><span class="sd">       from pyxu.util.misc import star_like_sample</span>
+<span class="linenos">130</span>
+<span class="linenos">131</span><span class="sd">       star = star_like_sample(N=256, w=8, s=20, po=3, x0=0.7)</span>
+<span class="linenos">132</span><span class="sd">       plt.figure()</span>
+<span class="linenos">133</span><span class="sd">       plt.imshow(star)</span>
+<span class="linenos">134</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">135</span>    <span class="k">assert</span> <span class="n">N</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span>
+<span class="linenos">136</span>    <span class="n">xp</span> <span class="o">=</span> <span class="n">ndi</span><span class="o">.</span><span class="n">module</span><span class="p">()</span>
+<span class="linenos">137</span>
+<span class="linenos">138</span>    <span class="n">grid</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
+<span class="linenos">139</span>    <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">grid</span><span class="p">)</span>
+<span class="linenos">140</span>    <span class="n">theta</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
+<span class="linenos">141</span>    <span class="n">image</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">xp</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">w</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
+<span class="linenos">142</span>    <span class="n">image</span> <span class="o">/=</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">xp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">s</span> <span class="o">*</span> <span class="p">(</span><span class="n">xp</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">y</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="n">x0</span><span class="p">))</span>
+<span class="linenos">143</span>    <span class="n">image</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
+<span class="linenos">144</span>    <span class="n">image</span> <span class="o">**=</span> <span class="n">po</span>
+<span class="linenos">145</span>    <span class="n">image</span> <span class="o">/=</span> <span class="n">xp</span><span class="o">.</span><span class="n">amax</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
+<span class="linenos">146</span>    <span class="k">return</span> <span class="n">image</span></div>
+
+<span class="linenos">147</span>
+<span class="linenos">148</span>
 <div class="viewcode-block" id="parse_params">
 <a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.parse_params">[docs]</a>
-<span class="linenos">152</span><span class="k">def</span> <span class="nf">parse_params</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Mapping</span><span class="p">:</span>
-<span class="linenos">153</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">154</span><span class="sd">    Get function parameterization.</span>
-<span class="linenos">155</span>
-<span class="linenos">156</span><span class="sd">    Returns</span>
-<span class="linenos">157</span><span class="sd">    -------</span>
-<span class="linenos">158</span><span class="sd">    params: ~collections.abc.Mapping</span>
-<span class="linenos">159</span><span class="sd">        (key, value) params as seen in body of `func` when called via `func(*args, **kwargs)`.</span>
-<span class="linenos">160</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">161</span>    <span class="n">sig</span> <span class="o">=</span> <span class="n">inspect</span><span class="o">.</span><span class="n">Signature</span><span class="o">.</span><span class="n">from_callable</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
-<span class="linenos">162</span>    <span class="n">f_args</span> <span class="o">=</span> <span class="n">sig</span><span class="o">.</span><span class="n">bind</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos">163</span>    <span class="n">f_args</span><span class="o">.</span><span class="n">apply_defaults</span><span class="p">()</span>
-<span class="linenos">164</span>
-<span class="linenos">165</span>    <span class="n">params</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span>
-<span class="linenos">166</span>        <span class="nb">zip</span><span class="p">(</span><span class="n">f_args</span><span class="o">.</span><span class="n">arguments</span><span class="o">.</span><span class="n">keys</span><span class="p">(),</span> <span class="n">f_args</span><span class="o">.</span><span class="n">args</span><span class="p">),</span>  <span class="c1"># positional arguments</span>
-<span class="linenos">167</span>        <span class="o">**</span><span class="n">f_args</span><span class="o">.</span><span class="n">kwargs</span><span class="p">,</span>
-<span class="linenos">168</span>    <span class="p">)</span>
-<span class="linenos">169</span>    <span class="k">return</span> <span class="n">params</span></div>
-
-<span class="linenos">170</span>
-<span class="linenos">171</span>
+<span class="linenos">149</span><span class="k">def</span> <span class="nf">parse_params</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Mapping</span><span class="p">:</span>
+<span class="linenos">150</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">151</span><span class="sd">    Get function parameterization.</span>
+<span class="linenos">152</span>
+<span class="linenos">153</span><span class="sd">    Returns</span>
+<span class="linenos">154</span><span class="sd">    -------</span>
+<span class="linenos">155</span><span class="sd">    params: ~collections.abc.Mapping</span>
+<span class="linenos">156</span><span class="sd">        (key, value) params as seen in body of `func` when called via `func(*args, **kwargs)`.</span>
+<span class="linenos">157</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">158</span>    <span class="n">sig</span> <span class="o">=</span> <span class="n">inspect</span><span class="o">.</span><span class="n">Signature</span><span class="o">.</span><span class="n">from_callable</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
+<span class="linenos">159</span>    <span class="n">f_args</span> <span class="o">=</span> <span class="n">sig</span><span class="o">.</span><span class="n">bind</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos">160</span>    <span class="n">f_args</span><span class="o">.</span><span class="n">apply_defaults</span><span class="p">()</span>
+<span class="linenos">161</span>
+<span class="linenos">162</span>    <span class="n">params</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span>
+<span class="linenos">163</span>        <span class="nb">zip</span><span class="p">(</span><span class="n">f_args</span><span class="o">.</span><span class="n">arguments</span><span class="o">.</span><span class="n">keys</span><span class="p">(),</span> <span class="n">f_args</span><span class="o">.</span><span class="n">args</span><span class="p">),</span>  <span class="c1"># positional arguments</span>
+<span class="linenos">164</span>        <span class="o">**</span><span class="n">f_args</span><span class="o">.</span><span class="n">kwargs</span><span class="p">,</span>
+<span class="linenos">165</span>    <span class="p">)</span>
+<span class="linenos">166</span>    <span class="k">return</span> <span class="n">params</span></div>
+
+<span class="linenos">167</span>
+<span class="linenos">168</span>
 <div class="viewcode-block" id="import_module">
 <a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.import_module">[docs]</a>
-<span class="linenos">172</span><span class="k">def</span> <span class="nf">import_module</span><span class="p">(</span><span class="n">name</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">fail_on_error</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">:</span>
-<span class="linenos">173</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">174</span><span class="sd">    Load a Python module dynamically.</span>
-<span class="linenos">175</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">176</span>    <span class="k">try</span><span class="p">:</span>
-<span class="linenos">177</span>        <span class="n">pkg</span> <span class="o">=</span> <span class="n">importlib</span><span class="o">.</span><span class="n">import_module</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
-<span class="linenos">178</span>    <span class="k">except</span> <span class="ne">ModuleNotFoundError</span><span class="p">:</span>
-<span class="linenos">179</span>        <span class="k">if</span> <span class="n">fail_on_error</span><span class="p">:</span>
-<span class="linenos">180</span>            <span class="k">raise</span>
-<span class="linenos">181</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">182</span>            <span class="n">pkg</span> <span class="o">=</span> <span class="kc">None</span>
-<span class="linenos">183</span>    <span class="k">return</span> <span class="n">pkg</span></div>
-
-<span class="linenos">184</span>
-<span class="linenos">185</span>
-<div class="viewcode-block" id="compute">
-<a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.compute">[docs]</a>
-<span class="linenos">186</span><span class="k">def</span> <span class="nf">compute</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="n">mode</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;compute&quot;</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos">187</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">188</span><span class="sd">    Force computation of Dask collections.</span>
-<span class="linenos">189</span>
-<span class="linenos">190</span><span class="sd">    Parameters</span>
-<span class="linenos">191</span><span class="sd">    ----------</span>
-<span class="linenos">192</span><span class="sd">    \*args: object, list</span>
-<span class="linenos">193</span><span class="sd">        Any number of objects.  If it is a dask object, it is evaluated and the result is returned.  Non-dask arguments</span>
-<span class="linenos">194</span><span class="sd">        are passed through unchanged.  Python collections are traversed to find/evaluate dask objects within.  (Use</span>
-<span class="linenos">195</span><span class="sd">        `traverse` =False to disable this behavior.)</span>
-<span class="linenos">196</span><span class="sd">    mode: str</span>
-<span class="linenos">197</span><span class="sd">        Dask evaluation strategy: compute or persist.</span>
-<span class="linenos">198</span><span class="sd">    \*\*kwargs: dict</span>
-<span class="linenos">199</span><span class="sd">        Extra keyword parameters forwarded to :py:func:`dask.compute` or :py:func:`dask.persist`.</span>
-<span class="linenos">200</span>
-<span class="linenos">201</span><span class="sd">    Returns</span>
-<span class="linenos">202</span><span class="sd">    -------</span>
-<span class="linenos">203</span><span class="sd">    \*cargs: object, list</span>
-<span class="linenos">204</span><span class="sd">        Evaluated objects. Non-dask arguments are passed through unchanged.</span>
-<span class="linenos">205</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">206</span>    <span class="k">try</span><span class="p">:</span>
-<span class="linenos">207</span>        <span class="n">func</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">compute</span><span class="o">=</span><span class="n">dask</span><span class="o">.</span><span class="n">compute</span><span class="p">,</span> <span class="n">persist</span><span class="o">=</span><span class="n">dask</span><span class="o">.</span><span class="n">persist</span><span class="p">)[</span><span class="n">mode</span><span class="o">.</span><span class="n">lower</span><span class="p">()]</span>
-<span class="linenos">208</span>    <span class="k">except</span> <span class="ne">Exception</span><span class="p">:</span>
-<span class="linenos">209</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;mode: expected compute/persist, got </span><span class="si">{</span><span class="n">mode</span><span class="si">}</span><span class="s2">.&quot;</span><span class="p">)</span>
-<span class="linenos">210</span>
-<span class="linenos">211</span>    <span class="n">cargs</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos">212</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<span class="linenos">213</span>        <span class="n">cargs</span> <span class="o">=</span> <span class="n">cargs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-<span class="linenos">214</span>    <span class="k">return</span> <span class="n">cargs</span></div>
-
-<span class="linenos">215</span>
-<span class="linenos">216</span>
-<div class="viewcode-block" id="to_NUMPY">
-<a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.to_NUMPY">[docs]</a>
-<span class="linenos">217</span><span class="k">def</span> <span class="nf">to_NUMPY</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos">218</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">219</span><span class="sd">    Convert an array from a specific backend to NUMPY.</span>
-<span class="linenos">220</span>
-<span class="linenos">221</span><span class="sd">    Parameters</span>
-<span class="linenos">222</span><span class="sd">    ----------</span>
-<span class="linenos">223</span><span class="sd">    x: NDArray</span>
-<span class="linenos">224</span><span class="sd">        Array to be converted.</span>
-<span class="linenos">225</span>
-<span class="linenos">226</span><span class="sd">    Returns</span>
-<span class="linenos">227</span><span class="sd">    -------</span>
-<span class="linenos">228</span><span class="sd">    y: NDArray</span>
-<span class="linenos">229</span><span class="sd">        Array with NumPy backend.</span>
-<span class="linenos">230</span>
-<span class="linenos">231</span><span class="sd">    Notes</span>
-<span class="linenos">232</span><span class="sd">    -----</span>
-<span class="linenos">233</span><span class="sd">    This function is a no-op if the array is already a NumPy array.</span>
-<span class="linenos">234</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">235</span>    <span class="n">N</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span>
-<span class="linenos">236</span>    <span class="n">ndi</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="linenos">237</span>    <span class="k">if</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">:</span>
-<span class="linenos">238</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span>
-<span class="linenos">239</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">DASK</span><span class="p">:</span>
-<span class="linenos">240</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">compute</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="linenos">241</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">CUPY</span><span class="p">:</span>
-<span class="linenos">242</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">get</span><span class="p">()</span>
-<span class="linenos">243</span>    <span class="k">else</span><span class="p">:</span>
-<span class="linenos">244</span>        <span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;Dev-action required: define behaviour for </span><span class="si">{</span><span class="n">ndi</span><span class="si">}</span><span class="s2">.&quot;</span>
-<span class="linenos">245</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
-<span class="linenos">246</span>    <span class="k">return</span> <span class="n">y</span></div>
-
-<span class="linenos">247</span>
-<span class="linenos">248</span>
+<span class="linenos">169</span><span class="k">def</span> <span class="nf">import_module</span><span class="p">(</span><span class="n">name</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">fail_on_error</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">:</span>
+<span class="linenos">170</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">171</span><span class="sd">    Load a Python module dynamically.</span>
+<span class="linenos">172</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">173</span>    <span class="k">try</span><span class="p">:</span>
+<span class="linenos">174</span>        <span class="n">pkg</span> <span class="o">=</span> <span class="n">importlib</span><span class="o">.</span><span class="n">import_module</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
+<span class="linenos">175</span>    <span class="k">except</span> <span class="ne">ModuleNotFoundError</span><span class="p">:</span>
+<span class="linenos">176</span>        <span class="k">if</span> <span class="n">fail_on_error</span><span class="p">:</span>
+<span class="linenos">177</span>            <span class="k">raise</span>
+<span class="linenos">178</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">179</span>            <span class="n">pkg</span> <span class="o">=</span> <span class="kc">None</span>
+<span class="linenos">180</span>    <span class="k">return</span> <span class="n">pkg</span></div>
+
+<span class="linenos">181</span>
+<span class="linenos">182</span>
 <div class="viewcode-block" id="copy_if_unsafe">
 <a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.copy_if_unsafe">[docs]</a>
-<span class="linenos">249</span><span class="k">def</span> <span class="nf">copy_if_unsafe</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos">250</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">251</span><span class="sd">    Copy array if it is unsafe to do in-place updates on it.</span>
-<span class="linenos">252</span>
-<span class="linenos">253</span><span class="sd">    In-place updates are unsafe if:</span>
-<span class="linenos">254</span>
-<span class="linenos">255</span><span class="sd">    * the array is read-only, OR</span>
-<span class="linenos">256</span><span class="sd">    * the array is a view onto another array.</span>
-<span class="linenos">257</span>
-<span class="linenos">258</span><span class="sd">    Parameters</span>
-<span class="linenos">259</span><span class="sd">    ----------</span>
-<span class="linenos">260</span><span class="sd">    x: NDArray</span>
-<span class="linenos">261</span>
-<span class="linenos">262</span><span class="sd">    Returns</span>
-<span class="linenos">263</span><span class="sd">    -------</span>
-<span class="linenos">264</span><span class="sd">    y: NDArray</span>
-<span class="linenos">265</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">266</span>    <span class="n">N</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span>
-<span class="linenos">267</span>    <span class="n">ndi</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="linenos">268</span>    <span class="k">if</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">DASK</span><span class="p">:</span>
-<span class="linenos">269</span>        <span class="c1"># Dask operations span a graph -&gt; always safe.</span>
-<span class="linenos">270</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span>
-<span class="linenos">271</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">:</span>
-<span class="linenos">272</span>        <span class="n">read_only</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">x</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">writeable</span>
-<span class="linenos">273</span>        <span class="n">reference</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">x</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">owndata</span>
-<span class="linenos">274</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span> <span class="k">if</span> <span class="p">(</span><span class="n">read_only</span> <span class="ow">or</span> <span class="n">reference</span><span class="p">)</span> <span class="k">else</span> <span class="n">x</span>
-<span class="linenos">275</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">CUPY</span><span class="p">:</span>
-<span class="linenos">276</span>        <span class="n">read_only</span> <span class="o">=</span> <span class="kc">False</span>  <span class="c1"># https://github.com/cupy/cupy/issues/2616</span>
-<span class="linenos">277</span>        <span class="n">reference</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">x</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">owndata</span>
-<span class="linenos">278</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span> <span class="k">if</span> <span class="p">(</span><span class="n">read_only</span> <span class="ow">or</span> <span class="n">reference</span><span class="p">)</span> <span class="k">else</span> <span class="n">x</span>
-<span class="linenos">279</span>    <span class="k">else</span><span class="p">:</span>
-<span class="linenos">280</span>        <span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;copy_if_unsafe() not yet defined for </span><span class="si">{</span><span class="n">ndi</span><span class="si">}</span><span class="s2">.&quot;</span>
-<span class="linenos">281</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
-<span class="linenos">282</span>    <span class="k">return</span> <span class="n">y</span></div>
-
-<span class="linenos">283</span>
-<span class="linenos">284</span>
+<span class="linenos">183</span><span class="k">def</span> <span class="nf">copy_if_unsafe</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos">184</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">185</span><span class="sd">    Copy array if it is unsafe to do in-place updates on it.</span>
+<span class="linenos">186</span>
+<span class="linenos">187</span><span class="sd">    In-place updates are unsafe if:</span>
+<span class="linenos">188</span>
+<span class="linenos">189</span><span class="sd">    * the array is read-only, OR</span>
+<span class="linenos">190</span><span class="sd">    * the array is a view onto another array.</span>
+<span class="linenos">191</span>
+<span class="linenos">192</span><span class="sd">    Parameters</span>
+<span class="linenos">193</span><span class="sd">    ----------</span>
+<span class="linenos">194</span><span class="sd">    x: NDArray</span>
+<span class="linenos">195</span>
+<span class="linenos">196</span><span class="sd">    Returns</span>
+<span class="linenos">197</span><span class="sd">    -------</span>
+<span class="linenos">198</span><span class="sd">    y: NDArray</span>
+<span class="linenos">199</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">200</span>    <span class="n">N</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span>
+<span class="linenos">201</span>    <span class="n">ndi</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="linenos">202</span>    <span class="k">if</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">DASK</span><span class="p">:</span>
+<span class="linenos">203</span>        <span class="c1"># Dask operations span a graph -&gt; always safe.</span>
+<span class="linenos">204</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span>
+<span class="linenos">205</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">:</span>
+<span class="linenos">206</span>        <span class="n">read_only</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">x</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">writeable</span>
+<span class="linenos">207</span>        <span class="n">reference</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">x</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">owndata</span>
+<span class="linenos">208</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span> <span class="k">if</span> <span class="p">(</span><span class="n">read_only</span> <span class="ow">or</span> <span class="n">reference</span><span class="p">)</span> <span class="k">else</span> <span class="n">x</span>
+<span class="linenos">209</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">CUPY</span><span class="p">:</span>
+<span class="linenos">210</span>        <span class="n">read_only</span> <span class="o">=</span> <span class="kc">False</span>  <span class="c1"># https://github.com/cupy/cupy/issues/2616</span>
+<span class="linenos">211</span>        <span class="n">reference</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">x</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">owndata</span>
+<span class="linenos">212</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span> <span class="k">if</span> <span class="p">(</span><span class="n">read_only</span> <span class="ow">or</span> <span class="n">reference</span><span class="p">)</span> <span class="k">else</span> <span class="n">x</span>
+<span class="linenos">213</span>    <span class="k">else</span><span class="p">:</span>
+<span class="linenos">214</span>        <span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;copy_if_unsafe() not yet defined for </span><span class="si">{</span><span class="n">ndi</span><span class="si">}</span><span class="s2">.&quot;</span>
+<span class="linenos">215</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
+<span class="linenos">216</span>    <span class="k">return</span> <span class="n">y</span></div>
+
+<span class="linenos">217</span>
+<span class="linenos">218</span>
 <div class="viewcode-block" id="read_only">
 <a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.read_only">[docs]</a>
-<span class="linenos">285</span><span class="k">def</span> <span class="nf">read_only</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
-<span class="linenos">286</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">287</span><span class="sd">    Make an array read-only.</span>
-<span class="linenos">288</span>
-<span class="linenos">289</span><span class="sd">    Parameters</span>
-<span class="linenos">290</span><span class="sd">    ----------</span>
-<span class="linenos">291</span><span class="sd">    x: NDArray</span>
-<span class="linenos">292</span>
-<span class="linenos">293</span><span class="sd">    Returns</span>
-<span class="linenos">294</span><span class="sd">    -------</span>
-<span class="linenos">295</span><span class="sd">    y: NDArray</span>
-<span class="linenos">296</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">297</span>    <span class="n">N</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span>
-<span class="linenos">298</span>    <span class="n">ndi</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="linenos">299</span>    <span class="k">if</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">DASK</span><span class="p">:</span>
-<span class="linenos">300</span>        <span class="c1"># Dask operations are read-only since graph-backed.</span>
-<span class="linenos">301</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span>
-<span class="linenos">302</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">:</span>
-<span class="linenos">303</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
-<span class="linenos">304</span>        <span class="n">y</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">writeable</span> <span class="o">=</span> <span class="kc">False</span>
-<span class="linenos">305</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">CUPY</span><span class="p">:</span>
-<span class="linenos">306</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
-<span class="linenos">307</span>        <span class="c1"># y.flags.writeable = False  # https://github.com/cupy/cupy/issues/2616</span>
-<span class="linenos">308</span>    <span class="k">else</span><span class="p">:</span>
-<span class="linenos">309</span>        <span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;read_only() not yet defined for </span><span class="si">{</span><span class="n">ndi</span><span class="si">}</span><span class="s2">.&quot;</span>
-<span class="linenos">310</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
-<span class="linenos">311</span>    <span class="k">return</span> <span class="n">y</span></div>
-
-<span class="linenos">312</span>
-<span class="linenos">313</span>
+<span class="linenos">219</span><span class="k">def</span> <span class="nf">read_only</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">:</span>
+<span class="linenos">220</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">221</span><span class="sd">    Make an array read-only.</span>
+<span class="linenos">222</span>
+<span class="linenos">223</span><span class="sd">    Parameters</span>
+<span class="linenos">224</span><span class="sd">    ----------</span>
+<span class="linenos">225</span><span class="sd">    x: NDArray</span>
+<span class="linenos">226</span>
+<span class="linenos">227</span><span class="sd">    Returns</span>
+<span class="linenos">228</span><span class="sd">    -------</span>
+<span class="linenos">229</span><span class="sd">    y: NDArray</span>
+<span class="linenos">230</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">231</span>    <span class="n">N</span> <span class="o">=</span> <span class="n">pxd</span><span class="o">.</span><span class="n">NDArrayInfo</span>
+<span class="linenos">232</span>    <span class="n">ndi</span> <span class="o">=</span> <span class="n">N</span><span class="o">.</span><span class="n">from_obj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="linenos">233</span>    <span class="k">if</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">DASK</span><span class="p">:</span>
+<span class="linenos">234</span>        <span class="c1"># Dask operations are read-only since graph-backed.</span>
+<span class="linenos">235</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span>
+<span class="linenos">236</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">NUMPY</span><span class="p">:</span>
+<span class="linenos">237</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
+<span class="linenos">238</span>        <span class="n">y</span><span class="o">.</span><span class="n">flags</span><span class="o">.</span><span class="n">writeable</span> <span class="o">=</span> <span class="kc">False</span>
+<span class="linenos">239</span>    <span class="k">elif</span> <span class="n">ndi</span> <span class="o">==</span> <span class="n">N</span><span class="o">.</span><span class="n">CUPY</span><span class="p">:</span>
+<span class="linenos">240</span>        <span class="n">y</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">()</span>
+<span class="linenos">241</span>        <span class="c1"># y.flags.writeable = False  # https://github.com/cupy/cupy/issues/2616</span>
+<span class="linenos">242</span>    <span class="k">else</span><span class="p">:</span>
+<span class="linenos">243</span>        <span class="n">msg</span> <span class="o">=</span> <span class="sa">f</span><span class="s2">&quot;read_only() not yet defined for </span><span class="si">{</span><span class="n">ndi</span><span class="si">}</span><span class="s2">.&quot;</span>
+<span class="linenos">244</span>        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="n">msg</span><span class="p">)</span>
+<span class="linenos">245</span>    <span class="k">return</span> <span class="n">y</span></div>
+
+<span class="linenos">246</span>
+<span class="linenos">247</span>
 <div class="viewcode-block" id="infer_sum_shape">
 <a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.infer_sum_shape">[docs]</a>
-<span class="linenos">314</span><span class="k">def</span> <span class="nf">infer_sum_shape</span><span class="p">(</span><span class="n">sh1</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span> <span class="n">sh2</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">:</span>
-<span class="linenos">315</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">316</span><span class="sd">    Infer shape of arithmetic operation :math:`A + B`.</span>
-<span class="linenos">317</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">318</span>    <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">D</span> <span class="o">=</span> <span class="o">*</span><span class="n">sh1</span><span class="p">,</span> <span class="o">*</span><span class="n">sh2</span>
-<span class="linenos">319</span>    <span class="k">if</span> <span class="n">B</span> <span class="o">==</span> <span class="n">D</span><span class="p">:</span>
-<span class="linenos">320</span>        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">broadcast_shapes</span><span class="p">((</span><span class="n">A</span><span class="p">,),</span> <span class="p">(</span><span class="n">C</span><span class="p">,))</span> <span class="o">+</span> <span class="p">(</span><span class="n">B</span><span class="p">,)</span>
-<span class="linenos">321</span>    <span class="k">else</span><span class="p">:</span>
-<span class="linenos">322</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Addition of </span><span class="si">{</span><span class="n">sh1</span><span class="si">}</span><span class="s2"> and </span><span class="si">{</span><span class="n">sh2</span><span class="si">}</span><span class="s2"> operators forbidden.&quot;</span><span class="p">)</span></div>
-
-<span class="linenos">323</span>
-<span class="linenos">324</span>
+<span class="linenos">248</span><span class="k">def</span> <span class="nf">infer_sum_shape</span><span class="p">(</span><span class="n">sh1</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span> <span class="n">sh2</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">:</span>
+<span class="linenos">249</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">250</span><span class="sd">    Infer shape of arithmetic operation :math:`A + B`.</span>
+<span class="linenos">251</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">252</span>    <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">D</span> <span class="o">=</span> <span class="o">*</span><span class="n">sh1</span><span class="p">,</span> <span class="o">*</span><span class="n">sh2</span>
+<span class="linenos">253</span>    <span class="k">if</span> <span class="n">B</span> <span class="o">==</span> <span class="n">D</span><span class="p">:</span>
+<span class="linenos">254</span>        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">broadcast_shapes</span><span class="p">((</span><span class="n">A</span><span class="p">,),</span> <span class="p">(</span><span class="n">C</span><span class="p">,))</span> <span class="o">+</span> <span class="p">(</span><span class="n">B</span><span class="p">,)</span>
+<span class="linenos">255</span>    <span class="k">else</span><span class="p">:</span>
+<span class="linenos">256</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Addition of </span><span class="si">{</span><span class="n">sh1</span><span class="si">}</span><span class="s2"> and </span><span class="si">{</span><span class="n">sh2</span><span class="si">}</span><span class="s2"> operators forbidden.&quot;</span><span class="p">)</span></div>
+
+<span class="linenos">257</span>
+<span class="linenos">258</span>
 <div class="viewcode-block" id="infer_composition_shape">
 <a class="viewcode-back" href="../../../api/util/misc.html#pyxu.util.infer_composition_shape">[docs]</a>
-<span class="linenos">325</span><span class="k">def</span> <span class="nf">infer_composition_shape</span><span class="p">(</span><span class="n">sh1</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span> <span class="n">sh2</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">:</span>
-<span class="linenos">326</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
-<span class="linenos">327</span><span class="sd">    Infer shape of arithmetic operation :math:`A \circ B`.</span>
-<span class="linenos">328</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">329</span>    <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">D</span> <span class="o">=</span> <span class="o">*</span><span class="n">sh1</span><span class="p">,</span> <span class="o">*</span><span class="n">sh2</span>
-<span class="linenos">330</span>    <span class="k">if</span> <span class="n">B</span> <span class="o">==</span> <span class="n">C</span><span class="p">:</span>
-<span class="linenos">331</span>        <span class="k">return</span> <span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
-<span class="linenos">332</span>    <span class="k">else</span><span class="p">:</span>
-<span class="linenos">333</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Composition of </span><span class="si">{</span><span class="n">sh1</span><span class="si">}</span><span class="s2"> and </span><span class="si">{</span><span class="n">sh2</span><span class="si">}</span><span class="s2"> operators forbidden.&quot;</span><span class="p">)</span></div>
+<span class="linenos">259</span><span class="k">def</span> <span class="nf">infer_composition_shape</span><span class="p">(</span><span class="n">sh1</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">,</span> <span class="n">sh2</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">OpShape</span><span class="p">:</span>
+<span class="linenos">260</span><span class="w">    </span><span class="sa">r</span><span class="sd">&quot;&quot;&quot;</span>
+<span class="linenos">261</span><span class="sd">    Infer shape of arithmetic operation :math:`A \circ B`.</span>
+<span class="linenos">262</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">263</span>    <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">D</span> <span class="o">=</span> <span class="o">*</span><span class="n">sh1</span><span class="p">,</span> <span class="o">*</span><span class="n">sh2</span>
+<span class="linenos">264</span>    <span class="k">if</span> <span class="n">B</span> <span class="o">==</span> <span class="n">C</span><span class="p">:</span>
+<span class="linenos">265</span>        <span class="k">return</span> <span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
+<span class="linenos">266</span>    <span class="k">else</span><span class="p">:</span>
+<span class="linenos">267</span>        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Composition of </span><span class="si">{</span><span class="n">sh1</span><span class="si">}</span><span class="s2"> and </span><span class="si">{</span><span class="n">sh2</span><span class="si">}</span><span class="s2"> operators forbidden.&quot;</span><span class="p">)</span></div>
 
 </pre></div>
 
diff --git a/_modules/pyxu/util/operator.html b/_modules/pyxu/util/operator.html
index eaba3e1c..dc860b89 100644
--- a/_modules/pyxu/util/operator.html
+++ b/_modules/pyxu/util/operator.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/plot_directive.css" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../../_static/copybutton.css?v=76b2166b" />
     <link rel="stylesheet" type="text/css" href="../../../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../../_static/doctools.js?v=888ff710"></script>
     <script src="../../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../../_static/clipboard.min.js?v=a7894cd8"></script>
diff --git a/_modules/typing.html b/_modules/typing.html
index 567dcf51..6d453d4d 100644
--- a/_modules/typing.html
+++ b/_modules/typing.html
@@ -27,8 +27,8 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
-    <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
     <link rel="stylesheet" type="text/css" href="../_static/togglebutton.css?v=13237357" />
@@ -37,13 +37,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -199,7 +199,7 @@
         </div>
       
       
-        <div class="navbar-item"><strong> v1.0.x </strong></div>
+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
       
         <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
     aria-label="Icon Links">
@@ -236,7 +236,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -341,7 +341,7 @@
     
       <div class="sidebar-header-items__end">
         
-          <div class="navbar-item"><strong> v1.0.x </strong></div>
+          <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
         
           <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
     aria-label="Icon Links">
@@ -378,7 +378,7 @@
           
           
           
-          <a href="mailto: matthieu.simeoni@gmail.com" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
             <label class="sr-only">Contact</label></a>
         </li>
         <li class="nav-item">
@@ -454,22 +454,22 @@ <h1>Source code for typing</h1><div class="highlight"><pre>
 <span></span><span class="linenos">   1</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">   2</span><span class="sd">The typing module: Support for gradual typing as defined by PEP 484 and subsequent PEPs.</span>
 <span class="linenos">   3</span>
-<span class="linenos">   4</span><span class="sd">Among other things, the module includes the following:</span>
-<span class="linenos">   5</span><span class="sd">* Generic, Protocol, and internal machinery to support generic aliases.</span>
-<span class="linenos">   6</span><span class="sd">  All subscripted types like X[int], Union[int, str] are generic aliases.</span>
-<span class="linenos">   7</span><span class="sd">* Various &quot;special forms&quot; that have unique meanings in type annotations:</span>
-<span class="linenos">   8</span><span class="sd">  NoReturn, Never, ClassVar, Self, Concatenate, Unpack, and others.</span>
-<span class="linenos">   9</span><span class="sd">* Classes whose instances can be type arguments to generic classes and functions:</span>
-<span class="linenos">  10</span><span class="sd">  TypeVar, ParamSpec, TypeVarTuple.</span>
-<span class="linenos">  11</span><span class="sd">* Public helper functions: get_type_hints, overload, cast, final, and others.</span>
-<span class="linenos">  12</span><span class="sd">* Several protocols to support duck-typing:</span>
-<span class="linenos">  13</span><span class="sd">  SupportsFloat, SupportsIndex, SupportsAbs, and others.</span>
-<span class="linenos">  14</span><span class="sd">* Special types: NewType, NamedTuple, TypedDict.</span>
-<span class="linenos">  15</span><span class="sd">* Deprecated wrapper submodules for re and io related types.</span>
-<span class="linenos">  16</span><span class="sd">* Deprecated aliases for builtin types and collections.abc ABCs.</span>
-<span class="linenos">  17</span>
-<span class="linenos">  18</span><span class="sd">Any name not present in __all__ is an implementation detail</span>
-<span class="linenos">  19</span><span class="sd">that may be changed without notice. Use at your own risk!</span>
+<span class="linenos">   4</span><span class="sd">Any name not present in __all__ is an implementation detail</span>
+<span class="linenos">   5</span><span class="sd">that may be changed without notice. Use at your own risk!</span>
+<span class="linenos">   6</span>
+<span class="linenos">   7</span><span class="sd">Among other things, the module includes the following:</span>
+<span class="linenos">   8</span><span class="sd">* Generic, Protocol, and internal machinery to support generic aliases.</span>
+<span class="linenos">   9</span><span class="sd">  All subscripted types like X[int], Union[int, str] are generic aliases.</span>
+<span class="linenos">  10</span><span class="sd">* Various &quot;special forms&quot; that have unique meanings in type annotations:</span>
+<span class="linenos">  11</span><span class="sd">  NoReturn, Never, ClassVar, Self, Concatenate, Unpack, and others.</span>
+<span class="linenos">  12</span><span class="sd">* Classes whose instances can be type arguments to generic classes and functions:</span>
+<span class="linenos">  13</span><span class="sd">  TypeVar, ParamSpec, TypeVarTuple.</span>
+<span class="linenos">  14</span><span class="sd">* Public helper functions: get_type_hints, overload, cast, final, and others.</span>
+<span class="linenos">  15</span><span class="sd">* Several protocols to support duck-typing:</span>
+<span class="linenos">  16</span><span class="sd">  SupportsFloat, SupportsIndex, SupportsAbs, and others.</span>
+<span class="linenos">  17</span><span class="sd">* Special types: NewType, NamedTuple, TypedDict.</span>
+<span class="linenos">  18</span><span class="sd">* Deprecated wrapper submodules for re and io related types.</span>
+<span class="linenos">  19</span><span class="sd">* Deprecated aliases for builtin types and collections.abc ABCs.</span>
 <span class="linenos">  20</span><span class="sd">&quot;&quot;&quot;</span>
 <span class="linenos">  21</span>
 <span class="linenos">  22</span><span class="kn">from</span> <span class="nn">abc</span> <span class="kn">import</span> <span class="n">abstractmethod</span><span class="p">,</span> <span class="n">ABCMeta</span>
@@ -660,3284 +660,3264 @@ <h1>Source code for typing</h1><div class="highlight"><pre>
 <span class="linenos"> 207</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal helper for munging collections.abc.Callable&#39;s __args__.</span>
 <span class="linenos"> 208</span>
 <span class="linenos"> 209</span><span class="sd">    The canonical representation for a Callable&#39;s __args__ flattens the</span>
-<span class="linenos"> 210</span><span class="sd">    argument types, see https://github.com/python/cpython/issues/86361.</span>
+<span class="linenos"> 210</span><span class="sd">    argument types, see https://bugs.python.org/issue42195. For example::</span>
 <span class="linenos"> 211</span>
-<span class="linenos"> 212</span><span class="sd">    For example::</span>
-<span class="linenos"> 213</span>
-<span class="linenos"> 214</span><span class="sd">        assert collections.abc.Callable[[int, int], str].__args__ == (int, int, str)</span>
-<span class="linenos"> 215</span><span class="sd">        assert collections.abc.Callable[ParamSpec, str].__args__ == (ParamSpec, str)</span>
-<span class="linenos"> 216</span>
-<span class="linenos"> 217</span><span class="sd">    As a result, if we need to reconstruct the Callable from its __args__,</span>
-<span class="linenos"> 218</span><span class="sd">    we need to unflatten it.</span>
-<span class="linenos"> 219</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 220</span>    <span class="k">return</span> <span class="p">(</span>
-<span class="linenos"> 221</span>        <span class="n">typ</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Callable</span>
-<span class="linenos"> 222</span>        <span class="ow">and</span> <span class="ow">not</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
-<span class="linenos"> 223</span>    <span class="p">)</span>
-<span class="linenos"> 224</span>
-<span class="linenos"> 225</span>
-<span class="linenos"> 226</span><span class="k">def</span> <span class="nf">_type_repr</span><span class="p">(</span><span class="n">obj</span><span class="p">):</span>
-<span class="linenos"> 227</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Return the repr() of an object, special-casing types (internal helper).</span>
-<span class="linenos"> 228</span>
-<span class="linenos"> 229</span><span class="sd">    If obj is a type, we return a shorter version than the default</span>
-<span class="linenos"> 230</span><span class="sd">    type.__repr__, based on the module and qualified name, which is</span>
-<span class="linenos"> 231</span><span class="sd">    typically enough to uniquely identify a type.  For everything</span>
-<span class="linenos"> 232</span><span class="sd">    else, we fall back on repr(obj).</span>
-<span class="linenos"> 233</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 234</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">GenericAlias</span><span class="p">):</span>
-<span class="linenos"> 235</span>        <span class="k">return</span> <span class="nb">repr</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
-<span class="linenos"> 236</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
-<span class="linenos"> 237</span>        <span class="k">if</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">==</span> <span class="s1">&#39;builtins&#39;</span><span class="p">:</span>
-<span class="linenos"> 238</span>            <span class="k">return</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__qualname__</span>
-<span class="linenos"> 239</span>        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">obj</span><span class="o">.</span><span class="vm">__module__</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="n">obj</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">&#39;</span>
-<span class="linenos"> 240</span>    <span class="k">if</span> <span class="n">obj</span> <span class="ow">is</span> <span class="o">...</span><span class="p">:</span>
-<span class="linenos"> 241</span>        <span class="k">return</span><span class="p">(</span><span class="s1">&#39;...&#39;</span><span class="p">)</span>
-<span class="linenos"> 242</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">FunctionType</span><span class="p">):</span>
-<span class="linenos"> 243</span>        <span class="k">return</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__name__</span>
-<span class="linenos"> 244</span>    <span class="k">return</span> <span class="nb">repr</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
-<span class="linenos"> 245</span>
-<span class="linenos"> 246</span>
-<span class="linenos"> 247</span><span class="k">def</span> <span class="nf">_collect_parameters</span><span class="p">(</span><span class="n">args</span><span class="p">):</span>
-<span class="linenos"> 248</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Collect all type variables and parameter specifications in args</span>
-<span class="linenos"> 249</span><span class="sd">    in order of first appearance (lexicographic order).</span>
+<span class="linenos"> 212</span><span class="sd">        collections.abc.Callable[[int, int], str].__args__ == (int, int, str)</span>
+<span class="linenos"> 213</span><span class="sd">        collections.abc.Callable[ParamSpec, str].__args__ == (ParamSpec, str)</span>
+<span class="linenos"> 214</span>
+<span class="linenos"> 215</span><span class="sd">    As a result, if we need to reconstruct the Callable from its __args__,</span>
+<span class="linenos"> 216</span><span class="sd">    we need to unflatten it.</span>
+<span class="linenos"> 217</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 218</span>    <span class="k">return</span> <span class="p">(</span>
+<span class="linenos"> 219</span>        <span class="n">typ</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Callable</span>
+<span class="linenos"> 220</span>        <span class="ow">and</span> <span class="ow">not</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
+<span class="linenos"> 221</span>    <span class="p">)</span>
+<span class="linenos"> 222</span>
+<span class="linenos"> 223</span>
+<span class="linenos"> 224</span><span class="k">def</span> <span class="nf">_type_repr</span><span class="p">(</span><span class="n">obj</span><span class="p">):</span>
+<span class="linenos"> 225</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Return the repr() of an object, special-casing types (internal helper).</span>
+<span class="linenos"> 226</span>
+<span class="linenos"> 227</span><span class="sd">    If obj is a type, we return a shorter version than the default</span>
+<span class="linenos"> 228</span><span class="sd">    type.__repr__, based on the module and qualified name, which is</span>
+<span class="linenos"> 229</span><span class="sd">    typically enough to uniquely identify a type.  For everything</span>
+<span class="linenos"> 230</span><span class="sd">    else, we fall back on repr(obj).</span>
+<span class="linenos"> 231</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 232</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">GenericAlias</span><span class="p">):</span>
+<span class="linenos"> 233</span>        <span class="k">return</span> <span class="nb">repr</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
+<span class="linenos"> 234</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
+<span class="linenos"> 235</span>        <span class="k">if</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">==</span> <span class="s1">&#39;builtins&#39;</span><span class="p">:</span>
+<span class="linenos"> 236</span>            <span class="k">return</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__qualname__</span>
+<span class="linenos"> 237</span>        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">obj</span><span class="o">.</span><span class="vm">__module__</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="n">obj</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">&#39;</span>
+<span class="linenos"> 238</span>    <span class="k">if</span> <span class="n">obj</span> <span class="ow">is</span> <span class="o">...</span><span class="p">:</span>
+<span class="linenos"> 239</span>        <span class="k">return</span><span class="p">(</span><span class="s1">&#39;...&#39;</span><span class="p">)</span>
+<span class="linenos"> 240</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">FunctionType</span><span class="p">):</span>
+<span class="linenos"> 241</span>        <span class="k">return</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__name__</span>
+<span class="linenos"> 242</span>    <span class="k">return</span> <span class="nb">repr</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
+<span class="linenos"> 243</span>
+<span class="linenos"> 244</span>
+<span class="linenos"> 245</span><span class="k">def</span> <span class="nf">_collect_parameters</span><span class="p">(</span><span class="n">args</span><span class="p">):</span>
+<span class="linenos"> 246</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Collect all type variables and parameter specifications in args</span>
+<span class="linenos"> 247</span><span class="sd">    in order of first appearance (lexicographic order).</span>
+<span class="linenos"> 248</span>
+<span class="linenos"> 249</span><span class="sd">    For example::</span>
 <span class="linenos"> 250</span>
-<span class="linenos"> 251</span><span class="sd">    For example::</span>
-<span class="linenos"> 252</span>
-<span class="linenos"> 253</span><span class="sd">        assert _collect_parameters((T, Callable[P, T])) == (T, P)</span>
-<span class="linenos"> 254</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 255</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos"> 256</span>    <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">args</span><span class="p">:</span>
-<span class="linenos"> 257</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
-<span class="linenos"> 258</span>            <span class="c1"># We don&#39;t want __parameters__ descriptor of a bare Python class.</span>
-<span class="linenos"> 259</span>            <span class="k">pass</span>
-<span class="linenos"> 260</span>        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos"> 261</span>            <span class="c1"># `t` might be a tuple, when `ParamSpec` is substituted with</span>
-<span class="linenos"> 262</span>            <span class="c1"># `[T, int]`, or `[int, *Ts]`, etc.</span>
-<span class="linenos"> 263</span>            <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">t</span><span class="p">:</span>
-<span class="linenos"> 264</span>                <span class="k">for</span> <span class="n">collected</span> <span class="ow">in</span> <span class="n">_collect_parameters</span><span class="p">([</span><span class="n">x</span><span class="p">]):</span>
-<span class="linenos"> 265</span>                    <span class="k">if</span> <span class="n">collected</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
-<span class="linenos"> 266</span>                        <span class="n">parameters</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">collected</span><span class="p">)</span>
-<span class="linenos"> 267</span>        <span class="k">elif</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="s1">&#39;__typing_subst__&#39;</span><span class="p">):</span>
-<span class="linenos"> 268</span>            <span class="k">if</span> <span class="n">t</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
-<span class="linenos"> 269</span>                <span class="n">parameters</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
-<span class="linenos"> 270</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 271</span>            <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="s1">&#39;__parameters__&#39;</span><span class="p">,</span> <span class="p">()):</span>
-<span class="linenos"> 272</span>                <span class="k">if</span> <span class="n">x</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
-<span class="linenos"> 273</span>                    <span class="n">parameters</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="linenos"> 274</span>    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span>
-<span class="linenos"> 275</span>
-<span class="linenos"> 276</span>
-<span class="linenos"> 277</span><span class="k">def</span> <span class="nf">_check_generic</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">parameters</span><span class="p">,</span> <span class="n">elen</span><span class="p">):</span>
-<span class="linenos"> 278</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Check correct count for parameters of a generic cls (internal helper).</span>
-<span class="linenos"> 279</span>
-<span class="linenos"> 280</span><span class="sd">    This gives a nice error message in case of count mismatch.</span>
-<span class="linenos"> 281</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 282</span>    <span class="k">if</span> <span class="ow">not</span> <span class="n">elen</span><span class="p">:</span>
-<span class="linenos"> 283</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">cls</span><span class="si">}</span><span class="s2"> is not a generic class&quot;</span><span class="p">)</span>
-<span class="linenos"> 284</span>    <span class="n">alen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span>
-<span class="linenos"> 285</span>    <span class="k">if</span> <span class="n">alen</span> <span class="o">!=</span> <span class="n">elen</span><span class="p">:</span>
-<span class="linenos"> 286</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Too </span><span class="si">{</span><span class="s1">&#39;many&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">alen</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">elen</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;few&#39;</span><span class="si">}</span><span class="s2"> arguments for </span><span class="si">{</span><span class="bp">cls</span><span class="si">}</span><span class="s2">;&quot;</span>
-<span class="linenos"> 287</span>                        <span class="sa">f</span><span class="s2">&quot; actual </span><span class="si">{</span><span class="n">alen</span><span class="si">}</span><span class="s2">, expected </span><span class="si">{</span><span class="n">elen</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos"> 288</span>
-<span class="linenos"> 289</span><span class="k">def</span> <span class="nf">_unpack_args</span><span class="p">(</span><span class="n">args</span><span class="p">):</span>
-<span class="linenos"> 290</span>    <span class="n">newargs</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos"> 291</span>    <span class="k">for</span> <span class="n">arg</span> <span class="ow">in</span> <span class="n">args</span><span class="p">:</span>
-<span class="linenos"> 292</span>        <span class="n">subargs</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="s1">&#39;__typing_unpacked_tuple_args__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
-<span class="linenos"> 293</span>        <span class="k">if</span> <span class="n">subargs</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="ow">not</span> <span class="p">(</span><span class="n">subargs</span> <span class="ow">and</span> <span class="n">subargs</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="o">...</span><span class="p">):</span>
-<span class="linenos"> 294</span>            <span class="n">newargs</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">subargs</span><span class="p">)</span>
-<span class="linenos"> 295</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 296</span>            <span class="n">newargs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span>
-<span class="linenos"> 297</span>    <span class="k">return</span> <span class="n">newargs</span>
-<span class="linenos"> 298</span>
-<span class="linenos"> 299</span><span class="k">def</span> <span class="nf">_deduplicate</span><span class="p">(</span><span class="n">params</span><span class="p">):</span>
-<span class="linenos"> 300</span>    <span class="c1"># Weed out strict duplicates, preserving the first of each occurrence.</span>
-<span class="linenos"> 301</span>    <span class="n">all_params</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
-<span class="linenos"> 302</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">all_params</span><span class="p">)</span> <span class="o">&lt;</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">):</span>
-<span class="linenos"> 303</span>        <span class="n">new_params</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos"> 304</span>        <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">params</span><span class="p">:</span>
-<span class="linenos"> 305</span>            <span class="k">if</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">all_params</span><span class="p">:</span>
-<span class="linenos"> 306</span>                <span class="n">new_params</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
-<span class="linenos"> 307</span>                <span class="n">all_params</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
-<span class="linenos"> 308</span>        <span class="n">params</span> <span class="o">=</span> <span class="n">new_params</span>
-<span class="linenos"> 309</span>        <span class="k">assert</span> <span class="ow">not</span> <span class="n">all_params</span><span class="p">,</span> <span class="n">all_params</span>
-<span class="linenos"> 310</span>    <span class="k">return</span> <span class="n">params</span>
-<span class="linenos"> 311</span>
-<span class="linenos"> 312</span>
-<span class="linenos"> 313</span><span class="k">def</span> <span class="nf">_remove_dups_flatten</span><span class="p">(</span><span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 314</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal helper for Union creation and substitution.</span>
-<span class="linenos"> 315</span>
-<span class="linenos"> 316</span><span class="sd">    Flatten Unions among parameters, then remove duplicates.</span>
-<span class="linenos"> 317</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 318</span>    <span class="c1"># Flatten out Union[Union[...], ...].</span>
-<span class="linenos"> 319</span>    <span class="n">params</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos"> 320</span>    <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
-<span class="linenos"> 321</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="p">(</span><span class="n">_UnionGenericAlias</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">)):</span>
-<span class="linenos"> 322</span>            <span class="n">params</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
-<span class="linenos"> 323</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 324</span>            <span class="n">params</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
+<span class="linenos"> 251</span><span class="sd">        assert _collect_parameters((T, Callable[P, T])) == (T, P)</span>
+<span class="linenos"> 252</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 253</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos"> 254</span>    <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">args</span><span class="p">:</span>
+<span class="linenos"> 255</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
+<span class="linenos"> 256</span>            <span class="c1"># We don&#39;t want __parameters__ descriptor of a bare Python class.</span>
+<span class="linenos"> 257</span>            <span class="k">pass</span>
+<span class="linenos"> 258</span>        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos"> 259</span>            <span class="c1"># `t` might be a tuple, when `ParamSpec` is substituted with</span>
+<span class="linenos"> 260</span>            <span class="c1"># `[T, int]`, or `[int, *Ts]`, etc.</span>
+<span class="linenos"> 261</span>            <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">t</span><span class="p">:</span>
+<span class="linenos"> 262</span>                <span class="k">for</span> <span class="n">collected</span> <span class="ow">in</span> <span class="n">_collect_parameters</span><span class="p">([</span><span class="n">x</span><span class="p">]):</span>
+<span class="linenos"> 263</span>                    <span class="k">if</span> <span class="n">collected</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
+<span class="linenos"> 264</span>                        <span class="n">parameters</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">collected</span><span class="p">)</span>
+<span class="linenos"> 265</span>        <span class="k">elif</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="s1">&#39;__typing_subst__&#39;</span><span class="p">):</span>
+<span class="linenos"> 266</span>            <span class="k">if</span> <span class="n">t</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
+<span class="linenos"> 267</span>                <span class="n">parameters</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
+<span class="linenos"> 268</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 269</span>            <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="s1">&#39;__parameters__&#39;</span><span class="p">,</span> <span class="p">()):</span>
+<span class="linenos"> 270</span>                <span class="k">if</span> <span class="n">x</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
+<span class="linenos"> 271</span>                    <span class="n">parameters</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="linenos"> 272</span>    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 273</span>
+<span class="linenos"> 274</span>
+<span class="linenos"> 275</span><span class="k">def</span> <span class="nf">_check_generic</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">parameters</span><span class="p">,</span> <span class="n">elen</span><span class="p">):</span>
+<span class="linenos"> 276</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Check correct count for parameters of a generic cls (internal helper).</span>
+<span class="linenos"> 277</span>
+<span class="linenos"> 278</span><span class="sd">    This gives a nice error message in case of count mismatch.</span>
+<span class="linenos"> 279</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 280</span>    <span class="k">if</span> <span class="ow">not</span> <span class="n">elen</span><span class="p">:</span>
+<span class="linenos"> 281</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">cls</span><span class="si">}</span><span class="s2"> is not a generic class&quot;</span><span class="p">)</span>
+<span class="linenos"> 282</span>    <span class="n">alen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 283</span>    <span class="k">if</span> <span class="n">alen</span> <span class="o">!=</span> <span class="n">elen</span><span class="p">:</span>
+<span class="linenos"> 284</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Too </span><span class="si">{</span><span class="s1">&#39;many&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">alen</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">elen</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;few&#39;</span><span class="si">}</span><span class="s2"> arguments for </span><span class="si">{</span><span class="bp">cls</span><span class="si">}</span><span class="s2">;&quot;</span>
+<span class="linenos"> 285</span>                        <span class="sa">f</span><span class="s2">&quot; actual </span><span class="si">{</span><span class="n">alen</span><span class="si">}</span><span class="s2">, expected </span><span class="si">{</span><span class="n">elen</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos"> 286</span>
+<span class="linenos"> 287</span><span class="k">def</span> <span class="nf">_unpack_args</span><span class="p">(</span><span class="n">args</span><span class="p">):</span>
+<span class="linenos"> 288</span>    <span class="n">newargs</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos"> 289</span>    <span class="k">for</span> <span class="n">arg</span> <span class="ow">in</span> <span class="n">args</span><span class="p">:</span>
+<span class="linenos"> 290</span>        <span class="n">subargs</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="s1">&#39;__typing_unpacked_tuple_args__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
+<span class="linenos"> 291</span>        <span class="k">if</span> <span class="n">subargs</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="ow">not</span> <span class="p">(</span><span class="n">subargs</span> <span class="ow">and</span> <span class="n">subargs</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="o">...</span><span class="p">):</span>
+<span class="linenos"> 292</span>            <span class="n">newargs</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">subargs</span><span class="p">)</span>
+<span class="linenos"> 293</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 294</span>            <span class="n">newargs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span>
+<span class="linenos"> 295</span>    <span class="k">return</span> <span class="n">newargs</span>
+<span class="linenos"> 296</span>
+<span class="linenos"> 297</span><span class="k">def</span> <span class="nf">_deduplicate</span><span class="p">(</span><span class="n">params</span><span class="p">):</span>
+<span class="linenos"> 298</span>    <span class="c1"># Weed out strict duplicates, preserving the first of each occurrence.</span>
+<span class="linenos"> 299</span>    <span class="n">all_params</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos"> 300</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">all_params</span><span class="p">)</span> <span class="o">&lt;</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">):</span>
+<span class="linenos"> 301</span>        <span class="n">new_params</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos"> 302</span>        <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">params</span><span class="p">:</span>
+<span class="linenos"> 303</span>            <span class="k">if</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">all_params</span><span class="p">:</span>
+<span class="linenos"> 304</span>                <span class="n">new_params</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
+<span class="linenos"> 305</span>                <span class="n">all_params</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
+<span class="linenos"> 306</span>        <span class="n">params</span> <span class="o">=</span> <span class="n">new_params</span>
+<span class="linenos"> 307</span>        <span class="k">assert</span> <span class="ow">not</span> <span class="n">all_params</span><span class="p">,</span> <span class="n">all_params</span>
+<span class="linenos"> 308</span>    <span class="k">return</span> <span class="n">params</span>
+<span class="linenos"> 309</span>
+<span class="linenos"> 310</span>
+<span class="linenos"> 311</span><span class="k">def</span> <span class="nf">_remove_dups_flatten</span><span class="p">(</span><span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 312</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal helper for Union creation and substitution.</span>
+<span class="linenos"> 313</span>
+<span class="linenos"> 314</span><span class="sd">    Flatten Unions among parameters, then remove duplicates.</span>
+<span class="linenos"> 315</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 316</span>    <span class="c1"># Flatten out Union[Union[...], ...].</span>
+<span class="linenos"> 317</span>    <span class="n">params</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos"> 318</span>    <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
+<span class="linenos"> 319</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="p">(</span><span class="n">_UnionGenericAlias</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">)):</span>
+<span class="linenos"> 320</span>            <span class="n">params</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
+<span class="linenos"> 321</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 322</span>            <span class="n">params</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
+<span class="linenos"> 323</span>
+<span class="linenos"> 324</span>    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_deduplicate</span><span class="p">(</span><span class="n">params</span><span class="p">))</span>
 <span class="linenos"> 325</span>
-<span class="linenos"> 326</span>    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_deduplicate</span><span class="p">(</span><span class="n">params</span><span class="p">))</span>
-<span class="linenos"> 327</span>
-<span class="linenos"> 328</span>
-<span class="linenos"> 329</span><span class="k">def</span> <span class="nf">_flatten_literal_params</span><span class="p">(</span><span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 330</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal helper for Literal creation: flatten Literals among parameters.&quot;&quot;&quot;</span>
-<span class="linenos"> 331</span>    <span class="n">params</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos"> 332</span>    <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
-<span class="linenos"> 333</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">_LiteralGenericAlias</span><span class="p">):</span>
-<span class="linenos"> 334</span>            <span class="n">params</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
-<span class="linenos"> 335</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 336</span>            <span class="n">params</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
-<span class="linenos"> 337</span>    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
-<span class="linenos"> 338</span>
+<span class="linenos"> 326</span>
+<span class="linenos"> 327</span><span class="k">def</span> <span class="nf">_flatten_literal_params</span><span class="p">(</span><span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 328</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal helper for Literal creation: flatten Literals among parameters.&quot;&quot;&quot;</span>
+<span class="linenos"> 329</span>    <span class="n">params</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos"> 330</span>    <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
+<span class="linenos"> 331</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">_LiteralGenericAlias</span><span class="p">):</span>
+<span class="linenos"> 332</span>            <span class="n">params</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
+<span class="linenos"> 333</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 334</span>            <span class="n">params</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
+<span class="linenos"> 335</span>    <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos"> 336</span>
+<span class="linenos"> 337</span>
+<span class="linenos"> 338</span><span class="n">_cleanups</span> <span class="o">=</span> <span class="p">[]</span>
 <span class="linenos"> 339</span>
-<span class="linenos"> 340</span><span class="n">_cleanups</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos"> 341</span>
-<span class="linenos"> 342</span>
-<span class="linenos"> 343</span><span class="k">def</span> <span class="nf">_tp_cache</span><span class="p">(</span><span class="n">func</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">/</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">typed</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
-<span class="linenos"> 344</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal wrapper caching __getitem__ of generic types.</span>
-<span class="linenos"> 345</span>
-<span class="linenos"> 346</span><span class="sd">    For non-hashable arguments, the original function is used as a fallback.</span>
-<span class="linenos"> 347</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 348</span>    <span class="k">def</span> <span class="nf">decorator</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
-<span class="linenos"> 349</span>        <span class="n">cached</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">lru_cache</span><span class="p">(</span><span class="n">typed</span><span class="o">=</span><span class="n">typed</span><span class="p">)(</span><span class="n">func</span><span class="p">)</span>
-<span class="linenos"> 350</span>        <span class="n">_cleanups</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">cached</span><span class="o">.</span><span class="n">cache_clear</span><span class="p">)</span>
-<span class="linenos"> 351</span>
-<span class="linenos"> 352</span>        <span class="nd">@functools</span><span class="o">.</span><span class="n">wraps</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
-<span class="linenos"> 353</span>        <span class="k">def</span> <span class="nf">inner</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
-<span class="linenos"> 354</span>            <span class="k">try</span><span class="p">:</span>
-<span class="linenos"> 355</span>                <span class="k">return</span> <span class="n">cached</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">)</span>
-<span class="linenos"> 356</span>            <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
-<span class="linenos"> 357</span>                <span class="k">pass</span>  <span class="c1"># All real errors (not unhashable args) are raised below.</span>
-<span class="linenos"> 358</span>            <span class="k">return</span> <span class="n">func</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">)</span>
-<span class="linenos"> 359</span>        <span class="k">return</span> <span class="n">inner</span>
+<span class="linenos"> 340</span>
+<span class="linenos"> 341</span><span class="k">def</span> <span class="nf">_tp_cache</span><span class="p">(</span><span class="n">func</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">/</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">typed</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="linenos"> 342</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal wrapper caching __getitem__ of generic types with a fallback to</span>
+<span class="linenos"> 343</span><span class="sd">    original function for non-hashable arguments.</span>
+<span class="linenos"> 344</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 345</span>    <span class="k">def</span> <span class="nf">decorator</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
+<span class="linenos"> 346</span>        <span class="n">cached</span> <span class="o">=</span> <span class="n">functools</span><span class="o">.</span><span class="n">lru_cache</span><span class="p">(</span><span class="n">typed</span><span class="o">=</span><span class="n">typed</span><span class="p">)(</span><span class="n">func</span><span class="p">)</span>
+<span class="linenos"> 347</span>        <span class="n">_cleanups</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">cached</span><span class="o">.</span><span class="n">cache_clear</span><span class="p">)</span>
+<span class="linenos"> 348</span>
+<span class="linenos"> 349</span>        <span class="nd">@functools</span><span class="o">.</span><span class="n">wraps</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
+<span class="linenos"> 350</span>        <span class="k">def</span> <span class="nf">inner</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
+<span class="linenos"> 351</span>            <span class="k">try</span><span class="p">:</span>
+<span class="linenos"> 352</span>                <span class="k">return</span> <span class="n">cached</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">)</span>
+<span class="linenos"> 353</span>            <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
+<span class="linenos"> 354</span>                <span class="k">pass</span>  <span class="c1"># All real errors (not unhashable args) are raised below.</span>
+<span class="linenos"> 355</span>            <span class="k">return</span> <span class="n">func</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">)</span>
+<span class="linenos"> 356</span>        <span class="k">return</span> <span class="n">inner</span>
+<span class="linenos"> 357</span>
+<span class="linenos"> 358</span>    <span class="k">if</span> <span class="n">func</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos"> 359</span>        <span class="k">return</span> <span class="n">decorator</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
 <span class="linenos"> 360</span>
-<span class="linenos"> 361</span>    <span class="k">if</span> <span class="n">func</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos"> 362</span>        <span class="k">return</span> <span class="n">decorator</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
-<span class="linenos"> 363</span>
-<span class="linenos"> 364</span>    <span class="k">return</span> <span class="n">decorator</span>
+<span class="linenos"> 361</span>    <span class="k">return</span> <span class="n">decorator</span>
+<span class="linenos"> 362</span>
+<span class="linenos"> 363</span><span class="k">def</span> <span class="nf">_eval_type</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span><span class="o">=</span><span class="nb">frozenset</span><span class="p">()):</span>
+<span class="linenos"> 364</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Evaluate all forward references in the given type t.</span>
 <span class="linenos"> 365</span>
-<span class="linenos"> 366</span><span class="k">def</span> <span class="nf">_eval_type</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span><span class="o">=</span><span class="nb">frozenset</span><span class="p">()):</span>
-<span class="linenos"> 367</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Evaluate all forward references in the given type t.</span>
-<span class="linenos"> 368</span>
-<span class="linenos"> 369</span><span class="sd">    For use of globalns and localns see the docstring for get_type_hints().</span>
-<span class="linenos"> 370</span><span class="sd">    recursive_guard is used to prevent infinite recursion with a recursive</span>
-<span class="linenos"> 371</span><span class="sd">    ForwardRef.</span>
-<span class="linenos"> 372</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 373</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">ForwardRef</span><span class="p">):</span>
-<span class="linenos"> 374</span>        <span class="k">return</span> <span class="n">t</span><span class="o">.</span><span class="n">_evaluate</span><span class="p">(</span><span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span><span class="p">)</span>
-<span class="linenos"> 375</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">)):</span>
-<span class="linenos"> 376</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">):</span>
-<span class="linenos"> 377</span>            <span class="n">args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span>
-<span class="linenos"> 378</span>                <span class="n">ForwardRef</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">arg</span>
-<span class="linenos"> 379</span>                <span class="k">for</span> <span class="n">arg</span> <span class="ow">in</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span>
-<span class="linenos"> 380</span>            <span class="p">)</span>
-<span class="linenos"> 381</span>            <span class="n">is_unpacked</span> <span class="o">=</span> <span class="n">t</span><span class="o">.</span><span class="n">__unpacked__</span>
-<span class="linenos"> 382</span>            <span class="k">if</span> <span class="n">_should_unflatten_callable_args</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
-<span class="linenos"> 383</span>                <span class="n">t</span> <span class="o">=</span> <span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">[(</span><span class="n">args</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">args</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])]</span>
-<span class="linenos"> 384</span>            <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 385</span>                <span class="n">t</span> <span class="o">=</span> <span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">[</span><span class="n">args</span><span class="p">]</span>
-<span class="linenos"> 386</span>            <span class="k">if</span> <span class="n">is_unpacked</span><span class="p">:</span>
-<span class="linenos"> 387</span>                <span class="n">t</span> <span class="o">=</span> <span class="n">Unpack</span><span class="p">[</span><span class="n">t</span><span class="p">]</span>
-<span class="linenos"> 388</span>        <span class="n">ev_args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_eval_type</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
-<span class="linenos"> 389</span>        <span class="k">if</span> <span class="n">ev_args</span> <span class="o">==</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
-<span class="linenos"> 390</span>            <span class="k">return</span> <span class="n">t</span>
-<span class="linenos"> 391</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">):</span>
-<span class="linenos"> 392</span>            <span class="k">return</span> <span class="n">GenericAlias</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">ev_args</span><span class="p">)</span>
-<span class="linenos"> 393</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">):</span>
-<span class="linenos"> 394</span>            <span class="k">return</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">or_</span><span class="p">,</span> <span class="n">ev_args</span><span class="p">)</span>
-<span class="linenos"> 395</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 396</span>            <span class="k">return</span> <span class="n">t</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">ev_args</span><span class="p">)</span>
-<span class="linenos"> 397</span>    <span class="k">return</span> <span class="n">t</span>
-<span class="linenos"> 398</span>
+<span class="linenos"> 366</span><span class="sd">    For use of globalns and localns see the docstring for get_type_hints().</span>
+<span class="linenos"> 367</span><span class="sd">    recursive_guard is used to prevent infinite recursion with a recursive</span>
+<span class="linenos"> 368</span><span class="sd">    ForwardRef.</span>
+<span class="linenos"> 369</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 370</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">ForwardRef</span><span class="p">):</span>
+<span class="linenos"> 371</span>        <span class="k">return</span> <span class="n">t</span><span class="o">.</span><span class="n">_evaluate</span><span class="p">(</span><span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span><span class="p">)</span>
+<span class="linenos"> 372</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">)):</span>
+<span class="linenos"> 373</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">):</span>
+<span class="linenos"> 374</span>            <span class="n">args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span>
+<span class="linenos"> 375</span>                <span class="n">ForwardRef</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">arg</span>
+<span class="linenos"> 376</span>                <span class="k">for</span> <span class="n">arg</span> <span class="ow">in</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span>
+<span class="linenos"> 377</span>            <span class="p">)</span>
+<span class="linenos"> 378</span>            <span class="n">is_unpacked</span> <span class="o">=</span> <span class="n">t</span><span class="o">.</span><span class="n">__unpacked__</span>
+<span class="linenos"> 379</span>            <span class="k">if</span> <span class="n">_should_unflatten_callable_args</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
+<span class="linenos"> 380</span>                <span class="n">t</span> <span class="o">=</span> <span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">[(</span><span class="n">args</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">args</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])]</span>
+<span class="linenos"> 381</span>            <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 382</span>                <span class="n">t</span> <span class="o">=</span> <span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">[</span><span class="n">args</span><span class="p">]</span>
+<span class="linenos"> 383</span>            <span class="k">if</span> <span class="n">is_unpacked</span><span class="p">:</span>
+<span class="linenos"> 384</span>                <span class="n">t</span> <span class="o">=</span> <span class="n">Unpack</span><span class="p">[</span><span class="n">t</span><span class="p">]</span>
+<span class="linenos"> 385</span>        <span class="n">ev_args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_eval_type</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
+<span class="linenos"> 386</span>        <span class="k">if</span> <span class="n">ev_args</span> <span class="o">==</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
+<span class="linenos"> 387</span>            <span class="k">return</span> <span class="n">t</span>
+<span class="linenos"> 388</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">):</span>
+<span class="linenos"> 389</span>            <span class="k">return</span> <span class="n">GenericAlias</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">ev_args</span><span class="p">)</span>
+<span class="linenos"> 390</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">):</span>
+<span class="linenos"> 391</span>            <span class="k">return</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">or_</span><span class="p">,</span> <span class="n">ev_args</span><span class="p">)</span>
+<span class="linenos"> 392</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 393</span>            <span class="k">return</span> <span class="n">t</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">ev_args</span><span class="p">)</span>
+<span class="linenos"> 394</span>    <span class="k">return</span> <span class="n">t</span>
+<span class="linenos"> 395</span>
+<span class="linenos"> 396</span>
+<span class="linenos"> 397</span><span class="k">class</span> <span class="nc">_Final</span><span class="p">:</span>
+<span class="linenos"> 398</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin to prohibit subclassing.&quot;&quot;&quot;</span>
 <span class="linenos"> 399</span>
-<span class="linenos"> 400</span><span class="k">class</span> <span class="nc">_Final</span><span class="p">:</span>
-<span class="linenos"> 401</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin to prohibit subclassing.&quot;&quot;&quot;</span>
-<span class="linenos"> 402</span>
-<span class="linenos"> 403</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;__weakref__&#39;</span><span class="p">,)</span>
-<span class="linenos"> 404</span>
-<span class="linenos"> 405</span>    <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">/</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
-<span class="linenos"> 406</span>        <span class="k">if</span> <span class="s1">&#39;_root&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwds</span><span class="p">:</span>
-<span class="linenos"> 407</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Cannot subclass special typing classes&quot;</span><span class="p">)</span>
+<span class="linenos"> 400</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;__weakref__&#39;</span><span class="p">,)</span>
+<span class="linenos"> 401</span>
+<span class="linenos"> 402</span>    <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">/</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
+<span class="linenos"> 403</span>        <span class="k">if</span> <span class="s1">&#39;_root&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">kwds</span><span class="p">:</span>
+<span class="linenos"> 404</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Cannot subclass special typing classes&quot;</span><span class="p">)</span>
+<span class="linenos"> 405</span>
+<span class="linenos"> 406</span><span class="k">class</span> <span class="nc">_Immutable</span><span class="p">:</span>
+<span class="linenos"> 407</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin to indicate that object should not be copied.&quot;&quot;&quot;</span>
 <span class="linenos"> 408</span>
-<span class="linenos"> 409</span><span class="k">class</span> <span class="nc">_Immutable</span><span class="p">:</span>
-<span class="linenos"> 410</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin to indicate that object should not be copied.&quot;&quot;&quot;</span>
-<span class="linenos"> 411</span>
-<span class="linenos"> 412</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos"> 409</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos"> 410</span>
+<span class="linenos"> 411</span>    <span class="k">def</span> <span class="nf">__copy__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 412</span>        <span class="k">return</span> <span class="bp">self</span>
 <span class="linenos"> 413</span>
-<span class="linenos"> 414</span>    <span class="k">def</span> <span class="nf">__copy__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 414</span>    <span class="k">def</span> <span class="nf">__deepcopy__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">memo</span><span class="p">):</span>
 <span class="linenos"> 415</span>        <span class="k">return</span> <span class="bp">self</span>
 <span class="linenos"> 416</span>
-<span class="linenos"> 417</span>    <span class="k">def</span> <span class="nf">__deepcopy__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">memo</span><span class="p">):</span>
-<span class="linenos"> 418</span>        <span class="k">return</span> <span class="bp">self</span>
-<span class="linenos"> 419</span>
+<span class="linenos"> 417</span>
+<span class="linenos"> 418</span><span class="k">class</span> <span class="nc">_NotIterable</span><span class="p">:</span>
+<span class="linenos"> 419</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin to prevent iteration, without being compatible with Iterable.</span>
 <span class="linenos"> 420</span>
-<span class="linenos"> 421</span><span class="k">class</span> <span class="nc">_NotIterable</span><span class="p">:</span>
-<span class="linenos"> 422</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin to prevent iteration, without being compatible with Iterable.</span>
-<span class="linenos"> 423</span>
-<span class="linenos"> 424</span><span class="sd">    That is, we could do::</span>
-<span class="linenos"> 425</span>
-<span class="linenos"> 426</span><span class="sd">        def __iter__(self): raise TypeError()</span>
+<span class="linenos"> 421</span><span class="sd">    That is, we could do::</span>
+<span class="linenos"> 422</span>
+<span class="linenos"> 423</span><span class="sd">        def __iter__(self): raise TypeError()</span>
+<span class="linenos"> 424</span>
+<span class="linenos"> 425</span><span class="sd">    But this would make users of this mixin duck type-compatible with</span>
+<span class="linenos"> 426</span><span class="sd">    collections.abc.Iterable - isinstance(foo, Iterable) would be True.</span>
 <span class="linenos"> 427</span>
-<span class="linenos"> 428</span><span class="sd">    But this would make users of this mixin duck type-compatible with</span>
-<span class="linenos"> 429</span><span class="sd">    collections.abc.Iterable - isinstance(foo, Iterable) would be True.</span>
-<span class="linenos"> 430</span>
-<span class="linenos"> 431</span><span class="sd">    Luckily, we can instead prevent iteration by setting __iter__ to None, which</span>
-<span class="linenos"> 432</span><span class="sd">    is treated specially.</span>
-<span class="linenos"> 433</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 428</span><span class="sd">    Luckily, we can instead prevent iteration by setting __iter__ to None, which</span>
+<span class="linenos"> 429</span><span class="sd">    is treated specially.</span>
+<span class="linenos"> 430</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 431</span>
+<span class="linenos"> 432</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos"> 433</span>    <span class="fm">__iter__</span> <span class="o">=</span> <span class="kc">None</span>
 <span class="linenos"> 434</span>
-<span class="linenos"> 435</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
-<span class="linenos"> 436</span>    <span class="fm">__iter__</span> <span class="o">=</span> <span class="kc">None</span>
-<span class="linenos"> 437</span>
-<span class="linenos"> 438</span>
-<span class="linenos"> 439</span><span class="c1"># Internal indicator of special typing constructs.</span>
-<span class="linenos"> 440</span><span class="c1"># See __doc__ instance attribute for specific docs.</span>
-<span class="linenos"> 441</span><span class="k">class</span> <span class="nc">_SpecialForm</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos"> 442</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;_name&#39;</span><span class="p">,</span> <span class="s1">&#39;__doc__&#39;</span><span class="p">,</span> <span class="s1">&#39;_getitem&#39;</span><span class="p">)</span>
-<span class="linenos"> 443</span>
-<span class="linenos"> 444</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">getitem</span><span class="p">):</span>
-<span class="linenos"> 445</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_getitem</span> <span class="o">=</span> <span class="n">getitem</span>
-<span class="linenos"> 446</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="o">=</span> <span class="n">getitem</span><span class="o">.</span><span class="vm">__name__</span>
-<span class="linenos"> 447</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="n">getitem</span><span class="o">.</span><span class="vm">__doc__</span>
-<span class="linenos"> 448</span>
-<span class="linenos"> 449</span>    <span class="k">def</span> <span class="fm">__getattr__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item</span><span class="p">):</span>
-<span class="linenos"> 450</span>        <span class="k">if</span> <span class="n">item</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="s1">&#39;__qualname__&#39;</span><span class="p">}:</span>
-<span class="linenos"> 451</span>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
-<span class="linenos"> 452</span>
-<span class="linenos"> 453</span>        <span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
+<span class="linenos"> 435</span>
+<span class="linenos"> 436</span><span class="c1"># Internal indicator of special typing constructs.</span>
+<span class="linenos"> 437</span><span class="c1"># See __doc__ instance attribute for specific docs.</span>
+<span class="linenos"> 438</span><span class="k">class</span> <span class="nc">_SpecialForm</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos"> 439</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;_name&#39;</span><span class="p">,</span> <span class="s1">&#39;__doc__&#39;</span><span class="p">,</span> <span class="s1">&#39;_getitem&#39;</span><span class="p">)</span>
+<span class="linenos"> 440</span>
+<span class="linenos"> 441</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">getitem</span><span class="p">):</span>
+<span class="linenos"> 442</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_getitem</span> <span class="o">=</span> <span class="n">getitem</span>
+<span class="linenos"> 443</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="o">=</span> <span class="n">getitem</span><span class="o">.</span><span class="vm">__name__</span>
+<span class="linenos"> 444</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="n">getitem</span><span class="o">.</span><span class="vm">__doc__</span>
+<span class="linenos"> 445</span>
+<span class="linenos"> 446</span>    <span class="k">def</span> <span class="fm">__getattr__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item</span><span class="p">):</span>
+<span class="linenos"> 447</span>        <span class="k">if</span> <span class="n">item</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="s1">&#39;__qualname__&#39;</span><span class="p">}:</span>
+<span class="linenos"> 448</span>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
+<span class="linenos"> 449</span>
+<span class="linenos"> 450</span>        <span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
+<span class="linenos"> 451</span>
+<span class="linenos"> 452</span>    <span class="k">def</span> <span class="nf">__mro_entries__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bases</span><span class="p">):</span>
+<span class="linenos"> 453</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Cannot subclass </span><span class="si">{</span><span class="bp">self</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
 <span class="linenos"> 454</span>
-<span class="linenos"> 455</span>    <span class="k">def</span> <span class="nf">__mro_entries__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bases</span><span class="p">):</span>
-<span class="linenos"> 456</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Cannot subclass </span><span class="si">{</span><span class="bp">self</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos"> 455</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 456</span>        <span class="k">return</span> <span class="s1">&#39;typing.&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
 <span class="linenos"> 457</span>
-<span class="linenos"> 458</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos"> 459</span>        <span class="k">return</span> <span class="s1">&#39;typing.&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
+<span class="linenos"> 458</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 459</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
 <span class="linenos"> 460</span>
-<span class="linenos"> 461</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos"> 462</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
+<span class="linenos"> 461</span>    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
+<span class="linenos"> 462</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Cannot instantiate </span><span class="si">{</span><span class="bp">self</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
 <span class="linenos"> 463</span>
-<span class="linenos"> 464</span>    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
-<span class="linenos"> 465</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Cannot instantiate </span><span class="si">{</span><span class="bp">self</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos"> 464</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos"> 465</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">]</span>
 <span class="linenos"> 466</span>
-<span class="linenos"> 467</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos"> 468</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">]</span>
+<span class="linenos"> 467</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos"> 468</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
 <span class="linenos"> 469</span>
-<span class="linenos"> 470</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos"> 471</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
+<span class="linenos"> 470</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">):</span>
+<span class="linenos"> 471</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> cannot be used with isinstance()&quot;</span><span class="p">)</span>
 <span class="linenos"> 472</span>
-<span class="linenos"> 473</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">):</span>
-<span class="linenos"> 474</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> cannot be used with isinstance()&quot;</span><span class="p">)</span>
+<span class="linenos"> 473</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="bp">cls</span><span class="p">):</span>
+<span class="linenos"> 474</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> cannot be used with issubclass()&quot;</span><span class="p">)</span>
 <span class="linenos"> 475</span>
-<span class="linenos"> 476</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="bp">cls</span><span class="p">):</span>
-<span class="linenos"> 477</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> cannot be used with issubclass()&quot;</span><span class="p">)</span>
-<span class="linenos"> 478</span>
-<span class="linenos"> 479</span>    <span class="nd">@_tp_cache</span>
-<span class="linenos"> 480</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 481</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_getitem</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">)</span>
-<span class="linenos"> 482</span>
-<span class="linenos"> 483</span>
-<span class="linenos"> 484</span><span class="k">class</span> <span class="nc">_LiteralSpecialForm</span><span class="p">(</span><span class="n">_SpecialForm</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos"> 485</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 486</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos"> 487</span>            <span class="n">parameters</span> <span class="o">=</span> <span class="p">(</span><span class="n">parameters</span><span class="p">,)</span>
-<span class="linenos"> 488</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_getitem</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">parameters</span><span class="p">)</span>
-<span class="linenos"> 489</span>
-<span class="linenos"> 490</span>
-<span class="linenos"> 491</span><span class="k">class</span> <span class="nc">_AnyMeta</span><span class="p">(</span><span class="nb">type</span><span class="p">):</span>
-<span class="linenos"> 492</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">):</span>
-<span class="linenos"> 493</span>        <span class="k">if</span> <span class="bp">self</span> <span class="ow">is</span> <span class="n">Any</span><span class="p">:</span>
-<span class="linenos"> 494</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;typing.Any cannot be used with isinstance()&quot;</span><span class="p">)</span>
-<span class="linenos"> 495</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__instancecheck__</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
-<span class="linenos"> 496</span>
-<span class="linenos"> 497</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos"> 498</span>        <span class="k">if</span> <span class="bp">self</span> <span class="ow">is</span> <span class="n">Any</span><span class="p">:</span>
-<span class="linenos"> 499</span>            <span class="k">return</span> <span class="s2">&quot;typing.Any&quot;</span>
-<span class="linenos"> 500</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__repr__</span><span class="p">()</span>  <span class="c1"># respect to subclasses</span>
-<span class="linenos"> 501</span>
+<span class="linenos"> 476</span>    <span class="nd">@_tp_cache</span>
+<span class="linenos"> 477</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 478</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_getitem</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 479</span>
+<span class="linenos"> 480</span>
+<span class="linenos"> 481</span><span class="k">class</span> <span class="nc">_LiteralSpecialForm</span><span class="p">(</span><span class="n">_SpecialForm</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos"> 482</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 483</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos"> 484</span>            <span class="n">parameters</span> <span class="o">=</span> <span class="p">(</span><span class="n">parameters</span><span class="p">,)</span>
+<span class="linenos"> 485</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_getitem</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 486</span>
+<span class="linenos"> 487</span>
+<span class="linenos"> 488</span><span class="k">class</span> <span class="nc">_AnyMeta</span><span class="p">(</span><span class="nb">type</span><span class="p">):</span>
+<span class="linenos"> 489</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">):</span>
+<span class="linenos"> 490</span>        <span class="k">if</span> <span class="bp">self</span> <span class="ow">is</span> <span class="n">Any</span><span class="p">:</span>
+<span class="linenos"> 491</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;typing.Any cannot be used with isinstance()&quot;</span><span class="p">)</span>
+<span class="linenos"> 492</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__instancecheck__</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
+<span class="linenos"> 493</span>
+<span class="linenos"> 494</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 495</span>        <span class="k">if</span> <span class="bp">self</span> <span class="ow">is</span> <span class="n">Any</span><span class="p">:</span>
+<span class="linenos"> 496</span>            <span class="k">return</span> <span class="s2">&quot;typing.Any&quot;</span>
+<span class="linenos"> 497</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__repr__</span><span class="p">()</span>  <span class="c1"># respect to subclasses</span>
+<span class="linenos"> 498</span>
+<span class="linenos"> 499</span>
+<span class="linenos"> 500</span><span class="k">class</span> <span class="nc">Any</span><span class="p">(</span><span class="n">metaclass</span><span class="o">=</span><span class="n">_AnyMeta</span><span class="p">):</span>
+<span class="linenos"> 501</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special type indicating an unconstrained type.</span>
 <span class="linenos"> 502</span>
-<span class="linenos"> 503</span><span class="k">class</span> <span class="nc">Any</span><span class="p">(</span><span class="n">metaclass</span><span class="o">=</span><span class="n">_AnyMeta</span><span class="p">):</span>
-<span class="linenos"> 504</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special type indicating an unconstrained type.</span>
-<span class="linenos"> 505</span>
-<span class="linenos"> 506</span><span class="sd">    - Any is compatible with every type.</span>
-<span class="linenos"> 507</span><span class="sd">    - Any assumed to have all methods.</span>
-<span class="linenos"> 508</span><span class="sd">    - All values assumed to be instances of Any.</span>
-<span class="linenos"> 509</span>
-<span class="linenos"> 510</span><span class="sd">    Note that all the above statements are true from the point of view of</span>
-<span class="linenos"> 511</span><span class="sd">    static type checkers. At runtime, Any should not be used with instance</span>
-<span class="linenos"> 512</span><span class="sd">    checks.</span>
-<span class="linenos"> 513</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 514</span>
-<span class="linenos"> 515</span>    <span class="k">def</span> <span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos"> 516</span>        <span class="k">if</span> <span class="bp">cls</span> <span class="ow">is</span> <span class="n">Any</span><span class="p">:</span>
-<span class="linenos"> 517</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Any cannot be instantiated&quot;</span><span class="p">)</span>
-<span class="linenos"> 518</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos"> 519</span>
-<span class="linenos"> 520</span>
-<span class="linenos"> 521</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 522</span><span class="k">def</span> <span class="nf">NoReturn</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 523</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special type indicating functions that never return.</span>
-<span class="linenos"> 524</span>
-<span class="linenos"> 525</span><span class="sd">    Example::</span>
-<span class="linenos"> 526</span>
-<span class="linenos"> 527</span><span class="sd">        from typing import NoReturn</span>
+<span class="linenos"> 503</span><span class="sd">    - Any is compatible with every type.</span>
+<span class="linenos"> 504</span><span class="sd">    - Any assumed to have all methods.</span>
+<span class="linenos"> 505</span><span class="sd">    - All values assumed to be instances of Any.</span>
+<span class="linenos"> 506</span>
+<span class="linenos"> 507</span><span class="sd">    Note that all the above statements are true from the point of view of</span>
+<span class="linenos"> 508</span><span class="sd">    static type checkers. At runtime, Any should not be used with instance</span>
+<span class="linenos"> 509</span><span class="sd">    checks.</span>
+<span class="linenos"> 510</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 511</span>
+<span class="linenos"> 512</span>    <span class="k">def</span> <span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos"> 513</span>        <span class="k">if</span> <span class="bp">cls</span> <span class="ow">is</span> <span class="n">Any</span><span class="p">:</span>
+<span class="linenos"> 514</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Any cannot be instantiated&quot;</span><span class="p">)</span>
+<span class="linenos"> 515</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos"> 516</span>
+<span class="linenos"> 517</span>
+<span class="linenos"> 518</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 519</span><span class="k">def</span> <span class="nf">NoReturn</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 520</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special type indicating functions that never return.</span>
+<span class="linenos"> 521</span>
+<span class="linenos"> 522</span><span class="sd">    Example::</span>
+<span class="linenos"> 523</span>
+<span class="linenos"> 524</span><span class="sd">        from typing import NoReturn</span>
+<span class="linenos"> 525</span>
+<span class="linenos"> 526</span><span class="sd">        def stop() -&gt; NoReturn:</span>
+<span class="linenos"> 527</span><span class="sd">            raise Exception(&#39;no way&#39;)</span>
 <span class="linenos"> 528</span>
-<span class="linenos"> 529</span><span class="sd">        def stop() -&gt; NoReturn:</span>
-<span class="linenos"> 530</span><span class="sd">            raise Exception(&#39;no way&#39;)</span>
-<span class="linenos"> 531</span>
-<span class="linenos"> 532</span><span class="sd">    NoReturn can also be used as a bottom type, a type that</span>
-<span class="linenos"> 533</span><span class="sd">    has no values. Starting in Python 3.11, the Never type should</span>
-<span class="linenos"> 534</span><span class="sd">    be used for this concept instead. Type checkers should treat the two</span>
-<span class="linenos"> 535</span><span class="sd">    equivalently.</span>
-<span class="linenos"> 536</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 537</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
-<span class="linenos"> 538</span>
-<span class="linenos"> 539</span><span class="c1"># This is semantically identical to NoReturn, but it is implemented</span>
-<span class="linenos"> 540</span><span class="c1"># separately so that type checkers can distinguish between the two</span>
-<span class="linenos"> 541</span><span class="c1"># if they want.</span>
-<span class="linenos"> 542</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 543</span><span class="k">def</span> <span class="nf">Never</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 544</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;The bottom type, a type that has no members.</span>
+<span class="linenos"> 529</span><span class="sd">    NoReturn can also be used as a bottom type, a type that</span>
+<span class="linenos"> 530</span><span class="sd">    has no values. Starting in Python 3.11, the Never type should</span>
+<span class="linenos"> 531</span><span class="sd">    be used for this concept instead. Type checkers should treat the two</span>
+<span class="linenos"> 532</span><span class="sd">    equivalently.</span>
+<span class="linenos"> 533</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 534</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
+<span class="linenos"> 535</span>
+<span class="linenos"> 536</span><span class="c1"># This is semantically identical to NoReturn, but it is implemented</span>
+<span class="linenos"> 537</span><span class="c1"># separately so that type checkers can distinguish between the two</span>
+<span class="linenos"> 538</span><span class="c1"># if they want.</span>
+<span class="linenos"> 539</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 540</span><span class="k">def</span> <span class="nf">Never</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 541</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;The bottom type, a type that has no members.</span>
+<span class="linenos"> 542</span>
+<span class="linenos"> 543</span><span class="sd">    This can be used to define a function that should never be</span>
+<span class="linenos"> 544</span><span class="sd">    called, or a function that never returns::</span>
 <span class="linenos"> 545</span>
-<span class="linenos"> 546</span><span class="sd">    This can be used to define a function that should never be</span>
-<span class="linenos"> 547</span><span class="sd">    called, or a function that never returns::</span>
-<span class="linenos"> 548</span>
-<span class="linenos"> 549</span><span class="sd">        from typing import Never</span>
+<span class="linenos"> 546</span><span class="sd">        from typing import Never</span>
+<span class="linenos"> 547</span>
+<span class="linenos"> 548</span><span class="sd">        def never_call_me(arg: Never) -&gt; None:</span>
+<span class="linenos"> 549</span><span class="sd">            pass</span>
 <span class="linenos"> 550</span>
-<span class="linenos"> 551</span><span class="sd">        def never_call_me(arg: Never) -&gt; None:</span>
-<span class="linenos"> 552</span><span class="sd">            pass</span>
-<span class="linenos"> 553</span>
-<span class="linenos"> 554</span><span class="sd">        def int_or_str(arg: int | str) -&gt; None:</span>
-<span class="linenos"> 555</span><span class="sd">            never_call_me(arg)  # type checker error</span>
-<span class="linenos"> 556</span><span class="sd">            match arg:</span>
-<span class="linenos"> 557</span><span class="sd">                case int():</span>
-<span class="linenos"> 558</span><span class="sd">                    print(&quot;It&#39;s an int&quot;)</span>
-<span class="linenos"> 559</span><span class="sd">                case str():</span>
-<span class="linenos"> 560</span><span class="sd">                    print(&quot;It&#39;s a str&quot;)</span>
-<span class="linenos"> 561</span><span class="sd">                case _:</span>
-<span class="linenos"> 562</span><span class="sd">                    never_call_me(arg)  # OK, arg is of type Never</span>
-<span class="linenos"> 563</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 564</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
-<span class="linenos"> 565</span>
-<span class="linenos"> 566</span>
-<span class="linenos"> 567</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 568</span><span class="k">def</span> <span class="nf">Self</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 569</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Used to spell the type of &quot;self&quot; in classes.</span>
-<span class="linenos"> 570</span>
-<span class="linenos"> 571</span><span class="sd">    Example::</span>
-<span class="linenos"> 572</span>
-<span class="linenos"> 573</span><span class="sd">        from typing import Self</span>
-<span class="linenos"> 574</span>
-<span class="linenos"> 575</span><span class="sd">        class Foo:</span>
-<span class="linenos"> 576</span><span class="sd">            def return_self(self) -&gt; Self:</span>
-<span class="linenos"> 577</span><span class="sd">                ...</span>
-<span class="linenos"> 578</span><span class="sd">                return self</span>
-<span class="linenos"> 579</span>
-<span class="linenos"> 580</span><span class="sd">    This is especially useful for:</span>
-<span class="linenos"> 581</span><span class="sd">        - classmethods that are used as alternative constructors</span>
-<span class="linenos"> 582</span><span class="sd">        - annotating an `__enter__` method which returns self</span>
-<span class="linenos"> 583</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 584</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
-<span class="linenos"> 585</span>
-<span class="linenos"> 586</span>
-<span class="linenos"> 587</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 588</span><span class="k">def</span> <span class="nf">LiteralString</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 589</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Represents an arbitrary literal string.</span>
-<span class="linenos"> 590</span>
-<span class="linenos"> 591</span><span class="sd">    Example::</span>
-<span class="linenos"> 592</span>
-<span class="linenos"> 593</span><span class="sd">        from typing import LiteralString</span>
+<span class="linenos"> 551</span><span class="sd">        def int_or_str(arg: int | str) -&gt; None:</span>
+<span class="linenos"> 552</span><span class="sd">            never_call_me(arg)  # type checker error</span>
+<span class="linenos"> 553</span><span class="sd">            match arg:</span>
+<span class="linenos"> 554</span><span class="sd">                case int():</span>
+<span class="linenos"> 555</span><span class="sd">                    print(&quot;It&#39;s an int&quot;)</span>
+<span class="linenos"> 556</span><span class="sd">                case str():</span>
+<span class="linenos"> 557</span><span class="sd">                    print(&quot;It&#39;s a str&quot;)</span>
+<span class="linenos"> 558</span><span class="sd">                case _:</span>
+<span class="linenos"> 559</span><span class="sd">                    never_call_me(arg)  # ok, arg is of type Never</span>
+<span class="linenos"> 560</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 561</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
+<span class="linenos"> 562</span>
+<span class="linenos"> 563</span>
+<span class="linenos"> 564</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 565</span><span class="k">def</span> <span class="nf">Self</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 566</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Used to spell the type of &quot;self&quot; in classes.</span>
+<span class="linenos"> 567</span>
+<span class="linenos"> 568</span><span class="sd">    Example::</span>
+<span class="linenos"> 569</span>
+<span class="linenos"> 570</span><span class="sd">        from typing import Self</span>
+<span class="linenos"> 571</span>
+<span class="linenos"> 572</span><span class="sd">        class Foo:</span>
+<span class="linenos"> 573</span><span class="sd">            def return_self(self) -&gt; Self:</span>
+<span class="linenos"> 574</span><span class="sd">                ...</span>
+<span class="linenos"> 575</span><span class="sd">                return self</span>
+<span class="linenos"> 576</span>
+<span class="linenos"> 577</span><span class="sd">    This is especially useful for:</span>
+<span class="linenos"> 578</span><span class="sd">        - classmethods that are used as alternative constructors</span>
+<span class="linenos"> 579</span><span class="sd">        - annotating an `__enter__` method which returns self</span>
+<span class="linenos"> 580</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 581</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
+<span class="linenos"> 582</span>
+<span class="linenos"> 583</span>
+<span class="linenos"> 584</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 585</span><span class="k">def</span> <span class="nf">LiteralString</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 586</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Represents an arbitrary literal string.</span>
+<span class="linenos"> 587</span>
+<span class="linenos"> 588</span><span class="sd">    Example::</span>
+<span class="linenos"> 589</span>
+<span class="linenos"> 590</span><span class="sd">        from typing import LiteralString</span>
+<span class="linenos"> 591</span>
+<span class="linenos"> 592</span><span class="sd">        def run_query(sql: LiteralString) -&gt; ...</span>
+<span class="linenos"> 593</span><span class="sd">            ...</span>
 <span class="linenos"> 594</span>
-<span class="linenos"> 595</span><span class="sd">        def run_query(sql: LiteralString) -&gt; None:</span>
-<span class="linenos"> 596</span><span class="sd">            ...</span>
-<span class="linenos"> 597</span>
-<span class="linenos"> 598</span><span class="sd">        def caller(arbitrary_string: str, literal_string: LiteralString) -&gt; None:</span>
-<span class="linenos"> 599</span><span class="sd">            run_query(&quot;SELECT * FROM students&quot;)  # OK</span>
-<span class="linenos"> 600</span><span class="sd">            run_query(literal_string)  # OK</span>
-<span class="linenos"> 601</span><span class="sd">            run_query(&quot;SELECT * FROM &quot; + literal_string)  # OK</span>
-<span class="linenos"> 602</span><span class="sd">            run_query(arbitrary_string)  # type checker error</span>
-<span class="linenos"> 603</span><span class="sd">            run_query(  # type checker error</span>
-<span class="linenos"> 604</span><span class="sd">                f&quot;SELECT * FROM students WHERE name = {arbitrary_string}&quot;</span>
-<span class="linenos"> 605</span><span class="sd">            )</span>
-<span class="linenos"> 606</span>
-<span class="linenos"> 607</span><span class="sd">    Only string literals and other LiteralStrings are compatible</span>
-<span class="linenos"> 608</span><span class="sd">    with LiteralString. This provides a tool to help prevent</span>
-<span class="linenos"> 609</span><span class="sd">    security issues such as SQL injection.</span>
-<span class="linenos"> 610</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 611</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
-<span class="linenos"> 612</span>
-<span class="linenos"> 613</span>
-<span class="linenos"> 614</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 615</span><span class="k">def</span> <span class="nf">ClassVar</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 616</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special type construct to mark class variables.</span>
-<span class="linenos"> 617</span>
-<span class="linenos"> 618</span><span class="sd">    An annotation wrapped in ClassVar indicates that a given</span>
-<span class="linenos"> 619</span><span class="sd">    attribute is intended to be used as a class variable and</span>
-<span class="linenos"> 620</span><span class="sd">    should not be set on instances of that class.</span>
-<span class="linenos"> 621</span>
-<span class="linenos"> 622</span><span class="sd">    Usage::</span>
-<span class="linenos"> 623</span>
-<span class="linenos"> 624</span><span class="sd">        class Starship:</span>
-<span class="linenos"> 625</span><span class="sd">            stats: ClassVar[dict[str, int]] = {} # class variable</span>
-<span class="linenos"> 626</span><span class="sd">            damage: int = 10                     # instance variable</span>
-<span class="linenos"> 627</span>
-<span class="linenos"> 628</span><span class="sd">    ClassVar accepts only types and cannot be further subscribed.</span>
-<span class="linenos"> 629</span>
-<span class="linenos"> 630</span><span class="sd">    Note that ClassVar is not a class itself, and should not</span>
-<span class="linenos"> 631</span><span class="sd">    be used with isinstance() or issubclass().</span>
-<span class="linenos"> 632</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 633</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s1"> accepts only single type.&#39;</span><span class="p">)</span>
-<span class="linenos"> 634</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
-<span class="linenos"> 635</span>
-<span class="linenos"> 636</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 637</span><span class="k">def</span> <span class="nf">Final</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 638</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing construct to indicate final names to type checkers.</span>
-<span class="linenos"> 639</span>
-<span class="linenos"> 640</span><span class="sd">    A final name cannot be re-assigned or overridden in a subclass.</span>
+<span class="linenos"> 595</span><span class="sd">        def caller(arbitrary_string: str, literal_string: LiteralString) -&gt; None:</span>
+<span class="linenos"> 596</span><span class="sd">            run_query(&quot;SELECT * FROM students&quot;)  # ok</span>
+<span class="linenos"> 597</span><span class="sd">            run_query(literal_string)  # ok</span>
+<span class="linenos"> 598</span><span class="sd">            run_query(&quot;SELECT * FROM &quot; + literal_string)  # ok</span>
+<span class="linenos"> 599</span><span class="sd">            run_query(arbitrary_string)  # type checker error</span>
+<span class="linenos"> 600</span><span class="sd">            run_query(  # type checker error</span>
+<span class="linenos"> 601</span><span class="sd">                f&quot;SELECT * FROM students WHERE name = {arbitrary_string}&quot;</span>
+<span class="linenos"> 602</span><span class="sd">            )</span>
+<span class="linenos"> 603</span>
+<span class="linenos"> 604</span><span class="sd">    Only string literals and other LiteralStrings are compatible</span>
+<span class="linenos"> 605</span><span class="sd">    with LiteralString. This provides a tool to help prevent</span>
+<span class="linenos"> 606</span><span class="sd">    security issues such as SQL injection.</span>
+<span class="linenos"> 607</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 608</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
+<span class="linenos"> 609</span>
+<span class="linenos"> 610</span>
+<span class="linenos"> 611</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 612</span><span class="k">def</span> <span class="nf">ClassVar</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 613</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special type construct to mark class variables.</span>
+<span class="linenos"> 614</span>
+<span class="linenos"> 615</span><span class="sd">    An annotation wrapped in ClassVar indicates that a given</span>
+<span class="linenos"> 616</span><span class="sd">    attribute is intended to be used as a class variable and</span>
+<span class="linenos"> 617</span><span class="sd">    should not be set on instances of that class. Usage::</span>
+<span class="linenos"> 618</span>
+<span class="linenos"> 619</span><span class="sd">        class Starship:</span>
+<span class="linenos"> 620</span><span class="sd">            stats: ClassVar[Dict[str, int]] = {} # class variable</span>
+<span class="linenos"> 621</span><span class="sd">            damage: int = 10                     # instance variable</span>
+<span class="linenos"> 622</span>
+<span class="linenos"> 623</span><span class="sd">    ClassVar accepts only types and cannot be further subscribed.</span>
+<span class="linenos"> 624</span>
+<span class="linenos"> 625</span><span class="sd">    Note that ClassVar is not a class itself, and should not</span>
+<span class="linenos"> 626</span><span class="sd">    be used with isinstance() or issubclass().</span>
+<span class="linenos"> 627</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 628</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s1"> accepts only single type.&#39;</span><span class="p">)</span>
+<span class="linenos"> 629</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
+<span class="linenos"> 630</span>
+<span class="linenos"> 631</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 632</span><span class="k">def</span> <span class="nf">Final</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 633</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing construct to indicate final names to type checkers.</span>
+<span class="linenos"> 634</span>
+<span class="linenos"> 635</span><span class="sd">    A final name cannot be re-assigned or overridden in a subclass.</span>
+<span class="linenos"> 636</span>
+<span class="linenos"> 637</span><span class="sd">    For example::</span>
+<span class="linenos"> 638</span>
+<span class="linenos"> 639</span><span class="sd">        MAX_SIZE: Final = 9000</span>
+<span class="linenos"> 640</span><span class="sd">        MAX_SIZE += 1  # Error reported by type checker</span>
 <span class="linenos"> 641</span>
-<span class="linenos"> 642</span><span class="sd">    For example::</span>
-<span class="linenos"> 643</span>
-<span class="linenos"> 644</span><span class="sd">        MAX_SIZE: Final = 9000</span>
-<span class="linenos"> 645</span><span class="sd">        MAX_SIZE += 1  # Error reported by type checker</span>
-<span class="linenos"> 646</span>
-<span class="linenos"> 647</span><span class="sd">        class Connection:</span>
-<span class="linenos"> 648</span><span class="sd">            TIMEOUT: Final[int] = 10</span>
-<span class="linenos"> 649</span>
-<span class="linenos"> 650</span><span class="sd">        class FastConnector(Connection):</span>
-<span class="linenos"> 651</span><span class="sd">            TIMEOUT = 1  # Error reported by type checker</span>
+<span class="linenos"> 642</span><span class="sd">        class Connection:</span>
+<span class="linenos"> 643</span><span class="sd">            TIMEOUT: Final[int] = 10</span>
+<span class="linenos"> 644</span>
+<span class="linenos"> 645</span><span class="sd">        class FastConnector(Connection):</span>
+<span class="linenos"> 646</span><span class="sd">            TIMEOUT = 1  # Error reported by type checker</span>
+<span class="linenos"> 647</span>
+<span class="linenos"> 648</span><span class="sd">    There is no runtime checking of these properties.</span>
+<span class="linenos"> 649</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 650</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s1"> accepts only single type.&#39;</span><span class="p">)</span>
+<span class="linenos"> 651</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
 <span class="linenos"> 652</span>
-<span class="linenos"> 653</span><span class="sd">    There is no runtime checking of these properties.</span>
-<span class="linenos"> 654</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 655</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s1"> accepts only single type.&#39;</span><span class="p">)</span>
-<span class="linenos"> 656</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
-<span class="linenos"> 657</span>
-<span class="linenos"> 658</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 659</span><span class="k">def</span> <span class="nf">Union</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 660</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Union type; Union[X, Y] means either X or Y.</span>
-<span class="linenos"> 661</span>
-<span class="linenos"> 662</span><span class="sd">    On Python 3.10 and higher, the | operator</span>
-<span class="linenos"> 663</span><span class="sd">    can also be used to denote unions;</span>
-<span class="linenos"> 664</span><span class="sd">    X | Y means the same thing to the type checker as Union[X, Y].</span>
-<span class="linenos"> 665</span>
-<span class="linenos"> 666</span><span class="sd">    To define a union, use e.g. Union[int, str]. Details:</span>
-<span class="linenos"> 667</span><span class="sd">    - The arguments must be types and there must be at least one.</span>
-<span class="linenos"> 668</span><span class="sd">    - None as an argument is a special case and is replaced by</span>
-<span class="linenos"> 669</span><span class="sd">      type(None).</span>
-<span class="linenos"> 670</span><span class="sd">    - Unions of unions are flattened, e.g.::</span>
-<span class="linenos"> 671</span>
-<span class="linenos"> 672</span><span class="sd">        assert Union[Union[int, str], float] == Union[int, str, float]</span>
-<span class="linenos"> 673</span>
-<span class="linenos"> 674</span><span class="sd">    - Unions of a single argument vanish, e.g.::</span>
-<span class="linenos"> 675</span>
-<span class="linenos"> 676</span><span class="sd">        assert Union[int] == int  # The constructor actually returns int</span>
-<span class="linenos"> 677</span>
-<span class="linenos"> 678</span><span class="sd">    - Redundant arguments are skipped, e.g.::</span>
-<span class="linenos"> 679</span>
-<span class="linenos"> 680</span><span class="sd">        assert Union[int, str, int] == Union[int, str]</span>
-<span class="linenos"> 681</span>
-<span class="linenos"> 682</span><span class="sd">    - When comparing unions, the argument order is ignored, e.g.::</span>
-<span class="linenos"> 683</span>
-<span class="linenos"> 684</span><span class="sd">        assert Union[int, str] == Union[str, int]</span>
-<span class="linenos"> 685</span>
-<span class="linenos"> 686</span><span class="sd">    - You cannot subclass or instantiate a union.</span>
-<span class="linenos"> 687</span><span class="sd">    - You can use Optional[X] as a shorthand for Union[X, None].</span>
-<span class="linenos"> 688</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 689</span>    <span class="k">if</span> <span class="n">parameters</span> <span class="o">==</span> <span class="p">():</span>
-<span class="linenos"> 690</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Cannot take a Union of no types.&quot;</span><span class="p">)</span>
-<span class="linenos"> 691</span>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos"> 692</span>        <span class="n">parameters</span> <span class="o">=</span> <span class="p">(</span><span class="n">parameters</span><span class="p">,)</span>
-<span class="linenos"> 693</span>    <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Union[arg, ...]: each arg must be a type.&quot;</span>
-<span class="linenos"> 694</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">)</span>
-<span class="linenos"> 695</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="n">_remove_dups_flatten</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span>
-<span class="linenos"> 696</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<span class="linenos"> 697</span>        <span class="k">return</span> <span class="n">parameters</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-<span class="linenos"> 698</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
-<span class="linenos"> 699</span>        <span class="k">return</span> <span class="n">_UnionGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s2">&quot;Optional&quot;</span><span class="p">)</span>
-<span class="linenos"> 700</span>    <span class="k">return</span> <span class="n">_UnionGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">)</span>
-<span class="linenos"> 701</span>
-<span class="linenos"> 702</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 703</span><span class="k">def</span> <span class="nf">Optional</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 704</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Optional[X] is equivalent to Union[X, None].&quot;&quot;&quot;</span>
-<span class="linenos"> 705</span>    <span class="n">arg</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> requires a single type.&quot;</span><span class="p">)</span>
-<span class="linenos"> 706</span>    <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">arg</span><span class="p">,</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">)]</span>
+<span class="linenos"> 653</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 654</span><span class="k">def</span> <span class="nf">Union</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 655</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Union type; Union[X, Y] means either X or Y.</span>
+<span class="linenos"> 656</span>
+<span class="linenos"> 657</span><span class="sd">    On Python 3.10 and higher, the | operator</span>
+<span class="linenos"> 658</span><span class="sd">    can also be used to denote unions;</span>
+<span class="linenos"> 659</span><span class="sd">    X | Y means the same thing to the type checker as Union[X, Y].</span>
+<span class="linenos"> 660</span>
+<span class="linenos"> 661</span><span class="sd">    To define a union, use e.g. Union[int, str]. Details:</span>
+<span class="linenos"> 662</span><span class="sd">    - The arguments must be types and there must be at least one.</span>
+<span class="linenos"> 663</span><span class="sd">    - None as an argument is a special case and is replaced by</span>
+<span class="linenos"> 664</span><span class="sd">      type(None).</span>
+<span class="linenos"> 665</span><span class="sd">    - Unions of unions are flattened, e.g.::</span>
+<span class="linenos"> 666</span>
+<span class="linenos"> 667</span><span class="sd">        assert Union[Union[int, str], float] == Union[int, str, float]</span>
+<span class="linenos"> 668</span>
+<span class="linenos"> 669</span><span class="sd">    - Unions of a single argument vanish, e.g.::</span>
+<span class="linenos"> 670</span>
+<span class="linenos"> 671</span><span class="sd">        assert Union[int] == int  # The constructor actually returns int</span>
+<span class="linenos"> 672</span>
+<span class="linenos"> 673</span><span class="sd">    - Redundant arguments are skipped, e.g.::</span>
+<span class="linenos"> 674</span>
+<span class="linenos"> 675</span><span class="sd">        assert Union[int, str, int] == Union[int, str]</span>
+<span class="linenos"> 676</span>
+<span class="linenos"> 677</span><span class="sd">    - When comparing unions, the argument order is ignored, e.g.::</span>
+<span class="linenos"> 678</span>
+<span class="linenos"> 679</span><span class="sd">        assert Union[int, str] == Union[str, int]</span>
+<span class="linenos"> 680</span>
+<span class="linenos"> 681</span><span class="sd">    - You cannot subclass or instantiate a union.</span>
+<span class="linenos"> 682</span><span class="sd">    - You can use Optional[X] as a shorthand for Union[X, None].</span>
+<span class="linenos"> 683</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 684</span>    <span class="k">if</span> <span class="n">parameters</span> <span class="o">==</span> <span class="p">():</span>
+<span class="linenos"> 685</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Cannot take a Union of no types.&quot;</span><span class="p">)</span>
+<span class="linenos"> 686</span>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos"> 687</span>        <span class="n">parameters</span> <span class="o">=</span> <span class="p">(</span><span class="n">parameters</span><span class="p">,)</span>
+<span class="linenos"> 688</span>    <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Union[arg, ...]: each arg must be a type.&quot;</span>
+<span class="linenos"> 689</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 690</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="n">_remove_dups_flatten</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 691</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<span class="linenos"> 692</span>        <span class="k">return</span> <span class="n">parameters</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<span class="linenos"> 693</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">:</span>
+<span class="linenos"> 694</span>        <span class="k">return</span> <span class="n">_UnionGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s2">&quot;Optional&quot;</span><span class="p">)</span>
+<span class="linenos"> 695</span>    <span class="k">return</span> <span class="n">_UnionGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 696</span>
+<span class="linenos"> 697</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 698</span><span class="k">def</span> <span class="nf">Optional</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 699</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Optional[X] is equivalent to Union[X, None].&quot;&quot;&quot;</span>
+<span class="linenos"> 700</span>    <span class="n">arg</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> requires a single type.&quot;</span><span class="p">)</span>
+<span class="linenos"> 701</span>    <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">arg</span><span class="p">,</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">)]</span>
+<span class="linenos"> 702</span>
+<span class="linenos"> 703</span><span class="nd">@_LiteralSpecialForm</span>
+<span class="linenos"> 704</span><span class="nd">@_tp_cache</span><span class="p">(</span><span class="n">typed</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<span class="linenos"> 705</span><span class="k">def</span> <span class="nf">Literal</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 706</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing form to define literal types (a.k.a. value types).</span>
 <span class="linenos"> 707</span>
-<span class="linenos"> 708</span><span class="nd">@_LiteralSpecialForm</span>
-<span class="linenos"> 709</span><span class="nd">@_tp_cache</span><span class="p">(</span><span class="n">typed</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="linenos"> 710</span><span class="k">def</span> <span class="nf">Literal</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 711</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing form to define literal types (a.k.a. value types).</span>
-<span class="linenos"> 712</span>
-<span class="linenos"> 713</span><span class="sd">    This form can be used to indicate to type checkers that the corresponding</span>
-<span class="linenos"> 714</span><span class="sd">    variable or function parameter has a value equivalent to the provided</span>
-<span class="linenos"> 715</span><span class="sd">    literal (or one of several literals)::</span>
-<span class="linenos"> 716</span>
-<span class="linenos"> 717</span><span class="sd">        def validate_simple(data: Any) -&gt; Literal[True]:  # always returns True</span>
-<span class="linenos"> 718</span><span class="sd">            ...</span>
-<span class="linenos"> 719</span>
-<span class="linenos"> 720</span><span class="sd">        MODE = Literal[&#39;r&#39;, &#39;rb&#39;, &#39;w&#39;, &#39;wb&#39;]</span>
-<span class="linenos"> 721</span><span class="sd">        def open_helper(file: str, mode: MODE) -&gt; str:</span>
-<span class="linenos"> 722</span><span class="sd">            ...</span>
-<span class="linenos"> 723</span>
-<span class="linenos"> 724</span><span class="sd">        open_helper(&#39;/some/path&#39;, &#39;r&#39;)  # Passes type check</span>
-<span class="linenos"> 725</span><span class="sd">        open_helper(&#39;/other/path&#39;, &#39;typo&#39;)  # Error in type checker</span>
-<span class="linenos"> 726</span>
-<span class="linenos"> 727</span><span class="sd">    Literal[...] cannot be subclassed. At runtime, an arbitrary value</span>
-<span class="linenos"> 728</span><span class="sd">    is allowed as type argument to Literal[...], but type checkers may</span>
-<span class="linenos"> 729</span><span class="sd">    impose restrictions.</span>
-<span class="linenos"> 730</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 731</span>    <span class="c1"># There is no &#39;_type_check&#39; call because arguments to Literal[...] are</span>
-<span class="linenos"> 732</span>    <span class="c1"># values, not types.</span>
-<span class="linenos"> 733</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="n">_flatten_literal_params</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 708</span><span class="sd">    This form can be used to indicate to type checkers that the corresponding</span>
+<span class="linenos"> 709</span><span class="sd">    variable or function parameter has a value equivalent to the provided</span>
+<span class="linenos"> 710</span><span class="sd">    literal (or one of several literals)::</span>
+<span class="linenos"> 711</span>
+<span class="linenos"> 712</span><span class="sd">        def validate_simple(data: Any) -&gt; Literal[True]:  # always returns True</span>
+<span class="linenos"> 713</span><span class="sd">            ...</span>
+<span class="linenos"> 714</span>
+<span class="linenos"> 715</span><span class="sd">        MODE = Literal[&#39;r&#39;, &#39;rb&#39;, &#39;w&#39;, &#39;wb&#39;]</span>
+<span class="linenos"> 716</span><span class="sd">        def open_helper(file: str, mode: MODE) -&gt; str:</span>
+<span class="linenos"> 717</span><span class="sd">            ...</span>
+<span class="linenos"> 718</span>
+<span class="linenos"> 719</span><span class="sd">        open_helper(&#39;/some/path&#39;, &#39;r&#39;)  # Passes type check</span>
+<span class="linenos"> 720</span><span class="sd">        open_helper(&#39;/other/path&#39;, &#39;typo&#39;)  # Error in type checker</span>
+<span class="linenos"> 721</span>
+<span class="linenos"> 722</span><span class="sd">    Literal[...] cannot be subclassed. At runtime, an arbitrary value</span>
+<span class="linenos"> 723</span><span class="sd">    is allowed as type argument to Literal[...], but type checkers may</span>
+<span class="linenos"> 724</span><span class="sd">    impose restrictions.</span>
+<span class="linenos"> 725</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 726</span>    <span class="c1"># There is no &#39;_type_check&#39; call because arguments to Literal[...] are</span>
+<span class="linenos"> 727</span>    <span class="c1"># values, not types.</span>
+<span class="linenos"> 728</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="n">_flatten_literal_params</span><span class="p">(</span><span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 729</span>
+<span class="linenos"> 730</span>    <span class="k">try</span><span class="p">:</span>
+<span class="linenos"> 731</span>        <span class="n">parameters</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">p</span> <span class="k">for</span> <span class="n">p</span><span class="p">,</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">_deduplicate</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">_value_and_type_iter</span><span class="p">(</span><span class="n">parameters</span><span class="p">))))</span>
+<span class="linenos"> 732</span>    <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>  <span class="c1"># unhashable parameters</span>
+<span class="linenos"> 733</span>        <span class="k">pass</span>
 <span class="linenos"> 734</span>
-<span class="linenos"> 735</span>    <span class="k">try</span><span class="p">:</span>
-<span class="linenos"> 736</span>        <span class="n">parameters</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">p</span> <span class="k">for</span> <span class="n">p</span><span class="p">,</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">_deduplicate</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">_value_and_type_iter</span><span class="p">(</span><span class="n">parameters</span><span class="p">))))</span>
-<span class="linenos"> 737</span>    <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>  <span class="c1"># unhashable parameters</span>
-<span class="linenos"> 738</span>        <span class="k">pass</span>
-<span class="linenos"> 739</span>
-<span class="linenos"> 740</span>    <span class="k">return</span> <span class="n">_LiteralGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 735</span>    <span class="k">return</span> <span class="n">_LiteralGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">)</span>
+<span class="linenos"> 736</span>
+<span class="linenos"> 737</span>
+<span class="linenos"> 738</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 739</span><span class="k">def</span> <span class="nf">TypeAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 740</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special form for marking type aliases.</span>
 <span class="linenos"> 741</span>
-<span class="linenos"> 742</span>
-<span class="linenos"> 743</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 744</span><span class="k">def</span> <span class="nf">TypeAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 745</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special form for marking type aliases.</span>
-<span class="linenos"> 746</span>
-<span class="linenos"> 747</span><span class="sd">    Use TypeAlias to indicate that an assignment should</span>
-<span class="linenos"> 748</span><span class="sd">    be recognized as a proper type alias definition by type</span>
-<span class="linenos"> 749</span><span class="sd">    checkers.</span>
-<span class="linenos"> 750</span>
-<span class="linenos"> 751</span><span class="sd">    For example::</span>
+<span class="linenos"> 742</span><span class="sd">    Use TypeAlias to indicate that an assignment should</span>
+<span class="linenos"> 743</span><span class="sd">    be recognized as a proper type alias definition by type</span>
+<span class="linenos"> 744</span><span class="sd">    checkers. For example::</span>
+<span class="linenos"> 745</span>
+<span class="linenos"> 746</span><span class="sd">        Predicate: TypeAlias = Callable[..., bool]</span>
+<span class="linenos"> 747</span>
+<span class="linenos"> 748</span><span class="sd">    It&#39;s invalid when used anywhere except as in the example above.</span>
+<span class="linenos"> 749</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 750</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
+<span class="linenos"> 751</span>
 <span class="linenos"> 752</span>
-<span class="linenos"> 753</span><span class="sd">        Predicate: TypeAlias = Callable[..., bool]</span>
-<span class="linenos"> 754</span>
-<span class="linenos"> 755</span><span class="sd">    It&#39;s invalid when used anywhere except as in the example above.</span>
-<span class="linenos"> 756</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 757</span>    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not subscriptable&quot;</span><span class="p">)</span>
-<span class="linenos"> 758</span>
-<span class="linenos"> 759</span>
-<span class="linenos"> 760</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 761</span><span class="k">def</span> <span class="nf">Concatenate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 762</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special form for annotating higher-order functions.</span>
-<span class="linenos"> 763</span>
-<span class="linenos"> 764</span><span class="sd">    ``Concatenate`` can be used in conjunction with ``ParamSpec`` and</span>
-<span class="linenos"> 765</span><span class="sd">    ``Callable`` to represent a higher-order function which adds, removes or</span>
-<span class="linenos"> 766</span><span class="sd">    transforms the parameters of a callable.</span>
-<span class="linenos"> 767</span>
-<span class="linenos"> 768</span><span class="sd">    For example::</span>
-<span class="linenos"> 769</span>
-<span class="linenos"> 770</span><span class="sd">        Callable[Concatenate[int, P], int]</span>
-<span class="linenos"> 771</span>
-<span class="linenos"> 772</span><span class="sd">    See PEP 612 for detailed information.</span>
-<span class="linenos"> 773</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 774</span>    <span class="k">if</span> <span class="n">parameters</span> <span class="o">==</span> <span class="p">():</span>
-<span class="linenos"> 775</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Cannot take a Concatenate of no types.&quot;</span><span class="p">)</span>
-<span class="linenos"> 776</span>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos"> 777</span>        <span class="n">parameters</span> <span class="o">=</span> <span class="p">(</span><span class="n">parameters</span><span class="p">,)</span>
-<span class="linenos"> 778</span>    <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">parameters</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="o">...</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">parameters</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">ParamSpec</span><span class="p">)):</span>
-<span class="linenos"> 779</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;The last parameter to Concatenate should be a &quot;</span>
-<span class="linenos"> 780</span>                        <span class="s2">&quot;ParamSpec variable or ellipsis.&quot;</span><span class="p">)</span>
-<span class="linenos"> 781</span>    <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Concatenate[arg, ...]: each arg must be a type.&quot;</span>
-<span class="linenos"> 782</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span> <span class="n">parameters</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
-<span class="linenos"> 783</span>    <span class="k">return</span> <span class="n">_ConcatenateGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">,</span>
-<span class="linenos"> 784</span>                                    <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="linenos"> 785</span>
-<span class="linenos"> 786</span>
-<span class="linenos"> 787</span><span class="nd">@_SpecialForm</span>
-<span class="linenos"> 788</span><span class="k">def</span> <span class="nf">TypeGuard</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos"> 789</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing construct for marking user-defined type guard functions.</span>
-<span class="linenos"> 790</span>
-<span class="linenos"> 791</span><span class="sd">    ``TypeGuard`` can be used to annotate the return type of a user-defined</span>
-<span class="linenos"> 792</span><span class="sd">    type guard function.  ``TypeGuard`` only accepts a single type argument.</span>
-<span class="linenos"> 793</span><span class="sd">    At runtime, functions marked this way should return a boolean.</span>
-<span class="linenos"> 794</span>
-<span class="linenos"> 795</span><span class="sd">    ``TypeGuard`` aims to benefit *type narrowing* -- a technique used by static</span>
-<span class="linenos"> 796</span><span class="sd">    type checkers to determine a more precise type of an expression within a</span>
-<span class="linenos"> 797</span><span class="sd">    program&#39;s code flow.  Usually type narrowing is done by analyzing</span>
-<span class="linenos"> 798</span><span class="sd">    conditional code flow and applying the narrowing to a block of code.  The</span>
-<span class="linenos"> 799</span><span class="sd">    conditional expression here is sometimes referred to as a &quot;type guard&quot;.</span>
+<span class="linenos"> 753</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 754</span><span class="k">def</span> <span class="nf">Concatenate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 755</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special form for annotating higher-order functions.</span>
+<span class="linenos"> 756</span>
+<span class="linenos"> 757</span><span class="sd">    ``Concatenate`` can be sed in conjunction with ``ParamSpec`` and</span>
+<span class="linenos"> 758</span><span class="sd">    ``Callable`` to represent a higher order function which adds, removes or</span>
+<span class="linenos"> 759</span><span class="sd">    transforms the parameters of a callable.</span>
+<span class="linenos"> 760</span>
+<span class="linenos"> 761</span><span class="sd">    For example::</span>
+<span class="linenos"> 762</span>
+<span class="linenos"> 763</span><span class="sd">        Callable[Concatenate[int, P], int]</span>
+<span class="linenos"> 764</span>
+<span class="linenos"> 765</span><span class="sd">    See PEP 612 for detailed information.</span>
+<span class="linenos"> 766</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 767</span>    <span class="k">if</span> <span class="n">parameters</span> <span class="o">==</span> <span class="p">():</span>
+<span class="linenos"> 768</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Cannot take a Concatenate of no types.&quot;</span><span class="p">)</span>
+<span class="linenos"> 769</span>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos"> 770</span>        <span class="n">parameters</span> <span class="o">=</span> <span class="p">(</span><span class="n">parameters</span><span class="p">,)</span>
+<span class="linenos"> 771</span>    <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">parameters</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="o">...</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">parameters</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">ParamSpec</span><span class="p">)):</span>
+<span class="linenos"> 772</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;The last parameter to Concatenate should be a &quot;</span>
+<span class="linenos"> 773</span>                        <span class="s2">&quot;ParamSpec variable or ellipsis.&quot;</span><span class="p">)</span>
+<span class="linenos"> 774</span>    <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Concatenate[arg, ...]: each arg must be a type.&quot;</span>
+<span class="linenos"> 775</span>    <span class="n">parameters</span> <span class="o">=</span> <span class="p">(</span><span class="o">*</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span> <span class="n">parameters</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
+<span class="linenos"> 776</span>    <span class="k">return</span> <span class="n">_ConcatenateGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">,</span>
+<span class="linenos"> 777</span>                                    <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<span class="linenos"> 778</span>
+<span class="linenos"> 779</span>
+<span class="linenos"> 780</span><span class="nd">@_SpecialForm</span>
+<span class="linenos"> 781</span><span class="k">def</span> <span class="nf">TypeGuard</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos"> 782</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing construct for marking user-defined type guard functions.</span>
+<span class="linenos"> 783</span>
+<span class="linenos"> 784</span><span class="sd">    ``TypeGuard`` can be used to annotate the return type of a user-defined</span>
+<span class="linenos"> 785</span><span class="sd">    type guard function.  ``TypeGuard`` only accepts a single type argument.</span>
+<span class="linenos"> 786</span><span class="sd">    At runtime, functions marked this way should return a boolean.</span>
+<span class="linenos"> 787</span>
+<span class="linenos"> 788</span><span class="sd">    ``TypeGuard`` aims to benefit *type narrowing* -- a technique used by static</span>
+<span class="linenos"> 789</span><span class="sd">    type checkers to determine a more precise type of an expression within a</span>
+<span class="linenos"> 790</span><span class="sd">    program&#39;s code flow.  Usually type narrowing is done by analyzing</span>
+<span class="linenos"> 791</span><span class="sd">    conditional code flow and applying the narrowing to a block of code.  The</span>
+<span class="linenos"> 792</span><span class="sd">    conditional expression here is sometimes referred to as a &quot;type guard&quot;.</span>
+<span class="linenos"> 793</span>
+<span class="linenos"> 794</span><span class="sd">    Sometimes it would be convenient to use a user-defined boolean function</span>
+<span class="linenos"> 795</span><span class="sd">    as a type guard.  Such a function should use ``TypeGuard[...]`` as its</span>
+<span class="linenos"> 796</span><span class="sd">    return type to alert static type checkers to this intention.</span>
+<span class="linenos"> 797</span>
+<span class="linenos"> 798</span><span class="sd">    Using  ``-&gt; TypeGuard`` tells the static type checker that for a given</span>
+<span class="linenos"> 799</span><span class="sd">    function:</span>
 <span class="linenos"> 800</span>
-<span class="linenos"> 801</span><span class="sd">    Sometimes it would be convenient to use a user-defined boolean function</span>
-<span class="linenos"> 802</span><span class="sd">    as a type guard.  Such a function should use ``TypeGuard[...]`` as its</span>
-<span class="linenos"> 803</span><span class="sd">    return type to alert static type checkers to this intention.</span>
+<span class="linenos"> 801</span><span class="sd">    1. The return value is a boolean.</span>
+<span class="linenos"> 802</span><span class="sd">    2. If the return value is ``True``, the type of its argument</span>
+<span class="linenos"> 803</span><span class="sd">       is the type inside ``TypeGuard``.</span>
 <span class="linenos"> 804</span>
-<span class="linenos"> 805</span><span class="sd">    Using  ``-&gt; TypeGuard`` tells the static type checker that for a given</span>
-<span class="linenos"> 806</span><span class="sd">    function:</span>
-<span class="linenos"> 807</span>
-<span class="linenos"> 808</span><span class="sd">    1. The return value is a boolean.</span>
-<span class="linenos"> 809</span><span class="sd">    2. If the return value is ``True``, the type of its argument</span>
-<span class="linenos"> 810</span><span class="sd">       is the type inside ``TypeGuard``.</span>
-<span class="linenos"> 811</span>
-<span class="linenos"> 812</span><span class="sd">       For example::</span>
-<span class="linenos"> 813</span>
-<span class="linenos"> 814</span><span class="sd">           def is_str(val: Union[str, float]):</span>
-<span class="linenos"> 815</span><span class="sd">               # &quot;isinstance&quot; type guard</span>
-<span class="linenos"> 816</span><span class="sd">               if isinstance(val, str):</span>
-<span class="linenos"> 817</span><span class="sd">                   # Type of ``val`` is narrowed to ``str``</span>
-<span class="linenos"> 818</span><span class="sd">                   ...</span>
-<span class="linenos"> 819</span><span class="sd">               else:</span>
-<span class="linenos"> 820</span><span class="sd">                   # Else, type of ``val`` is narrowed to ``float``.</span>
-<span class="linenos"> 821</span><span class="sd">                   ...</span>
+<span class="linenos"> 805</span><span class="sd">       For example::</span>
+<span class="linenos"> 806</span>
+<span class="linenos"> 807</span><span class="sd">           def is_str(val: Union[str, float]):</span>
+<span class="linenos"> 808</span><span class="sd">               # &quot;isinstance&quot; type guard</span>
+<span class="linenos"> 809</span><span class="sd">               if isinstance(val, str):</span>
+<span class="linenos"> 810</span><span class="sd">                   # Type of ``val`` is narrowed to ``str``</span>
+<span class="linenos"> 811</span><span class="sd">                   ...</span>
+<span class="linenos"> 812</span><span class="sd">               else:</span>
+<span class="linenos"> 813</span><span class="sd">                   # Else, type of ``val`` is narrowed to ``float``.</span>
+<span class="linenos"> 814</span><span class="sd">                   ...</span>
+<span class="linenos"> 815</span>
+<span class="linenos"> 816</span><span class="sd">    Strict type narrowing is not enforced -- ``TypeB`` need not be a narrower</span>
+<span class="linenos"> 817</span><span class="sd">    form of ``TypeA`` (it can even be a wider form) and this may lead to</span>
+<span class="linenos"> 818</span><span class="sd">    type-unsafe results.  The main reason is to allow for things like</span>
+<span class="linenos"> 819</span><span class="sd">    narrowing ``List[object]`` to ``List[str]`` even though the latter is not</span>
+<span class="linenos"> 820</span><span class="sd">    a subtype of the former, since ``List`` is invariant.  The responsibility of</span>
+<span class="linenos"> 821</span><span class="sd">    writing type-safe type guards is left to the user.</span>
 <span class="linenos"> 822</span>
-<span class="linenos"> 823</span><span class="sd">    Strict type narrowing is not enforced -- ``TypeB`` need not be a narrower</span>
-<span class="linenos"> 824</span><span class="sd">    form of ``TypeA`` (it can even be a wider form) and this may lead to</span>
-<span class="linenos"> 825</span><span class="sd">    type-unsafe results.  The main reason is to allow for things like</span>
-<span class="linenos"> 826</span><span class="sd">    narrowing ``List[object]`` to ``List[str]`` even though the latter is not</span>
-<span class="linenos"> 827</span><span class="sd">    a subtype of the former, since ``List`` is invariant.  The responsibility of</span>
-<span class="linenos"> 828</span><span class="sd">    writing type-safe type guards is left to the user.</span>
+<span class="linenos"> 823</span><span class="sd">    ``TypeGuard`` also works with type variables.  For more information, see</span>
+<span class="linenos"> 824</span><span class="sd">    PEP 647 (User-Defined Type Guards).</span>
+<span class="linenos"> 825</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 826</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s1"> accepts only single type.&#39;</span><span class="p">)</span>
+<span class="linenos"> 827</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
+<span class="linenos"> 828</span>
 <span class="linenos"> 829</span>
-<span class="linenos"> 830</span><span class="sd">    ``TypeGuard`` also works with type variables.  For more information, see</span>
-<span class="linenos"> 831</span><span class="sd">    PEP 647 (User-Defined Type Guards).</span>
-<span class="linenos"> 832</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 833</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s1"> accepts only single type.&#39;</span><span class="p">)</span>
-<span class="linenos"> 834</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
-<span class="linenos"> 835</span>
-<span class="linenos"> 836</span>
-<span class="linenos"> 837</span><span class="k">class</span> <span class="nc">ForwardRef</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos"> 838</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal wrapper to hold a forward reference.&quot;&quot;&quot;</span>
-<span class="linenos"> 839</span>
-<span class="linenos"> 840</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;__forward_arg__&#39;</span><span class="p">,</span> <span class="s1">&#39;__forward_code__&#39;</span><span class="p">,</span>
-<span class="linenos"> 841</span>                 <span class="s1">&#39;__forward_evaluated__&#39;</span><span class="p">,</span> <span class="s1">&#39;__forward_value__&#39;</span><span class="p">,</span>
-<span class="linenos"> 842</span>                 <span class="s1">&#39;__forward_is_argument__&#39;</span><span class="p">,</span> <span class="s1">&#39;__forward_is_class__&#39;</span><span class="p">,</span>
-<span class="linenos"> 843</span>                 <span class="s1">&#39;__forward_module__&#39;</span><span class="p">)</span>
-<span class="linenos"> 844</span>
-<span class="linenos"> 845</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg</span><span class="p">,</span> <span class="n">is_argument</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">is_class</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
-<span class="linenos"> 846</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
-<span class="linenos"> 847</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Forward reference must be a string -- got </span><span class="si">{</span><span class="n">arg</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos"> 848</span>
-<span class="linenos"> 849</span>        <span class="c1"># If we do `def f(*args: *Ts)`, then we&#39;ll have `arg = &#39;*Ts&#39;`.</span>
-<span class="linenos"> 850</span>        <span class="c1"># Unfortunately, this isn&#39;t a valid expression on its own, so we</span>
-<span class="linenos"> 851</span>        <span class="c1"># do the unpacking manually.</span>
-<span class="linenos"> 852</span>        <span class="k">if</span> <span class="n">arg</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;*&#39;</span><span class="p">:</span>
-<span class="linenos"> 853</span>            <span class="n">arg_to_compile</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;(</span><span class="si">{</span><span class="n">arg</span><span class="si">}</span><span class="s1">,)[0]&#39;</span>  <span class="c1"># E.g. (*Ts,)[0] or (*tuple[int, int],)[0]</span>
-<span class="linenos"> 854</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 855</span>            <span class="n">arg_to_compile</span> <span class="o">=</span> <span class="n">arg</span>
-<span class="linenos"> 856</span>        <span class="k">try</span><span class="p">:</span>
-<span class="linenos"> 857</span>            <span class="n">code</span> <span class="o">=</span> <span class="nb">compile</span><span class="p">(</span><span class="n">arg_to_compile</span><span class="p">,</span> <span class="s1">&#39;&lt;string&gt;&#39;</span><span class="p">,</span> <span class="s1">&#39;eval&#39;</span><span class="p">)</span>
-<span class="linenos"> 858</span>        <span class="k">except</span> <span class="ne">SyntaxError</span><span class="p">:</span>
-<span class="linenos"> 859</span>            <span class="k">raise</span> <span class="ne">SyntaxError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Forward reference must be an expression -- got </span><span class="si">{</span><span class="n">arg</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos"> 860</span>
-<span class="linenos"> 861</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="o">=</span> <span class="n">arg</span>
-<span class="linenos"> 862</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_code__</span> <span class="o">=</span> <span class="n">code</span>
-<span class="linenos"> 863</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_evaluated__</span> <span class="o">=</span> <span class="kc">False</span>
-<span class="linenos"> 864</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_value__</span> <span class="o">=</span> <span class="kc">None</span>
-<span class="linenos"> 865</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_is_argument__</span> <span class="o">=</span> <span class="n">is_argument</span>
-<span class="linenos"> 866</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_is_class__</span> <span class="o">=</span> <span class="n">is_class</span>
-<span class="linenos"> 867</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span> <span class="o">=</span> <span class="n">module</span>
-<span class="linenos"> 868</span>
-<span class="linenos"> 869</span>    <span class="k">def</span> <span class="nf">_evaluate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span><span class="p">):</span>
-<span class="linenos"> 870</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="ow">in</span> <span class="n">recursive_guard</span><span class="p">:</span>
-<span class="linenos"> 871</span>            <span class="k">return</span> <span class="bp">self</span>
-<span class="linenos"> 872</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_evaluated__</span> <span class="ow">or</span> <span class="n">localns</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">globalns</span><span class="p">:</span>
-<span class="linenos"> 873</span>            <span class="k">if</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos"> 874</span>                <span class="n">globalns</span> <span class="o">=</span> <span class="n">localns</span> <span class="o">=</span> <span class="p">{}</span>
-<span class="linenos"> 875</span>            <span class="k">elif</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos"> 876</span>                <span class="n">globalns</span> <span class="o">=</span> <span class="n">localns</span>
-<span class="linenos"> 877</span>            <span class="k">elif</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos"> 878</span>                <span class="n">localns</span> <span class="o">=</span> <span class="n">globalns</span>
-<span class="linenos"> 879</span>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos"> 880</span>                <span class="n">globalns</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span>
-<span class="linenos"> 881</span>                    <span class="n">sys</span><span class="o">.</span><span class="n">modules</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span> <span class="s1">&#39;__dict__&#39;</span><span class="p">,</span> <span class="n">globalns</span>
-<span class="linenos"> 882</span>                <span class="p">)</span>
-<span class="linenos"> 883</span>            <span class="n">type_</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span>
-<span class="linenos"> 884</span>                <span class="nb">eval</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_code__</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">),</span>
-<span class="linenos"> 885</span>                <span class="s2">&quot;Forward references must evaluate to types.&quot;</span><span class="p">,</span>
-<span class="linenos"> 886</span>                <span class="n">is_argument</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_is_argument__</span><span class="p">,</span>
-<span class="linenos"> 887</span>                <span class="n">allow_special_forms</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_is_class__</span><span class="p">,</span>
-<span class="linenos"> 888</span>            <span class="p">)</span>
-<span class="linenos"> 889</span>            <span class="bp">self</span><span class="o">.</span><span class="n">__forward_value__</span> <span class="o">=</span> <span class="n">_eval_type</span><span class="p">(</span>
-<span class="linenos"> 890</span>                <span class="n">type_</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span> <span class="o">|</span> <span class="p">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span><span class="p">}</span>
-<span class="linenos"> 891</span>            <span class="p">)</span>
-<span class="linenos"> 892</span>            <span class="bp">self</span><span class="o">.</span><span class="n">__forward_evaluated__</span> <span class="o">=</span> <span class="kc">True</span>
-<span class="linenos"> 893</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_value__</span>
-<span class="linenos"> 894</span>
-<span class="linenos"> 895</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos"> 896</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">ForwardRef</span><span class="p">):</span>
-<span class="linenos"> 897</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos"> 898</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_evaluated__</span> <span class="ow">and</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_evaluated__</span><span class="p">:</span>
-<span class="linenos"> 899</span>            <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="ow">and</span>
-<span class="linenos"> 900</span>                    <span class="bp">self</span><span class="o">.</span><span class="n">__forward_value__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_value__</span><span class="p">)</span>
-<span class="linenos"> 901</span>        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="ow">and</span>
-<span class="linenos"> 902</span>                <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_module__</span><span class="p">)</span>
-<span class="linenos"> 903</span>
-<span class="linenos"> 904</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos"> 905</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span><span class="p">))</span>
-<span class="linenos"> 906</span>
-<span class="linenos"> 907</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos"> 908</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">]</span>
-<span class="linenos"> 909</span>
-<span class="linenos"> 910</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos"> 911</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
+<span class="linenos"> 830</span><span class="k">class</span> <span class="nc">ForwardRef</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos"> 831</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal wrapper to hold a forward reference.&quot;&quot;&quot;</span>
+<span class="linenos"> 832</span>
+<span class="linenos"> 833</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;__forward_arg__&#39;</span><span class="p">,</span> <span class="s1">&#39;__forward_code__&#39;</span><span class="p">,</span>
+<span class="linenos"> 834</span>                 <span class="s1">&#39;__forward_evaluated__&#39;</span><span class="p">,</span> <span class="s1">&#39;__forward_value__&#39;</span><span class="p">,</span>
+<span class="linenos"> 835</span>                 <span class="s1">&#39;__forward_is_argument__&#39;</span><span class="p">,</span> <span class="s1">&#39;__forward_is_class__&#39;</span><span class="p">,</span>
+<span class="linenos"> 836</span>                 <span class="s1">&#39;__forward_module__&#39;</span><span class="p">)</span>
+<span class="linenos"> 837</span>
+<span class="linenos"> 838</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg</span><span class="p">,</span> <span class="n">is_argument</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">is_class</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="linenos"> 839</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+<span class="linenos"> 840</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Forward reference must be a string -- got </span><span class="si">{</span><span class="n">arg</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos"> 841</span>
+<span class="linenos"> 842</span>        <span class="c1"># If we do `def f(*args: *Ts)`, then we&#39;ll have `arg = &#39;*Ts&#39;`.</span>
+<span class="linenos"> 843</span>        <span class="c1"># Unfortunately, this isn&#39;t a valid expression on its own, so we</span>
+<span class="linenos"> 844</span>        <span class="c1"># do the unpacking manually.</span>
+<span class="linenos"> 845</span>        <span class="k">if</span> <span class="n">arg</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s1">&#39;*&#39;</span><span class="p">:</span>
+<span class="linenos"> 846</span>            <span class="n">arg_to_compile</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;(</span><span class="si">{</span><span class="n">arg</span><span class="si">}</span><span class="s1">,)[0]&#39;</span>  <span class="c1"># E.g. (*Ts,)[0] or (*tuple[int, int],)[0]</span>
+<span class="linenos"> 847</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 848</span>            <span class="n">arg_to_compile</span> <span class="o">=</span> <span class="n">arg</span>
+<span class="linenos"> 849</span>        <span class="k">try</span><span class="p">:</span>
+<span class="linenos"> 850</span>            <span class="n">code</span> <span class="o">=</span> <span class="nb">compile</span><span class="p">(</span><span class="n">arg_to_compile</span><span class="p">,</span> <span class="s1">&#39;&lt;string&gt;&#39;</span><span class="p">,</span> <span class="s1">&#39;eval&#39;</span><span class="p">)</span>
+<span class="linenos"> 851</span>        <span class="k">except</span> <span class="ne">SyntaxError</span><span class="p">:</span>
+<span class="linenos"> 852</span>            <span class="k">raise</span> <span class="ne">SyntaxError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Forward reference must be an expression -- got </span><span class="si">{</span><span class="n">arg</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos"> 853</span>
+<span class="linenos"> 854</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="o">=</span> <span class="n">arg</span>
+<span class="linenos"> 855</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_code__</span> <span class="o">=</span> <span class="n">code</span>
+<span class="linenos"> 856</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_evaluated__</span> <span class="o">=</span> <span class="kc">False</span>
+<span class="linenos"> 857</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_value__</span> <span class="o">=</span> <span class="kc">None</span>
+<span class="linenos"> 858</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_is_argument__</span> <span class="o">=</span> <span class="n">is_argument</span>
+<span class="linenos"> 859</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_is_class__</span> <span class="o">=</span> <span class="n">is_class</span>
+<span class="linenos"> 860</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span> <span class="o">=</span> <span class="n">module</span>
+<span class="linenos"> 861</span>
+<span class="linenos"> 862</span>    <span class="k">def</span> <span class="nf">_evaluate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span><span class="p">):</span>
+<span class="linenos"> 863</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="ow">in</span> <span class="n">recursive_guard</span><span class="p">:</span>
+<span class="linenos"> 864</span>            <span class="k">return</span> <span class="bp">self</span>
+<span class="linenos"> 865</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_evaluated__</span> <span class="ow">or</span> <span class="n">localns</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">globalns</span><span class="p">:</span>
+<span class="linenos"> 866</span>            <span class="k">if</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos"> 867</span>                <span class="n">globalns</span> <span class="o">=</span> <span class="n">localns</span> <span class="o">=</span> <span class="p">{}</span>
+<span class="linenos"> 868</span>            <span class="k">elif</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos"> 869</span>                <span class="n">globalns</span> <span class="o">=</span> <span class="n">localns</span>
+<span class="linenos"> 870</span>            <span class="k">elif</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos"> 871</span>                <span class="n">localns</span> <span class="o">=</span> <span class="n">globalns</span>
+<span class="linenos"> 872</span>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos"> 873</span>                <span class="n">globalns</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span>
+<span class="linenos"> 874</span>                    <span class="n">sys</span><span class="o">.</span><span class="n">modules</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span> <span class="s1">&#39;__dict__&#39;</span><span class="p">,</span> <span class="n">globalns</span>
+<span class="linenos"> 875</span>                <span class="p">)</span>
+<span class="linenos"> 876</span>            <span class="n">type_</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span>
+<span class="linenos"> 877</span>                <span class="nb">eval</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_code__</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">),</span>
+<span class="linenos"> 878</span>                <span class="s2">&quot;Forward references must evaluate to types.&quot;</span><span class="p">,</span>
+<span class="linenos"> 879</span>                <span class="n">is_argument</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_is_argument__</span><span class="p">,</span>
+<span class="linenos"> 880</span>                <span class="n">allow_special_forms</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_is_class__</span><span class="p">,</span>
+<span class="linenos"> 881</span>            <span class="p">)</span>
+<span class="linenos"> 882</span>            <span class="bp">self</span><span class="o">.</span><span class="n">__forward_value__</span> <span class="o">=</span> <span class="n">_eval_type</span><span class="p">(</span>
+<span class="linenos"> 883</span>                <span class="n">type_</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">,</span> <span class="n">recursive_guard</span> <span class="o">|</span> <span class="p">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span><span class="p">}</span>
+<span class="linenos"> 884</span>            <span class="p">)</span>
+<span class="linenos"> 885</span>            <span class="bp">self</span><span class="o">.</span><span class="n">__forward_evaluated__</span> <span class="o">=</span> <span class="kc">True</span>
+<span class="linenos"> 886</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_value__</span>
+<span class="linenos"> 887</span>
+<span class="linenos"> 888</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos"> 889</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">ForwardRef</span><span class="p">):</span>
+<span class="linenos"> 890</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos"> 891</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_evaluated__</span> <span class="ow">and</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_evaluated__</span><span class="p">:</span>
+<span class="linenos"> 892</span>            <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="ow">and</span>
+<span class="linenos"> 893</span>                    <span class="bp">self</span><span class="o">.</span><span class="n">__forward_value__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_value__</span><span class="p">)</span>
+<span class="linenos"> 894</span>        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_arg__</span> <span class="ow">and</span>
+<span class="linenos"> 895</span>                <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__forward_module__</span><span class="p">)</span>
+<span class="linenos"> 896</span>
+<span class="linenos"> 897</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 898</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span><span class="p">))</span>
+<span class="linenos"> 899</span>
+<span class="linenos"> 900</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos"> 901</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">]</span>
+<span class="linenos"> 902</span>
+<span class="linenos"> 903</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos"> 904</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
+<span class="linenos"> 905</span>
+<span class="linenos"> 906</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 907</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos"> 908</span>            <span class="n">module_repr</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
+<span class="linenos"> 909</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 910</span>            <span class="n">module_repr</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;, module=</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span><span class="si">!r}</span><span class="s1">&#39;</span>
+<span class="linenos"> 911</span>        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;ForwardRef(</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span><span class="si">!r}{</span><span class="n">module_repr</span><span class="si">}</span><span class="s1">)&#39;</span>
 <span class="linenos"> 912</span>
-<span class="linenos"> 913</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos"> 914</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos"> 915</span>            <span class="n">module_repr</span> <span class="o">=</span> <span class="s1">&#39;&#39;</span>
-<span class="linenos"> 916</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 917</span>            <span class="n">module_repr</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;, module=</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_module__</span><span class="si">!r}</span><span class="s1">&#39;</span>
-<span class="linenos"> 918</span>        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;ForwardRef(</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__forward_arg__</span><span class="si">!r}{</span><span class="n">module_repr</span><span class="si">}</span><span class="s1">)&#39;</span>
-<span class="linenos"> 919</span>
-<span class="linenos"> 920</span>
-<span class="linenos"> 921</span><span class="k">def</span> <span class="nf">_is_unpacked_typevartuple</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<span class="linenos"> 922</span>    <span class="k">return</span> <span class="p">((</span><span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="nb">type</span><span class="p">))</span> <span class="ow">and</span>
-<span class="linenos"> 923</span>            <span class="nb">getattr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">&#39;__typing_is_unpacked_typevartuple__&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">))</span>
-<span class="linenos"> 924</span>
+<span class="linenos"> 913</span>
+<span class="linenos"> 914</span><span class="k">def</span> <span class="nf">_is_unpacked_typevartuple</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<span class="linenos"> 915</span>    <span class="k">return</span> <span class="p">((</span><span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="nb">type</span><span class="p">))</span> <span class="ow">and</span>
+<span class="linenos"> 916</span>            <span class="nb">getattr</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">&#39;__typing_is_unpacked_typevartuple__&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">))</span>
+<span class="linenos"> 917</span>
+<span class="linenos"> 918</span>
+<span class="linenos"> 919</span><span class="k">def</span> <span class="nf">_is_typevar_like</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<span class="linenos"> 920</span>    <span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">(</span><span class="n">TypeVar</span><span class="p">,</span> <span class="n">ParamSpec</span><span class="p">))</span> <span class="ow">or</span> <span class="n">_is_unpacked_typevartuple</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="linenos"> 921</span>
+<span class="linenos"> 922</span>
+<span class="linenos"> 923</span><span class="k">class</span> <span class="nc">_PickleUsingNameMixin</span><span class="p">:</span>
+<span class="linenos"> 924</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin enabling pickling based on self.__name__.&quot;&quot;&quot;</span>
 <span class="linenos"> 925</span>
-<span class="linenos"> 926</span><span class="k">def</span> <span class="nf">_is_typevar_like</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">Any</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<span class="linenos"> 927</span>    <span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">(</span><span class="n">TypeVar</span><span class="p">,</span> <span class="n">ParamSpec</span><span class="p">))</span> <span class="ow">or</span> <span class="n">_is_unpacked_typevartuple</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="linenos"> 926</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 927</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span>
 <span class="linenos"> 928</span>
 <span class="linenos"> 929</span>
-<span class="linenos"> 930</span><span class="k">class</span> <span class="nc">_PickleUsingNameMixin</span><span class="p">:</span>
-<span class="linenos"> 931</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin enabling pickling based on self.__name__.&quot;&quot;&quot;</span>
+<span class="linenos"> 930</span><span class="k">class</span> <span class="nc">_BoundVarianceMixin</span><span class="p">:</span>
+<span class="linenos"> 931</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin giving __init__ bound and variance arguments.</span>
 <span class="linenos"> 932</span>
-<span class="linenos"> 933</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos"> 934</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span>
-<span class="linenos"> 935</span>
-<span class="linenos"> 936</span>
-<span class="linenos"> 937</span><span class="k">class</span> <span class="nc">_BoundVarianceMixin</span><span class="p">:</span>
-<span class="linenos"> 938</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mixin giving __init__ bound and variance arguments.</span>
-<span class="linenos"> 939</span>
-<span class="linenos"> 940</span><span class="sd">    This is used by TypeVar and ParamSpec, which both employ the notions of</span>
-<span class="linenos"> 941</span><span class="sd">    a type &#39;bound&#39; (restricting type arguments to be a subtype of some</span>
-<span class="linenos"> 942</span><span class="sd">    specified type) and type &#39;variance&#39; (determining subtype relations between</span>
-<span class="linenos"> 943</span><span class="sd">    generic types).</span>
-<span class="linenos"> 944</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos"> 945</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bound</span><span class="p">,</span> <span class="n">covariant</span><span class="p">,</span> <span class="n">contravariant</span><span class="p">):</span>
-<span class="linenos"> 946</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Used to setup TypeVars and ParamSpec&#39;s bound, covariant and</span>
-<span class="linenos"> 947</span><span class="sd">        contravariant attributes.</span>
-<span class="linenos"> 948</span><span class="sd">        &quot;&quot;&quot;</span>
-<span class="linenos"> 949</span>        <span class="k">if</span> <span class="n">covariant</span> <span class="ow">and</span> <span class="n">contravariant</span><span class="p">:</span>
-<span class="linenos"> 950</span>            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Bivariant types are not supported.&quot;</span><span class="p">)</span>
-<span class="linenos"> 951</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__covariant__</span> <span class="o">=</span> <span class="nb">bool</span><span class="p">(</span><span class="n">covariant</span><span class="p">)</span>
-<span class="linenos"> 952</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__contravariant__</span> <span class="o">=</span> <span class="nb">bool</span><span class="p">(</span><span class="n">contravariant</span><span class="p">)</span>
-<span class="linenos"> 953</span>        <span class="k">if</span> <span class="n">bound</span><span class="p">:</span>
-<span class="linenos"> 954</span>            <span class="bp">self</span><span class="o">.</span><span class="n">__bound__</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">bound</span><span class="p">,</span> <span class="s2">&quot;Bound must be a type.&quot;</span><span class="p">)</span>
-<span class="linenos"> 955</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 956</span>            <span class="bp">self</span><span class="o">.</span><span class="n">__bound__</span> <span class="o">=</span> <span class="kc">None</span>
-<span class="linenos"> 957</span>
-<span class="linenos"> 958</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
-<span class="linenos"> 959</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">]</span>
-<span class="linenos"> 960</span>
-<span class="linenos"> 961</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">left</span><span class="p">):</span>
-<span class="linenos"> 962</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
-<span class="linenos"> 963</span>
-<span class="linenos"> 964</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos"> 965</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__covariant__</span><span class="p">:</span>
-<span class="linenos"> 966</span>            <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;+&#39;</span>
-<span class="linenos"> 967</span>        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">__contravariant__</span><span class="p">:</span>
-<span class="linenos"> 968</span>            <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;-&#39;</span>
-<span class="linenos"> 969</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos"> 970</span>            <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;~&#39;</span>
-<span class="linenos"> 971</span>        <span class="k">return</span> <span class="n">prefix</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span>
+<span class="linenos"> 933</span><span class="sd">    This is used by TypeVar and ParamSpec, which both employ the notions of</span>
+<span class="linenos"> 934</span><span class="sd">    a type &#39;bound&#39; (restricting type arguments to be a subtype of some</span>
+<span class="linenos"> 935</span><span class="sd">    specified type) and type &#39;variance&#39; (determining subtype relations between</span>
+<span class="linenos"> 936</span><span class="sd">    generic types).</span>
+<span class="linenos"> 937</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos"> 938</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bound</span><span class="p">,</span> <span class="n">covariant</span><span class="p">,</span> <span class="n">contravariant</span><span class="p">):</span>
+<span class="linenos"> 939</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Used to setup TypeVars and ParamSpec&#39;s bound, covariant and</span>
+<span class="linenos"> 940</span><span class="sd">        contravariant attributes.</span>
+<span class="linenos"> 941</span><span class="sd">        &quot;&quot;&quot;</span>
+<span class="linenos"> 942</span>        <span class="k">if</span> <span class="n">covariant</span> <span class="ow">and</span> <span class="n">contravariant</span><span class="p">:</span>
+<span class="linenos"> 943</span>            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Bivariant types are not supported.&quot;</span><span class="p">)</span>
+<span class="linenos"> 944</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__covariant__</span> <span class="o">=</span> <span class="nb">bool</span><span class="p">(</span><span class="n">covariant</span><span class="p">)</span>
+<span class="linenos"> 945</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__contravariant__</span> <span class="o">=</span> <span class="nb">bool</span><span class="p">(</span><span class="n">contravariant</span><span class="p">)</span>
+<span class="linenos"> 946</span>        <span class="k">if</span> <span class="n">bound</span><span class="p">:</span>
+<span class="linenos"> 947</span>            <span class="bp">self</span><span class="o">.</span><span class="n">__bound__</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">bound</span><span class="p">,</span> <span class="s2">&quot;Bound must be a type.&quot;</span><span class="p">)</span>
+<span class="linenos"> 948</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 949</span>            <span class="bp">self</span><span class="o">.</span><span class="n">__bound__</span> <span class="o">=</span> <span class="kc">None</span>
+<span class="linenos"> 950</span>
+<span class="linenos"> 951</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
+<span class="linenos"> 952</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">]</span>
+<span class="linenos"> 953</span>
+<span class="linenos"> 954</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">left</span><span class="p">):</span>
+<span class="linenos"> 955</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
+<span class="linenos"> 956</span>
+<span class="linenos"> 957</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos"> 958</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__covariant__</span><span class="p">:</span>
+<span class="linenos"> 959</span>            <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;+&#39;</span>
+<span class="linenos"> 960</span>        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">__contravariant__</span><span class="p">:</span>
+<span class="linenos"> 961</span>            <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;-&#39;</span>
+<span class="linenos"> 962</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos"> 963</span>            <span class="n">prefix</span> <span class="o">=</span> <span class="s1">&#39;~&#39;</span>
+<span class="linenos"> 964</span>        <span class="k">return</span> <span class="n">prefix</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span>
+<span class="linenos"> 965</span>
+<span class="linenos"> 966</span>
+<span class="linenos"> 967</span><span class="k">class</span> <span class="nc">TypeVar</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_BoundVarianceMixin</span><span class="p">,</span> <span class="n">_PickleUsingNameMixin</span><span class="p">,</span>
+<span class="linenos"> 968</span>              <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos"> 969</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Type variable.</span>
+<span class="linenos"> 970</span>
+<span class="linenos"> 971</span><span class="sd">    Usage::</span>
 <span class="linenos"> 972</span>
-<span class="linenos"> 973</span>
-<span class="linenos"> 974</span><span class="k">class</span> <span class="nc">TypeVar</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_BoundVarianceMixin</span><span class="p">,</span> <span class="n">_PickleUsingNameMixin</span><span class="p">,</span>
-<span class="linenos"> 975</span>              <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos"> 976</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Type variable.</span>
-<span class="linenos"> 977</span>
-<span class="linenos"> 978</span><span class="sd">    Usage::</span>
-<span class="linenos"> 979</span>
-<span class="linenos"> 980</span><span class="sd">      T = TypeVar(&#39;T&#39;)  # Can be anything</span>
-<span class="linenos"> 981</span><span class="sd">      A = TypeVar(&#39;A&#39;, str, bytes)  # Must be str or bytes</span>
-<span class="linenos"> 982</span>
-<span class="linenos"> 983</span><span class="sd">    Type variables exist primarily for the benefit of static type</span>
-<span class="linenos"> 984</span><span class="sd">    checkers.  They serve as the parameters for generic types as well</span>
-<span class="linenos"> 985</span><span class="sd">    as for generic function definitions.  See class Generic for more</span>
-<span class="linenos"> 986</span><span class="sd">    information on generic types.  Generic functions work as follows:</span>
-<span class="linenos"> 987</span>
-<span class="linenos"> 988</span><span class="sd">      def repeat(x: T, n: int) -&gt; List[T]:</span>
-<span class="linenos"> 989</span><span class="sd">          &#39;&#39;&#39;Return a list containing n references to x.&#39;&#39;&#39;</span>
-<span class="linenos"> 990</span><span class="sd">          return [x]*n</span>
-<span class="linenos"> 991</span>
-<span class="linenos"> 992</span><span class="sd">      def longest(x: A, y: A) -&gt; A:</span>
-<span class="linenos"> 993</span><span class="sd">          &#39;&#39;&#39;Return the longest of two strings.&#39;&#39;&#39;</span>
-<span class="linenos"> 994</span><span class="sd">          return x if len(x) &gt;= len(y) else y</span>
+<span class="linenos"> 973</span><span class="sd">      T = TypeVar(&#39;T&#39;)  # Can be anything</span>
+<span class="linenos"> 974</span><span class="sd">      A = TypeVar(&#39;A&#39;, str, bytes)  # Must be str or bytes</span>
+<span class="linenos"> 975</span>
+<span class="linenos"> 976</span><span class="sd">    Type variables exist primarily for the benefit of static type</span>
+<span class="linenos"> 977</span><span class="sd">    checkers.  They serve as the parameters for generic types as well</span>
+<span class="linenos"> 978</span><span class="sd">    as for generic function definitions.  See class Generic for more</span>
+<span class="linenos"> 979</span><span class="sd">    information on generic types.  Generic functions work as follows:</span>
+<span class="linenos"> 980</span>
+<span class="linenos"> 981</span><span class="sd">      def repeat(x: T, n: int) -&gt; List[T]:</span>
+<span class="linenos"> 982</span><span class="sd">          &#39;&#39;&#39;Return a list containing n references to x.&#39;&#39;&#39;</span>
+<span class="linenos"> 983</span><span class="sd">          return [x]*n</span>
+<span class="linenos"> 984</span>
+<span class="linenos"> 985</span><span class="sd">      def longest(x: A, y: A) -&gt; A:</span>
+<span class="linenos"> 986</span><span class="sd">          &#39;&#39;&#39;Return the longest of two strings.&#39;&#39;&#39;</span>
+<span class="linenos"> 987</span><span class="sd">          return x if len(x) &gt;= len(y) else y</span>
+<span class="linenos"> 988</span>
+<span class="linenos"> 989</span><span class="sd">    The latter example&#39;s signature is essentially the overloading</span>
+<span class="linenos"> 990</span><span class="sd">    of (str, str) -&gt; str and (bytes, bytes) -&gt; bytes.  Also note</span>
+<span class="linenos"> 991</span><span class="sd">    that if the arguments are instances of some subclass of str,</span>
+<span class="linenos"> 992</span><span class="sd">    the return type is still plain str.</span>
+<span class="linenos"> 993</span>
+<span class="linenos"> 994</span><span class="sd">    At runtime, isinstance(x, T) and issubclass(C, T) will raise TypeError.</span>
 <span class="linenos"> 995</span>
-<span class="linenos"> 996</span><span class="sd">    The latter example&#39;s signature is essentially the overloading</span>
-<span class="linenos"> 997</span><span class="sd">    of (str, str) -&gt; str and (bytes, bytes) -&gt; bytes.  Also note</span>
-<span class="linenos"> 998</span><span class="sd">    that if the arguments are instances of some subclass of str,</span>
-<span class="linenos"> 999</span><span class="sd">    the return type is still plain str.</span>
+<span class="linenos"> 996</span><span class="sd">    Type variables defined with covariant=True or contravariant=True</span>
+<span class="linenos"> 997</span><span class="sd">    can be used to declare covariant or contravariant generic types.</span>
+<span class="linenos"> 998</span><span class="sd">    See PEP 484 for more details. By default generic types are invariant</span>
+<span class="linenos"> 999</span><span class="sd">    in all type variables.</span>
 <span class="linenos">1000</span>
-<span class="linenos">1001</span><span class="sd">    At runtime, isinstance(x, T) and issubclass(C, T) will raise TypeError.</span>
+<span class="linenos">1001</span><span class="sd">    Type variables can be introspected. e.g.:</span>
 <span class="linenos">1002</span>
-<span class="linenos">1003</span><span class="sd">    Type variables defined with covariant=True or contravariant=True</span>
-<span class="linenos">1004</span><span class="sd">    can be used to declare covariant or contravariant generic types.</span>
-<span class="linenos">1005</span><span class="sd">    See PEP 484 for more details. By default generic types are invariant</span>
-<span class="linenos">1006</span><span class="sd">    in all type variables.</span>
-<span class="linenos">1007</span>
-<span class="linenos">1008</span><span class="sd">    Type variables can be introspected. e.g.:</span>
-<span class="linenos">1009</span>
-<span class="linenos">1010</span><span class="sd">      T.__name__ == &#39;T&#39;</span>
-<span class="linenos">1011</span><span class="sd">      T.__constraints__ == ()</span>
-<span class="linenos">1012</span><span class="sd">      T.__covariant__ == False</span>
-<span class="linenos">1013</span><span class="sd">      T.__contravariant__ = False</span>
-<span class="linenos">1014</span><span class="sd">      A.__constraints__ == (str, bytes)</span>
-<span class="linenos">1015</span>
-<span class="linenos">1016</span><span class="sd">    Note that only type variables defined in global scope can be pickled.</span>
-<span class="linenos">1017</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1018</span>
-<span class="linenos">1019</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="o">*</span><span class="n">constraints</span><span class="p">,</span> <span class="n">bound</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
-<span class="linenos">1020</span>                 <span class="n">covariant</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">contravariant</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
-<span class="linenos">1021</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="n">name</span>
-<span class="linenos">1022</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">bound</span><span class="p">,</span> <span class="n">covariant</span><span class="p">,</span> <span class="n">contravariant</span><span class="p">)</span>
-<span class="linenos">1023</span>        <span class="k">if</span> <span class="n">constraints</span> <span class="ow">and</span> <span class="n">bound</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">1024</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Constraints cannot be combined with bound=...&quot;</span><span class="p">)</span>
-<span class="linenos">1025</span>        <span class="k">if</span> <span class="n">constraints</span> <span class="ow">and</span> <span class="nb">len</span><span class="p">(</span><span class="n">constraints</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<span class="linenos">1026</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;A single constraint is not allowed&quot;</span><span class="p">)</span>
-<span class="linenos">1027</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;TypeVar(name, constraint, ...): constraints must be types.&quot;</span>
-<span class="linenos">1028</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__constraints__</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">constraints</span><span class="p">)</span>
-<span class="linenos">1029</span>        <span class="n">def_mod</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
-<span class="linenos">1030</span>        <span class="k">if</span> <span class="n">def_mod</span> <span class="o">!=</span> <span class="s1">&#39;typing&#39;</span><span class="p">:</span>
-<span class="linenos">1031</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">def_mod</span>
-<span class="linenos">1032</span>
-<span class="linenos">1033</span>    <span class="k">def</span> <span class="nf">__typing_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg</span><span class="p">):</span>
-<span class="linenos">1034</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Parameters to generic types must be types.&quot;</span>
-<span class="linenos">1035</span>        <span class="n">arg</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">msg</span><span class="p">,</span> <span class="n">is_argument</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="linenos">1036</span>        <span class="k">if</span> <span class="p">((</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">)</span> <span class="ow">and</span> <span class="n">arg</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Unpack</span><span class="p">)</span> <span class="ow">or</span>
-<span class="linenos">1037</span>            <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="s1">&#39;__unpacked__&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">))):</span>
-<span class="linenos">1038</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">arg</span><span class="si">}</span><span class="s2"> is not valid as type argument&quot;</span><span class="p">)</span>
-<span class="linenos">1039</span>        <span class="k">return</span> <span class="n">arg</span>
-<span class="linenos">1040</span>
+<span class="linenos">1003</span><span class="sd">      T.__name__ == &#39;T&#39;</span>
+<span class="linenos">1004</span><span class="sd">      T.__constraints__ == ()</span>
+<span class="linenos">1005</span><span class="sd">      T.__covariant__ == False</span>
+<span class="linenos">1006</span><span class="sd">      T.__contravariant__ = False</span>
+<span class="linenos">1007</span><span class="sd">      A.__constraints__ == (str, bytes)</span>
+<span class="linenos">1008</span>
+<span class="linenos">1009</span><span class="sd">    Note that only type variables defined in global scope can be pickled.</span>
+<span class="linenos">1010</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">1011</span>
+<span class="linenos">1012</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="o">*</span><span class="n">constraints</span><span class="p">,</span> <span class="n">bound</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+<span class="linenos">1013</span>                 <span class="n">covariant</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">contravariant</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="linenos">1014</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="n">name</span>
+<span class="linenos">1015</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">bound</span><span class="p">,</span> <span class="n">covariant</span><span class="p">,</span> <span class="n">contravariant</span><span class="p">)</span>
+<span class="linenos">1016</span>        <span class="k">if</span> <span class="n">constraints</span> <span class="ow">and</span> <span class="n">bound</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">1017</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Constraints cannot be combined with bound=...&quot;</span><span class="p">)</span>
+<span class="linenos">1018</span>        <span class="k">if</span> <span class="n">constraints</span> <span class="ow">and</span> <span class="nb">len</span><span class="p">(</span><span class="n">constraints</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<span class="linenos">1019</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;A single constraint is not allowed&quot;</span><span class="p">)</span>
+<span class="linenos">1020</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;TypeVar(name, constraint, ...): constraints must be types.&quot;</span>
+<span class="linenos">1021</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__constraints__</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">constraints</span><span class="p">)</span>
+<span class="linenos">1022</span>        <span class="n">def_mod</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
+<span class="linenos">1023</span>        <span class="k">if</span> <span class="n">def_mod</span> <span class="o">!=</span> <span class="s1">&#39;typing&#39;</span><span class="p">:</span>
+<span class="linenos">1024</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">def_mod</span>
+<span class="linenos">1025</span>
+<span class="linenos">1026</span>    <span class="k">def</span> <span class="nf">__typing_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg</span><span class="p">):</span>
+<span class="linenos">1027</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Parameters to generic types must be types.&quot;</span>
+<span class="linenos">1028</span>        <span class="n">arg</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">msg</span><span class="p">,</span> <span class="n">is_argument</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<span class="linenos">1029</span>        <span class="k">if</span> <span class="p">((</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">)</span> <span class="ow">and</span> <span class="n">arg</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Unpack</span><span class="p">)</span> <span class="ow">or</span>
+<span class="linenos">1030</span>            <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="s1">&#39;__unpacked__&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">))):</span>
+<span class="linenos">1031</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">arg</span><span class="si">}</span><span class="s2"> is not valid as type argument&quot;</span><span class="p">)</span>
+<span class="linenos">1032</span>        <span class="k">return</span> <span class="n">arg</span>
+<span class="linenos">1033</span>
+<span class="linenos">1034</span>
+<span class="linenos">1035</span><span class="k">class</span> <span class="nc">TypeVarTuple</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_PickleUsingNameMixin</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1036</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Type variable tuple.</span>
+<span class="linenos">1037</span>
+<span class="linenos">1038</span><span class="sd">    Usage:</span>
+<span class="linenos">1039</span>
+<span class="linenos">1040</span><span class="sd">      Ts = TypeVarTuple(&#39;Ts&#39;)  # Can be given any name</span>
 <span class="linenos">1041</span>
-<span class="linenos">1042</span><span class="k">class</span> <span class="nc">TypeVarTuple</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_PickleUsingNameMixin</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1043</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Type variable tuple.</span>
-<span class="linenos">1044</span>
-<span class="linenos">1045</span><span class="sd">    Usage:</span>
-<span class="linenos">1046</span>
-<span class="linenos">1047</span><span class="sd">      Ts = TypeVarTuple(&#39;Ts&#39;)  # Can be given any name</span>
-<span class="linenos">1048</span>
-<span class="linenos">1049</span><span class="sd">    Just as a TypeVar (type variable) is a placeholder for a single type,</span>
-<span class="linenos">1050</span><span class="sd">    a TypeVarTuple is a placeholder for an *arbitrary* number of types. For</span>
-<span class="linenos">1051</span><span class="sd">    example, if we define a generic class using a TypeVarTuple:</span>
-<span class="linenos">1052</span>
-<span class="linenos">1053</span><span class="sd">      class C(Generic[*Ts]): ...</span>
+<span class="linenos">1042</span><span class="sd">    Just as a TypeVar (type variable) is a placeholder for a single type,</span>
+<span class="linenos">1043</span><span class="sd">    a TypeVarTuple is a placeholder for an *arbitrary* number of types. For</span>
+<span class="linenos">1044</span><span class="sd">    example, if we define a generic class using a TypeVarTuple:</span>
+<span class="linenos">1045</span>
+<span class="linenos">1046</span><span class="sd">      class C(Generic[*Ts]): ...</span>
+<span class="linenos">1047</span>
+<span class="linenos">1048</span><span class="sd">    Then we can parameterize that class with an arbitrary number of type</span>
+<span class="linenos">1049</span><span class="sd">    arguments:</span>
+<span class="linenos">1050</span>
+<span class="linenos">1051</span><span class="sd">      C[int]       # Fine</span>
+<span class="linenos">1052</span><span class="sd">      C[int, str]  # Also fine</span>
+<span class="linenos">1053</span><span class="sd">      C[()]        # Even this is fine</span>
 <span class="linenos">1054</span>
-<span class="linenos">1055</span><span class="sd">    Then we can parameterize that class with an arbitrary number of type</span>
-<span class="linenos">1056</span><span class="sd">    arguments:</span>
-<span class="linenos">1057</span>
-<span class="linenos">1058</span><span class="sd">      C[int]       # Fine</span>
-<span class="linenos">1059</span><span class="sd">      C[int, str]  # Also fine</span>
-<span class="linenos">1060</span><span class="sd">      C[()]        # Even this is fine</span>
-<span class="linenos">1061</span>
-<span class="linenos">1062</span><span class="sd">    For more details, see PEP 646.</span>
-<span class="linenos">1063</span>
-<span class="linenos">1064</span><span class="sd">    Note that only TypeVarTuples defined in global scope can be pickled.</span>
-<span class="linenos">1065</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1066</span>
-<span class="linenos">1067</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span>
-<span class="linenos">1068</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="n">name</span>
-<span class="linenos">1069</span>
-<span class="linenos">1070</span>        <span class="c1"># Used for pickling.</span>
-<span class="linenos">1071</span>        <span class="n">def_mod</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
-<span class="linenos">1072</span>        <span class="k">if</span> <span class="n">def_mod</span> <span class="o">!=</span> <span class="s1">&#39;typing&#39;</span><span class="p">:</span>
-<span class="linenos">1073</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">def_mod</span>
-<span class="linenos">1074</span>
-<span class="linenos">1075</span>    <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1076</span>        <span class="k">yield</span> <span class="n">Unpack</span><span class="p">[</span><span class="bp">self</span><span class="p">]</span>
-<span class="linenos">1077</span>
-<span class="linenos">1078</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1079</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span>
-<span class="linenos">1080</span>
-<span class="linenos">1081</span>    <span class="k">def</span> <span class="nf">__typing_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg</span><span class="p">):</span>
-<span class="linenos">1082</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Substitution of bare TypeVarTuple is not supported&quot;</span><span class="p">)</span>
+<span class="linenos">1055</span><span class="sd">    For more details, see PEP 646.</span>
+<span class="linenos">1056</span>
+<span class="linenos">1057</span><span class="sd">    Note that only TypeVarTuples defined in global scope can be pickled.</span>
+<span class="linenos">1058</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">1059</span>
+<span class="linenos">1060</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span>
+<span class="linenos">1061</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="n">name</span>
+<span class="linenos">1062</span>
+<span class="linenos">1063</span>        <span class="c1"># Used for pickling.</span>
+<span class="linenos">1064</span>        <span class="n">def_mod</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
+<span class="linenos">1065</span>        <span class="k">if</span> <span class="n">def_mod</span> <span class="o">!=</span> <span class="s1">&#39;typing&#39;</span><span class="p">:</span>
+<span class="linenos">1066</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">def_mod</span>
+<span class="linenos">1067</span>
+<span class="linenos">1068</span>    <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1069</span>        <span class="k">yield</span> <span class="n">Unpack</span><span class="p">[</span><span class="bp">self</span><span class="p">]</span>
+<span class="linenos">1070</span>
+<span class="linenos">1071</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1072</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span>
+<span class="linenos">1073</span>
+<span class="linenos">1074</span>    <span class="k">def</span> <span class="nf">__typing_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg</span><span class="p">):</span>
+<span class="linenos">1075</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Substitution of bare TypeVarTuple is not supported&quot;</span><span class="p">)</span>
+<span class="linenos">1076</span>
+<span class="linenos">1077</span>    <span class="k">def</span> <span class="nf">__typing_prepare_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alias</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
+<span class="linenos">1078</span>        <span class="n">params</span> <span class="o">=</span> <span class="n">alias</span><span class="o">.</span><span class="n">__parameters__</span>
+<span class="linenos">1079</span>        <span class="n">typevartuple_index</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+<span class="linenos">1080</span>        <span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="n">params</span><span class="p">[</span><span class="n">typevartuple_index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">:]:</span>
+<span class="linenos">1081</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">TypeVarTuple</span><span class="p">):</span>
+<span class="linenos">1082</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;More than one TypeVarTuple parameter in </span><span class="si">{</span><span class="n">alias</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
 <span class="linenos">1083</span>
-<span class="linenos">1084</span>    <span class="k">def</span> <span class="nf">__typing_prepare_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alias</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
-<span class="linenos">1085</span>        <span class="n">params</span> <span class="o">=</span> <span class="n">alias</span><span class="o">.</span><span class="n">__parameters__</span>
-<span class="linenos">1086</span>        <span class="n">typevartuple_index</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
-<span class="linenos">1087</span>        <span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="n">params</span><span class="p">[</span><span class="n">typevartuple_index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">:]:</span>
-<span class="linenos">1088</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">TypeVarTuple</span><span class="p">):</span>
-<span class="linenos">1089</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;More than one TypeVarTuple parameter in </span><span class="si">{</span><span class="n">alias</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos">1090</span>
-<span class="linenos">1091</span>        <span class="n">alen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
-<span class="linenos">1092</span>        <span class="n">plen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
-<span class="linenos">1093</span>        <span class="n">left</span> <span class="o">=</span> <span class="n">typevartuple_index</span>
-<span class="linenos">1094</span>        <span class="n">right</span> <span class="o">=</span> <span class="n">plen</span> <span class="o">-</span> <span class="n">typevartuple_index</span> <span class="o">-</span> <span class="mi">1</span>
-<span class="linenos">1095</span>        <span class="n">var_tuple_index</span> <span class="o">=</span> <span class="kc">None</span>
-<span class="linenos">1096</span>        <span class="n">fillarg</span> <span class="o">=</span> <span class="kc">None</span>
-<span class="linenos">1097</span>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">arg</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">args</span><span class="p">):</span>
-<span class="linenos">1098</span>            <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
-<span class="linenos">1099</span>                <span class="n">subargs</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="s1">&#39;__typing_unpacked_tuple_args__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
-<span class="linenos">1100</span>                <span class="k">if</span> <span class="n">subargs</span> <span class="ow">and</span> <span class="nb">len</span><span class="p">(</span><span class="n">subargs</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">subargs</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="o">...</span><span class="p">:</span>
-<span class="linenos">1101</span>                    <span class="k">if</span> <span class="n">var_tuple_index</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">1102</span>                        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;More than one unpacked arbitrary-length tuple argument&quot;</span><span class="p">)</span>
-<span class="linenos">1103</span>                    <span class="n">var_tuple_index</span> <span class="o">=</span> <span class="n">k</span>
-<span class="linenos">1104</span>                    <span class="n">fillarg</span> <span class="o">=</span> <span class="n">subargs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-<span class="linenos">1105</span>        <span class="k">if</span> <span class="n">var_tuple_index</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">1106</span>            <span class="n">left</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">var_tuple_index</span><span class="p">)</span>
-<span class="linenos">1107</span>            <span class="n">right</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">right</span><span class="p">,</span> <span class="n">alen</span> <span class="o">-</span> <span class="n">var_tuple_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">1108</span>        <span class="k">elif</span> <span class="n">left</span> <span class="o">+</span> <span class="n">right</span> <span class="o">&gt;</span> <span class="n">alen</span><span class="p">:</span>
-<span class="linenos">1109</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Too few arguments for </span><span class="si">{</span><span class="n">alias</span><span class="si">}</span><span class="s2">;&quot;</span>
-<span class="linenos">1110</span>                            <span class="sa">f</span><span class="s2">&quot; actual </span><span class="si">{</span><span class="n">alen</span><span class="si">}</span><span class="s2">, expected at least </span><span class="si">{</span><span class="n">plen</span><span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos">1111</span>
-<span class="linenos">1112</span>        <span class="k">return</span> <span class="p">(</span>
-<span class="linenos">1113</span>            <span class="o">*</span><span class="n">args</span><span class="p">[:</span><span class="n">left</span><span class="p">],</span>
-<span class="linenos">1114</span>            <span class="o">*</span><span class="p">([</span><span class="n">fillarg</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">typevartuple_index</span> <span class="o">-</span> <span class="n">left</span><span class="p">)),</span>
-<span class="linenos">1115</span>            <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">left</span><span class="p">:</span> <span class="n">alen</span> <span class="o">-</span> <span class="n">right</span><span class="p">]),</span>
-<span class="linenos">1116</span>            <span class="o">*</span><span class="p">([</span><span class="n">fillarg</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">plen</span> <span class="o">-</span> <span class="n">right</span> <span class="o">-</span> <span class="n">left</span> <span class="o">-</span> <span class="n">typevartuple_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)),</span>
-<span class="linenos">1117</span>            <span class="o">*</span><span class="n">args</span><span class="p">[</span><span class="n">alen</span> <span class="o">-</span> <span class="n">right</span><span class="p">:],</span>
-<span class="linenos">1118</span>        <span class="p">)</span>
-<span class="linenos">1119</span>
+<span class="linenos">1084</span>        <span class="n">alen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
+<span class="linenos">1085</span>        <span class="n">plen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos">1086</span>        <span class="n">left</span> <span class="o">=</span> <span class="n">typevartuple_index</span>
+<span class="linenos">1087</span>        <span class="n">right</span> <span class="o">=</span> <span class="n">plen</span> <span class="o">-</span> <span class="n">typevartuple_index</span> <span class="o">-</span> <span class="mi">1</span>
+<span class="linenos">1088</span>        <span class="n">var_tuple_index</span> <span class="o">=</span> <span class="kc">None</span>
+<span class="linenos">1089</span>        <span class="n">fillarg</span> <span class="o">=</span> <span class="kc">None</span>
+<span class="linenos">1090</span>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">arg</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">args</span><span class="p">):</span>
+<span class="linenos">1091</span>            <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
+<span class="linenos">1092</span>                <span class="n">subargs</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="s1">&#39;__typing_unpacked_tuple_args__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
+<span class="linenos">1093</span>                <span class="k">if</span> <span class="n">subargs</span> <span class="ow">and</span> <span class="nb">len</span><span class="p">(</span><span class="n">subargs</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">subargs</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="o">...</span><span class="p">:</span>
+<span class="linenos">1094</span>                    <span class="k">if</span> <span class="n">var_tuple_index</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">1095</span>                        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;More than one unpacked arbitrary-length tuple argument&quot;</span><span class="p">)</span>
+<span class="linenos">1096</span>                    <span class="n">var_tuple_index</span> <span class="o">=</span> <span class="n">k</span>
+<span class="linenos">1097</span>                    <span class="n">fillarg</span> <span class="o">=</span> <span class="n">subargs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<span class="linenos">1098</span>        <span class="k">if</span> <span class="n">var_tuple_index</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">1099</span>            <span class="n">left</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">var_tuple_index</span><span class="p">)</span>
+<span class="linenos">1100</span>            <span class="n">right</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">right</span><span class="p">,</span> <span class="n">alen</span> <span class="o">-</span> <span class="n">var_tuple_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">1101</span>        <span class="k">elif</span> <span class="n">left</span> <span class="o">+</span> <span class="n">right</span> <span class="o">&gt;</span> <span class="n">alen</span><span class="p">:</span>
+<span class="linenos">1102</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Too few arguments for </span><span class="si">{</span><span class="n">alias</span><span class="si">}</span><span class="s2">;&quot;</span>
+<span class="linenos">1103</span>                            <span class="sa">f</span><span class="s2">&quot; actual </span><span class="si">{</span><span class="n">alen</span><span class="si">}</span><span class="s2">, expected at least </span><span class="si">{</span><span class="n">plen</span><span class="o">-</span><span class="mi">1</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos">1104</span>
+<span class="linenos">1105</span>        <span class="k">return</span> <span class="p">(</span>
+<span class="linenos">1106</span>            <span class="o">*</span><span class="n">args</span><span class="p">[:</span><span class="n">left</span><span class="p">],</span>
+<span class="linenos">1107</span>            <span class="o">*</span><span class="p">([</span><span class="n">fillarg</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">typevartuple_index</span> <span class="o">-</span> <span class="n">left</span><span class="p">)),</span>
+<span class="linenos">1108</span>            <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">left</span><span class="p">:</span> <span class="n">alen</span> <span class="o">-</span> <span class="n">right</span><span class="p">]),</span>
+<span class="linenos">1109</span>            <span class="o">*</span><span class="p">([</span><span class="n">fillarg</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">plen</span> <span class="o">-</span> <span class="n">right</span> <span class="o">-</span> <span class="n">left</span> <span class="o">-</span> <span class="n">typevartuple_index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)),</span>
+<span class="linenos">1110</span>            <span class="o">*</span><span class="n">args</span><span class="p">[</span><span class="n">alen</span> <span class="o">-</span> <span class="n">right</span><span class="p">:],</span>
+<span class="linenos">1111</span>        <span class="p">)</span>
+<span class="linenos">1112</span>
+<span class="linenos">1113</span>
+<span class="linenos">1114</span><span class="k">class</span> <span class="nc">ParamSpecArgs</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1115</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;The args for a ParamSpec object.</span>
+<span class="linenos">1116</span>
+<span class="linenos">1117</span><span class="sd">    Given a ParamSpec object P, P.args is an instance of ParamSpecArgs.</span>
+<span class="linenos">1118</span>
+<span class="linenos">1119</span><span class="sd">    ParamSpecArgs objects have a reference back to their ParamSpec:</span>
 <span class="linenos">1120</span>
-<span class="linenos">1121</span><span class="k">class</span> <span class="nc">ParamSpecArgs</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1122</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;The args for a ParamSpec object.</span>
-<span class="linenos">1123</span>
-<span class="linenos">1124</span><span class="sd">    Given a ParamSpec object P, P.args is an instance of ParamSpecArgs.</span>
-<span class="linenos">1125</span>
-<span class="linenos">1126</span><span class="sd">    ParamSpecArgs objects have a reference back to their ParamSpec:</span>
-<span class="linenos">1127</span>
-<span class="linenos">1128</span><span class="sd">       P.args.__origin__ is P</span>
-<span class="linenos">1129</span>
-<span class="linenos">1130</span><span class="sd">    This type is meant for runtime introspection and has no special meaning to</span>
-<span class="linenos">1131</span><span class="sd">    static type checkers.</span>
-<span class="linenos">1132</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1133</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
-<span class="linenos">1134</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">=</span> <span class="n">origin</span>
-<span class="linenos">1135</span>
-<span class="linenos">1136</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1137</span>        <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">.args&quot;</span>
-<span class="linenos">1138</span>
-<span class="linenos">1139</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos">1140</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">ParamSpecArgs</span><span class="p">):</span>
-<span class="linenos">1141</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">1142</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__origin__</span>
-<span class="linenos">1143</span>
+<span class="linenos">1121</span><span class="sd">       P.args.__origin__ is P</span>
+<span class="linenos">1122</span>
+<span class="linenos">1123</span><span class="sd">    This type is meant for runtime introspection and has no special meaning to</span>
+<span class="linenos">1124</span><span class="sd">    static type checkers.</span>
+<span class="linenos">1125</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">1126</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
+<span class="linenos">1127</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">=</span> <span class="n">origin</span>
+<span class="linenos">1128</span>
+<span class="linenos">1129</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1130</span>        <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">.args&quot;</span>
+<span class="linenos">1131</span>
+<span class="linenos">1132</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos">1133</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">ParamSpecArgs</span><span class="p">):</span>
+<span class="linenos">1134</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">1135</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__origin__</span>
+<span class="linenos">1136</span>
+<span class="linenos">1137</span>
+<span class="linenos">1138</span><span class="k">class</span> <span class="nc">ParamSpecKwargs</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1139</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;The kwargs for a ParamSpec object.</span>
+<span class="linenos">1140</span>
+<span class="linenos">1141</span><span class="sd">    Given a ParamSpec object P, P.kwargs is an instance of ParamSpecKwargs.</span>
+<span class="linenos">1142</span>
+<span class="linenos">1143</span><span class="sd">    ParamSpecKwargs objects have a reference back to their ParamSpec:</span>
 <span class="linenos">1144</span>
-<span class="linenos">1145</span><span class="k">class</span> <span class="nc">ParamSpecKwargs</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1146</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;The kwargs for a ParamSpec object.</span>
-<span class="linenos">1147</span>
-<span class="linenos">1148</span><span class="sd">    Given a ParamSpec object P, P.kwargs is an instance of ParamSpecKwargs.</span>
-<span class="linenos">1149</span>
-<span class="linenos">1150</span><span class="sd">    ParamSpecKwargs objects have a reference back to their ParamSpec:</span>
-<span class="linenos">1151</span>
-<span class="linenos">1152</span><span class="sd">       P.kwargs.__origin__ is P</span>
-<span class="linenos">1153</span>
-<span class="linenos">1154</span><span class="sd">    This type is meant for runtime introspection and has no special meaning to</span>
-<span class="linenos">1155</span><span class="sd">    static type checkers.</span>
-<span class="linenos">1156</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1157</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
-<span class="linenos">1158</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">=</span> <span class="n">origin</span>
-<span class="linenos">1159</span>
-<span class="linenos">1160</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1161</span>        <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">.kwargs&quot;</span>
-<span class="linenos">1162</span>
-<span class="linenos">1163</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos">1164</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">ParamSpecKwargs</span><span class="p">):</span>
-<span class="linenos">1165</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">1166</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__origin__</span>
+<span class="linenos">1145</span><span class="sd">       P.kwargs.__origin__ is P</span>
+<span class="linenos">1146</span>
+<span class="linenos">1147</span><span class="sd">    This type is meant for runtime introspection and has no special meaning to</span>
+<span class="linenos">1148</span><span class="sd">    static type checkers.</span>
+<span class="linenos">1149</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">1150</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
+<span class="linenos">1151</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">=</span> <span class="n">origin</span>
+<span class="linenos">1152</span>
+<span class="linenos">1153</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1154</span>        <span class="k">return</span> <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">.kwargs&quot;</span>
+<span class="linenos">1155</span>
+<span class="linenos">1156</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos">1157</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">ParamSpecKwargs</span><span class="p">):</span>
+<span class="linenos">1158</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">1159</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__origin__</span>
+<span class="linenos">1160</span>
+<span class="linenos">1161</span>
+<span class="linenos">1162</span><span class="k">class</span> <span class="nc">ParamSpec</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_BoundVarianceMixin</span><span class="p">,</span> <span class="n">_PickleUsingNameMixin</span><span class="p">,</span>
+<span class="linenos">1163</span>                <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1164</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Parameter specification variable.</span>
+<span class="linenos">1165</span>
+<span class="linenos">1166</span><span class="sd">    Usage::</span>
 <span class="linenos">1167</span>
-<span class="linenos">1168</span>
-<span class="linenos">1169</span><span class="k">class</span> <span class="nc">ParamSpec</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_Immutable</span><span class="p">,</span> <span class="n">_BoundVarianceMixin</span><span class="p">,</span> <span class="n">_PickleUsingNameMixin</span><span class="p">,</span>
-<span class="linenos">1170</span>                <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1171</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Parameter specification variable.</span>
-<span class="linenos">1172</span>
-<span class="linenos">1173</span><span class="sd">    Usage::</span>
-<span class="linenos">1174</span>
-<span class="linenos">1175</span><span class="sd">       P = ParamSpec(&#39;P&#39;)</span>
-<span class="linenos">1176</span>
-<span class="linenos">1177</span><span class="sd">    Parameter specification variables exist primarily for the benefit of static</span>
-<span class="linenos">1178</span><span class="sd">    type checkers.  They are used to forward the parameter types of one</span>
-<span class="linenos">1179</span><span class="sd">    callable to another callable, a pattern commonly found in higher order</span>
-<span class="linenos">1180</span><span class="sd">    functions and decorators.  They are only valid when used in ``Concatenate``,</span>
-<span class="linenos">1181</span><span class="sd">    or as the first argument to ``Callable``, or as parameters for user-defined</span>
-<span class="linenos">1182</span><span class="sd">    Generics.  See class Generic for more information on generic types.  An</span>
-<span class="linenos">1183</span><span class="sd">    example for annotating a decorator::</span>
-<span class="linenos">1184</span>
-<span class="linenos">1185</span><span class="sd">       T = TypeVar(&#39;T&#39;)</span>
-<span class="linenos">1186</span><span class="sd">       P = ParamSpec(&#39;P&#39;)</span>
+<span class="linenos">1168</span><span class="sd">       P = ParamSpec(&#39;P&#39;)</span>
+<span class="linenos">1169</span>
+<span class="linenos">1170</span><span class="sd">    Parameter specification variables exist primarily for the benefit of static</span>
+<span class="linenos">1171</span><span class="sd">    type checkers.  They are used to forward the parameter types of one</span>
+<span class="linenos">1172</span><span class="sd">    callable to another callable, a pattern commonly found in higher order</span>
+<span class="linenos">1173</span><span class="sd">    functions and decorators.  They are only valid when used in ``Concatenate``,</span>
+<span class="linenos">1174</span><span class="sd">    or as the first argument to ``Callable``, or as parameters for user-defined</span>
+<span class="linenos">1175</span><span class="sd">    Generics.  See class Generic for more information on generic types.  An</span>
+<span class="linenos">1176</span><span class="sd">    example for annotating a decorator::</span>
+<span class="linenos">1177</span>
+<span class="linenos">1178</span><span class="sd">       T = TypeVar(&#39;T&#39;)</span>
+<span class="linenos">1179</span><span class="sd">       P = ParamSpec(&#39;P&#39;)</span>
+<span class="linenos">1180</span>
+<span class="linenos">1181</span><span class="sd">       def add_logging(f: Callable[P, T]) -&gt; Callable[P, T]:</span>
+<span class="linenos">1182</span><span class="sd">           &#39;&#39;&#39;A type-safe decorator to add logging to a function.&#39;&#39;&#39;</span>
+<span class="linenos">1183</span><span class="sd">           def inner(*args: P.args, **kwargs: P.kwargs) -&gt; T:</span>
+<span class="linenos">1184</span><span class="sd">               logging.info(f&#39;{f.__name__} was called&#39;)</span>
+<span class="linenos">1185</span><span class="sd">               return f(*args, **kwargs)</span>
+<span class="linenos">1186</span><span class="sd">           return inner</span>
 <span class="linenos">1187</span>
-<span class="linenos">1188</span><span class="sd">       def add_logging(f: Callable[P, T]) -&gt; Callable[P, T]:</span>
-<span class="linenos">1189</span><span class="sd">           &#39;&#39;&#39;A type-safe decorator to add logging to a function.&#39;&#39;&#39;</span>
-<span class="linenos">1190</span><span class="sd">           def inner(*args: P.args, **kwargs: P.kwargs) -&gt; T:</span>
-<span class="linenos">1191</span><span class="sd">               logging.info(f&#39;{f.__name__} was called&#39;)</span>
-<span class="linenos">1192</span><span class="sd">               return f(*args, **kwargs)</span>
-<span class="linenos">1193</span><span class="sd">           return inner</span>
+<span class="linenos">1188</span><span class="sd">       @add_logging</span>
+<span class="linenos">1189</span><span class="sd">       def add_two(x: float, y: float) -&gt; float:</span>
+<span class="linenos">1190</span><span class="sd">           &#39;&#39;&#39;Add two numbers together.&#39;&#39;&#39;</span>
+<span class="linenos">1191</span><span class="sd">           return x + y</span>
+<span class="linenos">1192</span>
+<span class="linenos">1193</span><span class="sd">    Parameter specification variables can be introspected. e.g.:</span>
 <span class="linenos">1194</span>
-<span class="linenos">1195</span><span class="sd">       @add_logging</span>
-<span class="linenos">1196</span><span class="sd">       def add_two(x: float, y: float) -&gt; float:</span>
-<span class="linenos">1197</span><span class="sd">           &#39;&#39;&#39;Add two numbers together.&#39;&#39;&#39;</span>
-<span class="linenos">1198</span><span class="sd">           return x + y</span>
-<span class="linenos">1199</span>
-<span class="linenos">1200</span><span class="sd">    Parameter specification variables can be introspected. e.g.:</span>
-<span class="linenos">1201</span>
-<span class="linenos">1202</span><span class="sd">       P.__name__ == &#39;P&#39;</span>
-<span class="linenos">1203</span>
-<span class="linenos">1204</span><span class="sd">    Note that only parameter specification variables defined in global scope can</span>
-<span class="linenos">1205</span><span class="sd">    be pickled.</span>
-<span class="linenos">1206</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1207</span>
-<span class="linenos">1208</span>    <span class="nd">@property</span>
-<span class="linenos">1209</span>    <span class="k">def</span> <span class="nf">args</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1210</span>        <span class="k">return</span> <span class="n">ParamSpecArgs</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
-<span class="linenos">1211</span>
-<span class="linenos">1212</span>    <span class="nd">@property</span>
-<span class="linenos">1213</span>    <span class="k">def</span> <span class="nf">kwargs</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1214</span>        <span class="k">return</span> <span class="n">ParamSpecKwargs</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+<span class="linenos">1195</span><span class="sd">       P.__name__ == &#39;P&#39;</span>
+<span class="linenos">1196</span>
+<span class="linenos">1197</span><span class="sd">    Note that only parameter specification variables defined in global scope can</span>
+<span class="linenos">1198</span><span class="sd">    be pickled.</span>
+<span class="linenos">1199</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">1200</span>
+<span class="linenos">1201</span>    <span class="nd">@property</span>
+<span class="linenos">1202</span>    <span class="k">def</span> <span class="nf">args</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1203</span>        <span class="k">return</span> <span class="n">ParamSpecArgs</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+<span class="linenos">1204</span>
+<span class="linenos">1205</span>    <span class="nd">@property</span>
+<span class="linenos">1206</span>    <span class="k">def</span> <span class="nf">kwargs</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1207</span>        <span class="k">return</span> <span class="n">ParamSpecKwargs</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+<span class="linenos">1208</span>
+<span class="linenos">1209</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">bound</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">contravariant</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="linenos">1210</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="n">name</span>
+<span class="linenos">1211</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">bound</span><span class="p">,</span> <span class="n">covariant</span><span class="p">,</span> <span class="n">contravariant</span><span class="p">)</span>
+<span class="linenos">1212</span>        <span class="n">def_mod</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
+<span class="linenos">1213</span>        <span class="k">if</span> <span class="n">def_mod</span> <span class="o">!=</span> <span class="s1">&#39;typing&#39;</span><span class="p">:</span>
+<span class="linenos">1214</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">def_mod</span>
 <span class="linenos">1215</span>
-<span class="linenos">1216</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">bound</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">contravariant</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
-<span class="linenos">1217</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="n">name</span>
-<span class="linenos">1218</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">bound</span><span class="p">,</span> <span class="n">covariant</span><span class="p">,</span> <span class="n">contravariant</span><span class="p">)</span>
-<span class="linenos">1219</span>        <span class="n">def_mod</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
-<span class="linenos">1220</span>        <span class="k">if</span> <span class="n">def_mod</span> <span class="o">!=</span> <span class="s1">&#39;typing&#39;</span><span class="p">:</span>
-<span class="linenos">1221</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">def_mod</span>
-<span class="linenos">1222</span>
-<span class="linenos">1223</span>    <span class="k">def</span> <span class="nf">__typing_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg</span><span class="p">):</span>
-<span class="linenos">1224</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)):</span>
-<span class="linenos">1225</span>            <span class="n">arg</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="s2">&quot;Expected a type.&quot;</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">arg</span><span class="p">)</span>
-<span class="linenos">1226</span>        <span class="k">elif</span> <span class="ow">not</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">arg</span><span class="p">):</span>
-<span class="linenos">1227</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Expected a list of types, an ellipsis, &quot;</span>
-<span class="linenos">1228</span>                            <span class="sa">f</span><span class="s2">&quot;ParamSpec, or Concatenate. Got </span><span class="si">{</span><span class="n">arg</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos">1229</span>        <span class="k">return</span> <span class="n">arg</span>
-<span class="linenos">1230</span>
-<span class="linenos">1231</span>    <span class="k">def</span> <span class="nf">__typing_prepare_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alias</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
-<span class="linenos">1232</span>        <span class="n">params</span> <span class="o">=</span> <span class="n">alias</span><span class="o">.</span><span class="n">__parameters__</span>
-<span class="linenos">1233</span>        <span class="n">i</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
-<span class="linenos">1234</span>        <span class="k">if</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">):</span>
-<span class="linenos">1235</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Too few arguments for </span><span class="si">{</span><span class="n">alias</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos">1236</span>        <span class="c1"># Special case where Z[[int, str, bool]] == Z[int, str, bool] in PEP 612.</span>
-<span class="linenos">1237</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
-<span class="linenos">1238</span>            <span class="k">assert</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span>
-<span class="linenos">1239</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,)</span>
-<span class="linenos">1240</span>        <span class="c1"># Convert lists to tuples to help other libraries cache the results.</span>
-<span class="linenos">1241</span>        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">):</span>
-<span class="linenos">1242</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">[:</span><span class="n">i</span><span class="p">],</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]),</span> <span class="o">*</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">:])</span>
-<span class="linenos">1243</span>        <span class="k">return</span> <span class="n">args</span>
-<span class="linenos">1244</span>
-<span class="linenos">1245</span><span class="k">def</span> <span class="nf">_is_dunder</span><span class="p">(</span><span class="n">attr</span><span class="p">):</span>
-<span class="linenos">1246</span>    <span class="k">return</span> <span class="n">attr</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">&#39;__&#39;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">attr</span><span class="o">.</span><span class="n">endswith</span><span class="p">(</span><span class="s1">&#39;__&#39;</span><span class="p">)</span>
-<span class="linenos">1247</span>
-<span class="linenos">1248</span><span class="k">class</span> <span class="nc">_BaseGenericAlias</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1249</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;The central part of the internal API.</span>
+<span class="linenos">1216</span>    <span class="k">def</span> <span class="nf">__typing_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg</span><span class="p">):</span>
+<span class="linenos">1217</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)):</span>
+<span class="linenos">1218</span>            <span class="n">arg</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="s2">&quot;Expected a type.&quot;</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">arg</span><span class="p">)</span>
+<span class="linenos">1219</span>        <span class="k">elif</span> <span class="ow">not</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">arg</span><span class="p">):</span>
+<span class="linenos">1220</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Expected a list of types, an ellipsis, &quot;</span>
+<span class="linenos">1221</span>                            <span class="sa">f</span><span class="s2">&quot;ParamSpec, or Concatenate. Got </span><span class="si">{</span><span class="n">arg</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos">1222</span>        <span class="k">return</span> <span class="n">arg</span>
+<span class="linenos">1223</span>
+<span class="linenos">1224</span>    <span class="k">def</span> <span class="nf">__typing_prepare_subst__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alias</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
+<span class="linenos">1225</span>        <span class="n">params</span> <span class="o">=</span> <span class="n">alias</span><span class="o">.</span><span class="n">__parameters__</span>
+<span class="linenos">1226</span>        <span class="n">i</span> <span class="o">=</span> <span class="n">params</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+<span class="linenos">1227</span>        <span class="k">if</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">):</span>
+<span class="linenos">1228</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Too few arguments for </span><span class="si">{</span><span class="n">alias</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos">1229</span>        <span class="c1"># Special case where Z[[int, str, bool]] == Z[int, str, bool] in PEP 612.</span>
+<span class="linenos">1230</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
+<span class="linenos">1231</span>            <span class="k">assert</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span>
+<span class="linenos">1232</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,)</span>
+<span class="linenos">1233</span>        <span class="c1"># Convert lists to tuples to help other libraries cache the results.</span>
+<span class="linenos">1234</span>        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">):</span>
+<span class="linenos">1235</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">[:</span><span class="n">i</span><span class="p">],</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]),</span> <span class="o">*</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">:])</span>
+<span class="linenos">1236</span>        <span class="k">return</span> <span class="n">args</span>
+<span class="linenos">1237</span>
+<span class="linenos">1238</span><span class="k">def</span> <span class="nf">_is_dunder</span><span class="p">(</span><span class="n">attr</span><span class="p">):</span>
+<span class="linenos">1239</span>    <span class="k">return</span> <span class="n">attr</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">&#39;__&#39;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">attr</span><span class="o">.</span><span class="n">endswith</span><span class="p">(</span><span class="s1">&#39;__&#39;</span><span class="p">)</span>
+<span class="linenos">1240</span>
+<span class="linenos">1241</span><span class="k">class</span> <span class="nc">_BaseGenericAlias</span><span class="p">(</span><span class="n">_Final</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1242</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;The central part of the internal API.</span>
+<span class="linenos">1243</span>
+<span class="linenos">1244</span><span class="sd">    This represents a generic version of type &#39;origin&#39; with type arguments &#39;params&#39;.</span>
+<span class="linenos">1245</span><span class="sd">    There are two kind of these aliases: user defined and special. The special ones</span>
+<span class="linenos">1246</span><span class="sd">    are wrappers around builtin collections and ABCs in collections.abc. These must</span>
+<span class="linenos">1247</span><span class="sd">    have &#39;name&#39; always set. If &#39;inst&#39; is False, then the alias can&#39;t be instantiated;</span>
+<span class="linenos">1248</span><span class="sd">    this is used by e.g. typing.List and typing.Dict.</span>
+<span class="linenos">1249</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">1250</span>
-<span class="linenos">1251</span><span class="sd">    This represents a generic version of type &#39;origin&#39; with type arguments &#39;params&#39;.</span>
-<span class="linenos">1252</span><span class="sd">    There are two kind of these aliases: user defined and special. The special ones</span>
-<span class="linenos">1253</span><span class="sd">    are wrappers around builtin collections and ABCs in collections.abc. These must</span>
-<span class="linenos">1254</span><span class="sd">    have &#39;name&#39; always set. If &#39;inst&#39; is False, then the alias can&#39;t be instantiated;</span>
-<span class="linenos">1255</span><span class="sd">    this is used by e.g. typing.List and typing.Dict.</span>
-<span class="linenos">1256</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1257</span>
-<span class="linenos">1258</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-<span class="linenos">1259</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_inst</span> <span class="o">=</span> <span class="n">inst</span>
-<span class="linenos">1260</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="o">=</span> <span class="n">name</span>
-<span class="linenos">1261</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">=</span> <span class="n">origin</span>
-<span class="linenos">1262</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__slots__</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># This is not documented.</span>
-<span class="linenos">1263</span>
-<span class="linenos">1264</span>    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos">1265</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">_inst</span><span class="p">:</span>
-<span class="linenos">1266</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Type </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="si">}</span><span class="s2"> cannot be instantiated; &quot;</span>
-<span class="linenos">1267</span>                            <span class="sa">f</span><span class="s2">&quot;use </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">() instead&quot;</span><span class="p">)</span>
-<span class="linenos">1268</span>        <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos">1269</span>        <span class="k">try</span><span class="p">:</span>
-<span class="linenos">1270</span>            <span class="n">result</span><span class="o">.</span><span class="n">__orig_class__</span> <span class="o">=</span> <span class="bp">self</span>
-<span class="linenos">1271</span>        <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
-<span class="linenos">1272</span>            <span class="k">pass</span>
-<span class="linenos">1273</span>        <span class="k">return</span> <span class="n">result</span>
-<span class="linenos">1274</span>
-<span class="linenos">1275</span>    <span class="k">def</span> <span class="nf">__mro_entries__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bases</span><span class="p">):</span>
-<span class="linenos">1276</span>        <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos">1277</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
-<span class="linenos">1278</span>            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
-<span class="linenos">1279</span>        <span class="n">i</span> <span class="o">=</span> <span class="n">bases</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
-<span class="linenos">1280</span>        <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">:]:</span>
-<span class="linenos">1281</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">_BaseGenericAlias</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">issubclass</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">Generic</span><span class="p">):</span>
-<span class="linenos">1282</span>                <span class="k">break</span>
-<span class="linenos">1283</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1284</span>            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Generic</span><span class="p">)</span>
-<span class="linenos">1285</span>        <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
-<span class="linenos">1286</span>
-<span class="linenos">1287</span>    <span class="k">def</span> <span class="fm">__getattr__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">):</span>
-<span class="linenos">1288</span>        <span class="k">if</span> <span class="n">attr</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="s1">&#39;__qualname__&#39;</span><span class="p">}:</span>
-<span class="linenos">1289</span>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="o">.</span><span class="vm">__name__</span>
-<span class="linenos">1290</span>
-<span class="linenos">1291</span>        <span class="c1"># We are careful for copy and pickle.</span>
-<span class="linenos">1292</span>        <span class="c1"># Also for simplicity we don&#39;t relay any dunder names</span>
-<span class="linenos">1293</span>        <span class="k">if</span> <span class="s1">&#39;__origin__&#39;</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">_is_dunder</span><span class="p">(</span><span class="n">attr</span><span class="p">):</span>
-<span class="linenos">1294</span>            <span class="k">return</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">attr</span><span class="p">)</span>
-<span class="linenos">1295</span>        <span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span>
+<span class="linenos">1251</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="linenos">1252</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_inst</span> <span class="o">=</span> <span class="n">inst</span>
+<span class="linenos">1253</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="o">=</span> <span class="n">name</span>
+<span class="linenos">1254</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">=</span> <span class="n">origin</span>
+<span class="linenos">1255</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__slots__</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># This is not documented.</span>
+<span class="linenos">1256</span>
+<span class="linenos">1257</span>    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos">1258</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">_inst</span><span class="p">:</span>
+<span class="linenos">1259</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Type </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="si">}</span><span class="s2"> cannot be instantiated; &quot;</span>
+<span class="linenos">1260</span>                            <span class="sa">f</span><span class="s2">&quot;use </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">() instead&quot;</span><span class="p">)</span>
+<span class="linenos">1261</span>        <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos">1262</span>        <span class="k">try</span><span class="p">:</span>
+<span class="linenos">1263</span>            <span class="n">result</span><span class="o">.</span><span class="n">__orig_class__</span> <span class="o">=</span> <span class="bp">self</span>
+<span class="linenos">1264</span>        <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+<span class="linenos">1265</span>            <span class="k">pass</span>
+<span class="linenos">1266</span>        <span class="k">return</span> <span class="n">result</span>
+<span class="linenos">1267</span>
+<span class="linenos">1268</span>    <span class="k">def</span> <span class="nf">__mro_entries__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bases</span><span class="p">):</span>
+<span class="linenos">1269</span>        <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos">1270</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
+<span class="linenos">1271</span>            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
+<span class="linenos">1272</span>        <span class="n">i</span> <span class="o">=</span> <span class="n">bases</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+<span class="linenos">1273</span>        <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">:]:</span>
+<span class="linenos">1274</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">_BaseGenericAlias</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">issubclass</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">Generic</span><span class="p">):</span>
+<span class="linenos">1275</span>                <span class="k">break</span>
+<span class="linenos">1276</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1277</span>            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Generic</span><span class="p">)</span>
+<span class="linenos">1278</span>        <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
+<span class="linenos">1279</span>
+<span class="linenos">1280</span>    <span class="k">def</span> <span class="fm">__getattr__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">):</span>
+<span class="linenos">1281</span>        <span class="k">if</span> <span class="n">attr</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="s1">&#39;__qualname__&#39;</span><span class="p">}:</span>
+<span class="linenos">1282</span>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="o">.</span><span class="vm">__name__</span>
+<span class="linenos">1283</span>
+<span class="linenos">1284</span>        <span class="c1"># We are careful for copy and pickle.</span>
+<span class="linenos">1285</span>        <span class="c1"># Also for simplicity we don&#39;t relay any dunder names</span>
+<span class="linenos">1286</span>        <span class="k">if</span> <span class="s1">&#39;__origin__&#39;</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">_is_dunder</span><span class="p">(</span><span class="n">attr</span><span class="p">):</span>
+<span class="linenos">1287</span>            <span class="k">return</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">attr</span><span class="p">)</span>
+<span class="linenos">1288</span>        <span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span>
+<span class="linenos">1289</span>
+<span class="linenos">1290</span>    <span class="k">def</span> <span class="fm">__setattr__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">,</span> <span class="n">val</span><span class="p">):</span>
+<span class="linenos">1291</span>        <span class="k">if</span> <span class="n">_is_dunder</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span> <span class="ow">or</span> <span class="n">attr</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;_name&#39;</span><span class="p">,</span> <span class="s1">&#39;_inst&#39;</span><span class="p">,</span> <span class="s1">&#39;_nparams&#39;</span><span class="p">,</span>
+<span class="linenos">1292</span>                                        <span class="s1">&#39;_paramspec_tvars&#39;</span><span class="p">}:</span>
+<span class="linenos">1293</span>            <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">(</span><span class="n">attr</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<span class="linenos">1294</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1295</span>            <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">attr</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
 <span class="linenos">1296</span>
-<span class="linenos">1297</span>    <span class="k">def</span> <span class="fm">__setattr__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">,</span> <span class="n">val</span><span class="p">):</span>
-<span class="linenos">1298</span>        <span class="k">if</span> <span class="n">_is_dunder</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span> <span class="ow">or</span> <span class="n">attr</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;_name&#39;</span><span class="p">,</span> <span class="s1">&#39;_inst&#39;</span><span class="p">,</span> <span class="s1">&#39;_nparams&#39;</span><span class="p">,</span>
-<span class="linenos">1299</span>                                        <span class="s1">&#39;_paramspec_tvars&#39;</span><span class="p">}:</span>
-<span class="linenos">1300</span>            <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">(</span><span class="n">attr</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
-<span class="linenos">1301</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1302</span>            <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">attr</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<span class="linenos">1297</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">):</span>
+<span class="linenos">1298</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__subclasscheck__</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">obj</span><span class="p">))</span>
+<span class="linenos">1299</span>
+<span class="linenos">1300</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="bp">cls</span><span class="p">):</span>
+<span class="linenos">1301</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Subscripted generics cannot be used with&quot;</span>
+<span class="linenos">1302</span>                        <span class="s2">&quot; class and instance checks&quot;</span><span class="p">)</span>
 <span class="linenos">1303</span>
-<span class="linenos">1304</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">):</span>
-<span class="linenos">1305</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__subclasscheck__</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">obj</span><span class="p">))</span>
-<span class="linenos">1306</span>
-<span class="linenos">1307</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="bp">cls</span><span class="p">):</span>
-<span class="linenos">1308</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Subscripted generics cannot be used with&quot;</span>
-<span class="linenos">1309</span>                        <span class="s2">&quot; class and instance checks&quot;</span><span class="p">)</span>
-<span class="linenos">1310</span>
-<span class="linenos">1311</span>    <span class="k">def</span> <span class="fm">__dir__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1312</span>        <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__dir__</span><span class="p">()</span>
-<span class="linenos">1313</span>                <span class="o">+</span> <span class="p">[</span><span class="n">attr</span> <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="nb">dir</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">_is_dunder</span><span class="p">(</span><span class="n">attr</span><span class="p">)]))</span>
-<span class="linenos">1314</span>
-<span class="linenos">1315</span>
-<span class="linenos">1316</span><span class="c1"># Special typing constructs Union, Optional, Generic, Callable and Tuple</span>
-<span class="linenos">1317</span><span class="c1"># use three special attributes for internal bookkeeping of generic types:</span>
-<span class="linenos">1318</span><span class="c1"># * __parameters__ is a tuple of unique free type parameters of a generic</span>
-<span class="linenos">1319</span><span class="c1">#   type, for example, Dict[T, T].__parameters__ == (T,);</span>
-<span class="linenos">1320</span><span class="c1"># * __origin__ keeps a reference to a type that was subscripted,</span>
-<span class="linenos">1321</span><span class="c1">#   e.g., Union[T, int].__origin__ == Union, or the non-generic version of</span>
-<span class="linenos">1322</span><span class="c1">#   the type.</span>
-<span class="linenos">1323</span><span class="c1"># * __args__ is a tuple of all arguments used in subscripting,</span>
-<span class="linenos">1324</span><span class="c1">#   e.g., Dict[T, int].__args__ == (T, int).</span>
-<span class="linenos">1325</span>
-<span class="linenos">1326</span>
-<span class="linenos">1327</span><span class="k">class</span> <span class="nc">_GenericAlias</span><span class="p">(</span><span class="n">_BaseGenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1328</span>    <span class="c1"># The type of parameterized generics.</span>
-<span class="linenos">1329</span>    <span class="c1">#</span>
-<span class="linenos">1330</span>    <span class="c1"># That is, for example, `type(List[int])` is `_GenericAlias`.</span>
-<span class="linenos">1331</span>    <span class="c1">#</span>
-<span class="linenos">1332</span>    <span class="c1"># Objects which are instances of this class include:</span>
-<span class="linenos">1333</span>    <span class="c1"># * Parameterized container types, e.g. `Tuple[int]`, `List[int]`.</span>
-<span class="linenos">1334</span>    <span class="c1">#  * Note that native container types, e.g. `tuple`, `list`, use</span>
-<span class="linenos">1335</span>    <span class="c1">#    `types.GenericAlias` instead.</span>
-<span class="linenos">1336</span>    <span class="c1"># * Parameterized classes:</span>
-<span class="linenos">1337</span>    <span class="c1">#     T = TypeVar(&#39;T&#39;)</span>
-<span class="linenos">1338</span>    <span class="c1">#     class C(Generic[T]): pass</span>
-<span class="linenos">1339</span>    <span class="c1">#     # C[int] is a _GenericAlias</span>
-<span class="linenos">1340</span>    <span class="c1"># * `Callable` aliases, generic `Callable` aliases, and</span>
-<span class="linenos">1341</span>    <span class="c1">#   parameterized `Callable` aliases:</span>
-<span class="linenos">1342</span>    <span class="c1">#     T = TypeVar(&#39;T&#39;)</span>
-<span class="linenos">1343</span>    <span class="c1">#     # _CallableGenericAlias inherits from _GenericAlias.</span>
-<span class="linenos">1344</span>    <span class="c1">#     A = Callable[[], None]  # _CallableGenericAlias</span>
-<span class="linenos">1345</span>    <span class="c1">#     B = Callable[[T], None]  # _CallableGenericAlias</span>
-<span class="linenos">1346</span>    <span class="c1">#     C = B[int]  # _CallableGenericAlias</span>
-<span class="linenos">1347</span>    <span class="c1"># * Parameterized `Final`, `ClassVar` and `TypeGuard`:</span>
-<span class="linenos">1348</span>    <span class="c1">#     # All _GenericAlias</span>
-<span class="linenos">1349</span>    <span class="c1">#     Final[int]</span>
-<span class="linenos">1350</span>    <span class="c1">#     ClassVar[float]</span>
-<span class="linenos">1351</span>    <span class="c1">#     TypeVar[bool]</span>
-<span class="linenos">1352</span>
-<span class="linenos">1353</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
-<span class="linenos">1354</span>                 <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
-<span class="linenos">1355</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="n">inst</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="n">name</span><span class="p">)</span>
-<span class="linenos">1356</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos">1357</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,)</span>
-<span class="linenos">1358</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="o">...</span> <span class="k">if</span> <span class="n">a</span> <span class="ow">is</span> <span class="n">_TypingEllipsis</span> <span class="k">else</span>
-<span class="linenos">1359</span>                              <span class="n">a</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">args</span><span class="p">)</span>
-<span class="linenos">1360</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__parameters__</span> <span class="o">=</span> <span class="n">_collect_parameters</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
-<span class="linenos">1361</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_paramspec_tvars</span> <span class="o">=</span> <span class="n">_paramspec_tvars</span>
-<span class="linenos">1362</span>        <span class="k">if</span> <span class="ow">not</span> <span class="n">name</span><span class="p">:</span>
-<span class="linenos">1363</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">origin</span><span class="o">.</span><span class="vm">__module__</span>
-<span class="linenos">1364</span>
-<span class="linenos">1365</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos">1366</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">):</span>
-<span class="linenos">1367</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">1368</span>        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__origin__</span>
-<span class="linenos">1369</span>                <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
-<span class="linenos">1370</span>
-<span class="linenos">1371</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1372</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">))</span>
-<span class="linenos">1373</span>
-<span class="linenos">1374</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
-<span class="linenos">1375</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">]</span>
-<span class="linenos">1376</span>
-<span class="linenos">1377</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">left</span><span class="p">):</span>
-<span class="linenos">1378</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
-<span class="linenos">1379</span>
-<span class="linenos">1380</span>    <span class="nd">@_tp_cache</span>
-<span class="linenos">1381</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
-<span class="linenos">1382</span>        <span class="c1"># Parameterizes an already-parameterized object.</span>
-<span class="linenos">1383</span>        <span class="c1">#</span>
-<span class="linenos">1384</span>        <span class="c1"># For example, we arrive here doing something like:</span>
-<span class="linenos">1385</span>        <span class="c1">#   T1 = TypeVar(&#39;T1&#39;)</span>
-<span class="linenos">1386</span>        <span class="c1">#   T2 = TypeVar(&#39;T2&#39;)</span>
-<span class="linenos">1387</span>        <span class="c1">#   T3 = TypeVar(&#39;T3&#39;)</span>
-<span class="linenos">1388</span>        <span class="c1">#   class A(Generic[T1]): pass</span>
-<span class="linenos">1389</span>        <span class="c1">#   B = A[T2]  # B is a _GenericAlias</span>
-<span class="linenos">1390</span>        <span class="c1">#   C = B[T3]  # Invokes _GenericAlias.__getitem__</span>
-<span class="linenos">1391</span>        <span class="c1">#</span>
-<span class="linenos">1392</span>        <span class="c1"># We also arrive here when parameterizing a generic `Callable` alias:</span>
-<span class="linenos">1393</span>        <span class="c1">#   T = TypeVar(&#39;T&#39;)</span>
-<span class="linenos">1394</span>        <span class="c1">#   C = Callable[[T], None]</span>
-<span class="linenos">1395</span>        <span class="c1">#   C[int]  # Invokes _GenericAlias.__getitem__</span>
-<span class="linenos">1396</span>
-<span class="linenos">1397</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">in</span> <span class="p">(</span><span class="n">Generic</span><span class="p">,</span> <span class="n">Protocol</span><span class="p">):</span>
-<span class="linenos">1398</span>            <span class="c1"># Can&#39;t subscript Generic[...] or Protocol[...].</span>
-<span class="linenos">1399</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Cannot subscript already-subscripted </span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos">1400</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">__parameters__</span><span class="p">:</span>
-<span class="linenos">1401</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not a generic class&quot;</span><span class="p">)</span>
-<span class="linenos">1402</span>
-<span class="linenos">1403</span>        <span class="c1"># Preprocess `args`.</span>
-<span class="linenos">1404</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos">1405</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,)</span>
-<span class="linenos">1406</span>        <span class="n">args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_convert</span><span class="p">(</span><span class="n">p</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">args</span><span class="p">)</span>
-<span class="linenos">1407</span>        <span class="n">args</span> <span class="o">=</span> <span class="n">_unpack_args</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
-<span class="linenos">1408</span>        <span class="n">new_args</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_determine_new_args</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
-<span class="linenos">1409</span>        <span class="n">r</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">new_args</span><span class="p">)</span>
-<span class="linenos">1410</span>        <span class="k">return</span> <span class="n">r</span>
-<span class="linenos">1411</span>
-<span class="linenos">1412</span>    <span class="k">def</span> <span class="nf">_determine_new_args</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
-<span class="linenos">1413</span>        <span class="c1"># Determines new __args__ for __getitem__.</span>
-<span class="linenos">1414</span>        <span class="c1">#</span>
-<span class="linenos">1415</span>        <span class="c1"># For example, suppose we had:</span>
-<span class="linenos">1416</span>        <span class="c1">#   T1 = TypeVar(&#39;T1&#39;)</span>
-<span class="linenos">1417</span>        <span class="c1">#   T2 = TypeVar(&#39;T2&#39;)</span>
-<span class="linenos">1418</span>        <span class="c1">#   class A(Generic[T1, T2]): pass</span>
-<span class="linenos">1419</span>        <span class="c1">#   T3 = TypeVar(&#39;T3&#39;)</span>
-<span class="linenos">1420</span>        <span class="c1">#   B = A[int, T3]</span>
-<span class="linenos">1421</span>        <span class="c1">#   C = B[str]</span>
-<span class="linenos">1422</span>        <span class="c1"># `B.__args__` is `(int, T3)`, so `C.__args__` should be `(int, str)`.</span>
-<span class="linenos">1423</span>        <span class="c1"># Unfortunately, this is harder than it looks, because if `T3` is</span>
-<span class="linenos">1424</span>        <span class="c1"># anything more exotic than a plain `TypeVar`, we need to consider</span>
-<span class="linenos">1425</span>        <span class="c1"># edge cases.</span>
-<span class="linenos">1426</span>
-<span class="linenos">1427</span>        <span class="n">params</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__parameters__</span>
-<span class="linenos">1428</span>        <span class="c1"># In the example above, this would be {T3: str}</span>
-<span class="linenos">1429</span>        <span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="n">params</span><span class="p">:</span>
-<span class="linenos">1430</span>            <span class="n">prepare</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="s1">&#39;__typing_prepare_subst__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
-<span class="linenos">1431</span>            <span class="k">if</span> <span class="n">prepare</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">1432</span>                <span class="n">args</span> <span class="o">=</span> <span class="n">prepare</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span>
-<span class="linenos">1433</span>        <span class="n">alen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
-<span class="linenos">1434</span>        <span class="n">plen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
-<span class="linenos">1435</span>        <span class="k">if</span> <span class="n">alen</span> <span class="o">!=</span> <span class="n">plen</span><span class="p">:</span>
-<span class="linenos">1436</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Too </span><span class="si">{</span><span class="s1">&#39;many&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">alen</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">plen</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;few&#39;</span><span class="si">}</span><span class="s2"> arguments for </span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2">;&quot;</span>
-<span class="linenos">1437</span>                            <span class="sa">f</span><span class="s2">&quot; actual </span><span class="si">{</span><span class="n">alen</span><span class="si">}</span><span class="s2">, expected </span><span class="si">{</span><span class="n">plen</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos">1438</span>        <span class="n">new_arg_by_param</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">args</span><span class="p">))</span>
-<span class="linenos">1439</span>        <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_make_substitution</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">,</span> <span class="n">new_arg_by_param</span><span class="p">))</span>
-<span class="linenos">1440</span>
-<span class="linenos">1441</span>    <span class="k">def</span> <span class="nf">_make_substitution</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">new_arg_by_param</span><span class="p">):</span>
-<span class="linenos">1442</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Create a list of new type arguments.&quot;&quot;&quot;</span>
-<span class="linenos">1443</span>        <span class="n">new_args</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos">1444</span>        <span class="k">for</span> <span class="n">old_arg</span> <span class="ow">in</span> <span class="n">args</span><span class="p">:</span>
-<span class="linenos">1445</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
-<span class="linenos">1446</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">old_arg</span><span class="p">)</span>
-<span class="linenos">1447</span>                <span class="k">continue</span>
-<span class="linenos">1448</span>
-<span class="linenos">1449</span>            <span class="n">substfunc</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="s1">&#39;__typing_subst__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
-<span class="linenos">1450</span>            <span class="k">if</span> <span class="n">substfunc</span><span class="p">:</span>
-<span class="linenos">1451</span>                <span class="n">new_arg</span> <span class="o">=</span> <span class="n">substfunc</span><span class="p">(</span><span class="n">new_arg_by_param</span><span class="p">[</span><span class="n">old_arg</span><span class="p">])</span>
-<span class="linenos">1452</span>            <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1453</span>                <span class="n">subparams</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="s1">&#39;__parameters__&#39;</span><span class="p">,</span> <span class="p">())</span>
-<span class="linenos">1454</span>                <span class="k">if</span> <span class="ow">not</span> <span class="n">subparams</span><span class="p">:</span>
-<span class="linenos">1455</span>                    <span class="n">new_arg</span> <span class="o">=</span> <span class="n">old_arg</span>
-<span class="linenos">1456</span>                <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1457</span>                    <span class="n">subargs</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos">1458</span>                    <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">subparams</span><span class="p">:</span>
-<span class="linenos">1459</span>                        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">TypeVarTuple</span><span class="p">):</span>
-<span class="linenos">1460</span>                            <span class="n">subargs</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">new_arg_by_param</span><span class="p">[</span><span class="n">x</span><span class="p">])</span>
-<span class="linenos">1461</span>                        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1462</span>                            <span class="n">subargs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_arg_by_param</span><span class="p">[</span><span class="n">x</span><span class="p">])</span>
-<span class="linenos">1463</span>                    <span class="n">new_arg</span> <span class="o">=</span> <span class="n">old_arg</span><span class="p">[</span><span class="nb">tuple</span><span class="p">(</span><span class="n">subargs</span><span class="p">)]</span>
-<span class="linenos">1464</span>
-<span class="linenos">1465</span>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Callable</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">new_arg</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos">1466</span>                <span class="c1"># Consider the following `Callable`.</span>
-<span class="linenos">1467</span>                <span class="c1">#   C = Callable[[int], str]</span>
-<span class="linenos">1468</span>                <span class="c1"># Here, `C.__args__` should be (int, str) - NOT ([int], str).</span>
-<span class="linenos">1469</span>                <span class="c1"># That means that if we had something like...</span>
-<span class="linenos">1470</span>                <span class="c1">#   P = ParamSpec(&#39;P&#39;)</span>
-<span class="linenos">1471</span>                <span class="c1">#   T = TypeVar(&#39;T&#39;)</span>
-<span class="linenos">1472</span>                <span class="c1">#   C = Callable[P, T]</span>
-<span class="linenos">1473</span>                <span class="c1">#   D = C[[int, str], float]</span>
-<span class="linenos">1474</span>                <span class="c1"># ...we need to be careful; `new_args` should end up as</span>
-<span class="linenos">1475</span>                <span class="c1"># `(int, str, float)` rather than `([int, str], float)`.</span>
-<span class="linenos">1476</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
-<span class="linenos">1477</span>            <span class="k">elif</span> <span class="n">_is_unpacked_typevartuple</span><span class="p">(</span><span class="n">old_arg</span><span class="p">):</span>
-<span class="linenos">1478</span>                <span class="c1"># Consider the following `_GenericAlias`, `B`:</span>
-<span class="linenos">1479</span>                <span class="c1">#   class A(Generic[*Ts]): ...</span>
-<span class="linenos">1480</span>                <span class="c1">#   B = A[T, *Ts]</span>
-<span class="linenos">1481</span>                <span class="c1"># If we then do:</span>
-<span class="linenos">1482</span>                <span class="c1">#   B[float, int, str]</span>
-<span class="linenos">1483</span>                <span class="c1"># The `new_arg` corresponding to `T` will be `float`, and the</span>
-<span class="linenos">1484</span>                <span class="c1"># `new_arg` corresponding to `*Ts` will be `(int, str)`. We</span>
-<span class="linenos">1485</span>                <span class="c1"># should join all these types together in a flat list</span>
-<span class="linenos">1486</span>                <span class="c1"># `(float, int, str)` - so again, we should `extend`.</span>
-<span class="linenos">1487</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
-<span class="linenos">1488</span>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos">1489</span>                <span class="c1"># Corner case:</span>
-<span class="linenos">1490</span>                <span class="c1">#    P = ParamSpec(&#39;P&#39;)</span>
-<span class="linenos">1491</span>                <span class="c1">#    T = TypeVar(&#39;T&#39;)</span>
-<span class="linenos">1492</span>                <span class="c1">#    class Base(Generic[P]): ...</span>
-<span class="linenos">1493</span>                <span class="c1"># Can be substituted like this:</span>
-<span class="linenos">1494</span>                <span class="c1">#    X = Base[[int, T]]</span>
-<span class="linenos">1495</span>                <span class="c1"># In this case, `old_arg` will be a tuple:</span>
-<span class="linenos">1496</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
-<span class="linenos">1497</span>                    <span class="nb">tuple</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_make_substitution</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="n">new_arg_by_param</span><span class="p">)),</span>
-<span class="linenos">1498</span>                <span class="p">)</span>
-<span class="linenos">1499</span>            <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1500</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
-<span class="linenos">1501</span>        <span class="k">return</span> <span class="n">new_args</span>
-<span class="linenos">1502</span>
-<span class="linenos">1503</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
-<span class="linenos">1504</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_inst</span><span class="p">,</span>
-<span class="linenos">1505</span>                              <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_paramspec_tvars</span><span class="p">)</span>
-<span class="linenos">1506</span>
-<span class="linenos">1507</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1508</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">:</span>
-<span class="linenos">1509</span>            <span class="n">name</span> <span class="o">=</span> <span class="s1">&#39;typing.&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
-<span class="linenos">1510</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1511</span>            <span class="n">name</span> <span class="o">=</span> <span class="n">_type_repr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
-<span class="linenos">1512</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
-<span class="linenos">1513</span>            <span class="n">args</span> <span class="o">=</span> <span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">])</span>
-<span class="linenos">1514</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1515</span>            <span class="c1"># To ensure the repr is eval-able.</span>
-<span class="linenos">1516</span>            <span class="n">args</span> <span class="o">=</span> <span class="s2">&quot;()&quot;</span>
-<span class="linenos">1517</span>        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s1">[</span><span class="si">{</span><span class="n">args</span><span class="si">}</span><span class="s1">]&#39;</span>
-<span class="linenos">1518</span>
-<span class="linenos">1519</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1520</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">:</span>
-<span class="linenos">1521</span>            <span class="n">origin</span> <span class="o">=</span> <span class="nb">globals</span><span class="p">()[</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">]</span>
-<span class="linenos">1522</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1523</span>            <span class="n">origin</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span>
-<span class="linenos">1524</span>        <span class="n">args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
-<span class="linenos">1525</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">and</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos">1526</span>            <span class="n">args</span><span class="p">,</span> <span class="o">=</span> <span class="n">args</span>
-<span class="linenos">1527</span>        <span class="k">return</span> <span class="n">operator</span><span class="o">.</span><span class="n">getitem</span><span class="p">,</span> <span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span>
-<span class="linenos">1528</span>
-<span class="linenos">1529</span>    <span class="k">def</span> <span class="nf">__mro_entries__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bases</span><span class="p">):</span>
-<span class="linenos">1530</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">_SpecialForm</span><span class="p">):</span>
-<span class="linenos">1531</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Cannot subclass </span><span class="si">{</span><span class="bp">self</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos">1532</span>
-<span class="linenos">1533</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">:</span>  <span class="c1"># generic version of an ABC or built-in class</span>
-<span class="linenos">1534</span>            <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">__mro_entries__</span><span class="p">(</span><span class="n">bases</span><span class="p">)</span>
-<span class="linenos">1535</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Generic</span><span class="p">:</span>
-<span class="linenos">1536</span>            <span class="k">if</span> <span class="n">Protocol</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
-<span class="linenos">1537</span>                <span class="k">return</span> <span class="p">()</span>
-<span class="linenos">1538</span>            <span class="n">i</span> <span class="o">=</span> <span class="n">bases</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
-<span class="linenos">1539</span>            <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">:]:</span>
-<span class="linenos">1540</span>                <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">_BaseGenericAlias</span><span class="p">)</span> <span class="ow">and</span> <span class="n">b</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">self</span><span class="p">:</span>
-<span class="linenos">1541</span>                    <span class="k">return</span> <span class="p">()</span>
-<span class="linenos">1542</span>        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,)</span>
-<span class="linenos">1543</span>
-<span class="linenos">1544</span>    <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1545</span>        <span class="k">yield</span> <span class="n">Unpack</span><span class="p">[</span><span class="bp">self</span><span class="p">]</span>
-<span class="linenos">1546</span>
-<span class="linenos">1547</span>
-<span class="linenos">1548</span><span class="c1"># _nparams is the number of accepted parameters, e.g. 0 for Hashable,</span>
-<span class="linenos">1549</span><span class="c1"># 1 for List and 2 for Dict.  It may be -1 if variable number of</span>
-<span class="linenos">1550</span><span class="c1"># parameters are accepted (needs custom __getitem__).</span>
-<span class="linenos">1551</span>
-<span class="linenos">1552</span><span class="k">class</span> <span class="nc">_SpecialGenericAlias</span><span class="p">(</span><span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_BaseGenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1553</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">,</span> <span class="n">nparams</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
-<span class="linenos">1554</span>        <span class="k">if</span> <span class="n">name</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">1555</span>            <span class="n">name</span> <span class="o">=</span> <span class="n">origin</span><span class="o">.</span><span class="vm">__name__</span>
-<span class="linenos">1556</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="n">inst</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="n">name</span><span class="p">)</span>
-<span class="linenos">1557</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_nparams</span> <span class="o">=</span> <span class="n">nparams</span>
-<span class="linenos">1558</span>        <span class="k">if</span> <span class="n">origin</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">==</span> <span class="s1">&#39;builtins&#39;</span><span class="p">:</span>
-<span class="linenos">1559</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;A generic version of </span><span class="si">{</span><span class="n">origin</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">.&#39;</span>
-<span class="linenos">1560</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1561</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;A generic version of </span><span class="si">{</span><span class="n">origin</span><span class="o">.</span><span class="vm">__module__</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="n">origin</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">.&#39;</span>
-<span class="linenos">1562</span>
-<span class="linenos">1563</span>    <span class="nd">@_tp_cache</span>
-<span class="linenos">1564</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1565</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos">1566</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="n">params</span><span class="p">,)</span>
-<span class="linenos">1567</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Parameters to generic types must be types.&quot;</span>
-<span class="linenos">1568</span>        <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">)</span>
-<span class="linenos">1569</span>        <span class="n">_check_generic</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nparams</span><span class="p">)</span>
-<span class="linenos">1570</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos">1304</span>    <span class="k">def</span> <span class="fm">__dir__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1305</span>        <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__dir__</span><span class="p">()</span>
+<span class="linenos">1306</span>                <span class="o">+</span> <span class="p">[</span><span class="n">attr</span> <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="nb">dir</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span> <span class="k">if</span> <span class="ow">not</span> <span class="n">_is_dunder</span><span class="p">(</span><span class="n">attr</span><span class="p">)]))</span>
+<span class="linenos">1307</span>
+<span class="linenos">1308</span>
+<span class="linenos">1309</span><span class="c1"># Special typing constructs Union, Optional, Generic, Callable and Tuple</span>
+<span class="linenos">1310</span><span class="c1"># use three special attributes for internal bookkeeping of generic types:</span>
+<span class="linenos">1311</span><span class="c1"># * __parameters__ is a tuple of unique free type parameters of a generic</span>
+<span class="linenos">1312</span><span class="c1">#   type, for example, Dict[T, T].__parameters__ == (T,);</span>
+<span class="linenos">1313</span><span class="c1"># * __origin__ keeps a reference to a type that was subscripted,</span>
+<span class="linenos">1314</span><span class="c1">#   e.g., Union[T, int].__origin__ == Union, or the non-generic version of</span>
+<span class="linenos">1315</span><span class="c1">#   the type.</span>
+<span class="linenos">1316</span><span class="c1"># * __args__ is a tuple of all arguments used in subscripting,</span>
+<span class="linenos">1317</span><span class="c1">#   e.g., Dict[T, int].__args__ == (T, int).</span>
+<span class="linenos">1318</span>
+<span class="linenos">1319</span>
+<span class="linenos">1320</span><span class="k">class</span> <span class="nc">_GenericAlias</span><span class="p">(</span><span class="n">_BaseGenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1321</span>    <span class="c1"># The type of parameterized generics.</span>
+<span class="linenos">1322</span>    <span class="c1">#</span>
+<span class="linenos">1323</span>    <span class="c1"># That is, for example, `type(List[int])` is `_GenericAlias`.</span>
+<span class="linenos">1324</span>    <span class="c1">#</span>
+<span class="linenos">1325</span>    <span class="c1"># Objects which are instances of this class include:</span>
+<span class="linenos">1326</span>    <span class="c1"># * Parameterized container types, e.g. `Tuple[int]`, `List[int]`.</span>
+<span class="linenos">1327</span>    <span class="c1">#  * Note that native container types, e.g. `tuple`, `list`, use</span>
+<span class="linenos">1328</span>    <span class="c1">#    `types.GenericAlias` instead.</span>
+<span class="linenos">1329</span>    <span class="c1"># * Parameterized classes:</span>
+<span class="linenos">1330</span>    <span class="c1">#     T = TypeVar(&#39;T&#39;)</span>
+<span class="linenos">1331</span>    <span class="c1">#     class C(Generic[T]): pass</span>
+<span class="linenos">1332</span>    <span class="c1">#     # C[int] is a _GenericAlias</span>
+<span class="linenos">1333</span>    <span class="c1"># * `Callable` aliases, generic `Callable` aliases, and</span>
+<span class="linenos">1334</span>    <span class="c1">#   parameterized `Callable` aliases:</span>
+<span class="linenos">1335</span>    <span class="c1">#     T = TypeVar(&#39;T&#39;)</span>
+<span class="linenos">1336</span>    <span class="c1">#     # _CallableGenericAlias inherits from _GenericAlias.</span>
+<span class="linenos">1337</span>    <span class="c1">#     A = Callable[[], None]  # _CallableGenericAlias</span>
+<span class="linenos">1338</span>    <span class="c1">#     B = Callable[[T], None]  # _CallableGenericAlias</span>
+<span class="linenos">1339</span>    <span class="c1">#     C = B[int]  # _CallableGenericAlias</span>
+<span class="linenos">1340</span>    <span class="c1"># * Parameterized `Final`, `ClassVar` and `TypeGuard`:</span>
+<span class="linenos">1341</span>    <span class="c1">#     # All _GenericAlias</span>
+<span class="linenos">1342</span>    <span class="c1">#     Final[int]</span>
+<span class="linenos">1343</span>    <span class="c1">#     ClassVar[float]</span>
+<span class="linenos">1344</span>    <span class="c1">#     TypeVar[bool]</span>
+<span class="linenos">1345</span>
+<span class="linenos">1346</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+<span class="linenos">1347</span>                 <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="linenos">1348</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="n">inst</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="n">name</span><span class="p">)</span>
+<span class="linenos">1349</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos">1350</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,)</span>
+<span class="linenos">1351</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="o">...</span> <span class="k">if</span> <span class="n">a</span> <span class="ow">is</span> <span class="n">_TypingEllipsis</span> <span class="k">else</span>
+<span class="linenos">1352</span>                              <span class="n">a</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">args</span><span class="p">)</span>
+<span class="linenos">1353</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__parameters__</span> <span class="o">=</span> <span class="n">_collect_parameters</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
+<span class="linenos">1354</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_paramspec_tvars</span> <span class="o">=</span> <span class="n">_paramspec_tvars</span>
+<span class="linenos">1355</span>        <span class="k">if</span> <span class="ow">not</span> <span class="n">name</span><span class="p">:</span>
+<span class="linenos">1356</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">origin</span><span class="o">.</span><span class="vm">__module__</span>
+<span class="linenos">1357</span>
+<span class="linenos">1358</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos">1359</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">):</span>
+<span class="linenos">1360</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">1361</span>        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__origin__</span>
+<span class="linenos">1362</span>                <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
+<span class="linenos">1363</span>
+<span class="linenos">1364</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1365</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">))</span>
+<span class="linenos">1366</span>
+<span class="linenos">1367</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
+<span class="linenos">1368</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">]</span>
+<span class="linenos">1369</span>
+<span class="linenos">1370</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">left</span><span class="p">):</span>
+<span class="linenos">1371</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
+<span class="linenos">1372</span>
+<span class="linenos">1373</span>    <span class="nd">@_tp_cache</span>
+<span class="linenos">1374</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
+<span class="linenos">1375</span>        <span class="c1"># Parameterizes an already-parameterized object.</span>
+<span class="linenos">1376</span>        <span class="c1">#</span>
+<span class="linenos">1377</span>        <span class="c1"># For example, we arrive here doing something like:</span>
+<span class="linenos">1378</span>        <span class="c1">#   T1 = TypeVar(&#39;T1&#39;)</span>
+<span class="linenos">1379</span>        <span class="c1">#   T2 = TypeVar(&#39;T2&#39;)</span>
+<span class="linenos">1380</span>        <span class="c1">#   T3 = TypeVar(&#39;T3&#39;)</span>
+<span class="linenos">1381</span>        <span class="c1">#   class A(Generic[T1]): pass</span>
+<span class="linenos">1382</span>        <span class="c1">#   B = A[T2]  # B is a _GenericAlias</span>
+<span class="linenos">1383</span>        <span class="c1">#   C = B[T3]  # Invokes _GenericAlias.__getitem__</span>
+<span class="linenos">1384</span>        <span class="c1">#</span>
+<span class="linenos">1385</span>        <span class="c1"># We also arrive here when parameterizing a generic `Callable` alias:</span>
+<span class="linenos">1386</span>        <span class="c1">#   T = TypeVar(&#39;T&#39;)</span>
+<span class="linenos">1387</span>        <span class="c1">#   C = Callable[[T], None]</span>
+<span class="linenos">1388</span>        <span class="c1">#   C[int]  # Invokes _GenericAlias.__getitem__</span>
+<span class="linenos">1389</span>
+<span class="linenos">1390</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">in</span> <span class="p">(</span><span class="n">Generic</span><span class="p">,</span> <span class="n">Protocol</span><span class="p">):</span>
+<span class="linenos">1391</span>            <span class="c1"># Can&#39;t subscript Generic[...] or Protocol[...].</span>
+<span class="linenos">1392</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Cannot subscript already-subscripted </span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos">1393</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">__parameters__</span><span class="p">:</span>
+<span class="linenos">1394</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2"> is not a generic class&quot;</span><span class="p">)</span>
+<span class="linenos">1395</span>
+<span class="linenos">1396</span>        <span class="c1"># Preprocess `args`.</span>
+<span class="linenos">1397</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos">1398</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,)</span>
+<span class="linenos">1399</span>        <span class="n">args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_convert</span><span class="p">(</span><span class="n">p</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">args</span><span class="p">)</span>
+<span class="linenos">1400</span>        <span class="n">args</span> <span class="o">=</span> <span class="n">_unpack_args</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
+<span class="linenos">1401</span>        <span class="n">new_args</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_determine_new_args</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
+<span class="linenos">1402</span>        <span class="n">r</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">new_args</span><span class="p">)</span>
+<span class="linenos">1403</span>        <span class="k">return</span> <span class="n">r</span>
+<span class="linenos">1404</span>
+<span class="linenos">1405</span>    <span class="k">def</span> <span class="nf">_determine_new_args</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
+<span class="linenos">1406</span>        <span class="c1"># Determines new __args__ for __getitem__.</span>
+<span class="linenos">1407</span>        <span class="c1">#</span>
+<span class="linenos">1408</span>        <span class="c1"># For example, suppose we had:</span>
+<span class="linenos">1409</span>        <span class="c1">#   T1 = TypeVar(&#39;T1&#39;)</span>
+<span class="linenos">1410</span>        <span class="c1">#   T2 = TypeVar(&#39;T2&#39;)</span>
+<span class="linenos">1411</span>        <span class="c1">#   class A(Generic[T1, T2]): pass</span>
+<span class="linenos">1412</span>        <span class="c1">#   T3 = TypeVar(&#39;T3&#39;)</span>
+<span class="linenos">1413</span>        <span class="c1">#   B = A[int, T3]</span>
+<span class="linenos">1414</span>        <span class="c1">#   C = B[str]</span>
+<span class="linenos">1415</span>        <span class="c1"># `B.__args__` is `(int, T3)`, so `C.__args__` should be `(int, str)`.</span>
+<span class="linenos">1416</span>        <span class="c1"># Unfortunately, this is harder than it looks, because if `T3` is</span>
+<span class="linenos">1417</span>        <span class="c1"># anything more exotic than a plain `TypeVar`, we need to consider</span>
+<span class="linenos">1418</span>        <span class="c1"># edge cases.</span>
+<span class="linenos">1419</span>
+<span class="linenos">1420</span>        <span class="n">params</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__parameters__</span>
+<span class="linenos">1421</span>        <span class="c1"># In the example above, this would be {T3: str}</span>
+<span class="linenos">1422</span>        <span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="n">params</span><span class="p">:</span>
+<span class="linenos">1423</span>            <span class="n">prepare</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="s1">&#39;__typing_prepare_subst__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
+<span class="linenos">1424</span>            <span class="k">if</span> <span class="n">prepare</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">1425</span>                <span class="n">args</span> <span class="o">=</span> <span class="n">prepare</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span>
+<span class="linenos">1426</span>        <span class="n">alen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
+<span class="linenos">1427</span>        <span class="n">plen</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos">1428</span>        <span class="k">if</span> <span class="n">alen</span> <span class="o">!=</span> <span class="n">plen</span><span class="p">:</span>
+<span class="linenos">1429</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Too </span><span class="si">{</span><span class="s1">&#39;many&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">alen</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">plen</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;few&#39;</span><span class="si">}</span><span class="s2"> arguments for </span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s2">;&quot;</span>
+<span class="linenos">1430</span>                            <span class="sa">f</span><span class="s2">&quot; actual </span><span class="si">{</span><span class="n">alen</span><span class="si">}</span><span class="s2">, expected </span><span class="si">{</span><span class="n">plen</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos">1431</span>        <span class="n">new_arg_by_param</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">args</span><span class="p">))</span>
+<span class="linenos">1432</span>        <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_make_substitution</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">,</span> <span class="n">new_arg_by_param</span><span class="p">))</span>
+<span class="linenos">1433</span>
+<span class="linenos">1434</span>    <span class="k">def</span> <span class="nf">_make_substitution</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">new_arg_by_param</span><span class="p">):</span>
+<span class="linenos">1435</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Create a list of new type arguments.&quot;&quot;&quot;</span>
+<span class="linenos">1436</span>        <span class="n">new_args</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos">1437</span>        <span class="k">for</span> <span class="n">old_arg</span> <span class="ow">in</span> <span class="n">args</span><span class="p">:</span>
+<span class="linenos">1438</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
+<span class="linenos">1439</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">old_arg</span><span class="p">)</span>
+<span class="linenos">1440</span>                <span class="k">continue</span>
+<span class="linenos">1441</span>
+<span class="linenos">1442</span>            <span class="n">substfunc</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="s1">&#39;__typing_subst__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
+<span class="linenos">1443</span>            <span class="k">if</span> <span class="n">substfunc</span><span class="p">:</span>
+<span class="linenos">1444</span>                <span class="n">new_arg</span> <span class="o">=</span> <span class="n">substfunc</span><span class="p">(</span><span class="n">new_arg_by_param</span><span class="p">[</span><span class="n">old_arg</span><span class="p">])</span>
+<span class="linenos">1445</span>            <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1446</span>                <span class="n">subparams</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="s1">&#39;__parameters__&#39;</span><span class="p">,</span> <span class="p">())</span>
+<span class="linenos">1447</span>                <span class="k">if</span> <span class="ow">not</span> <span class="n">subparams</span><span class="p">:</span>
+<span class="linenos">1448</span>                    <span class="n">new_arg</span> <span class="o">=</span> <span class="n">old_arg</span>
+<span class="linenos">1449</span>                <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1450</span>                    <span class="n">subargs</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos">1451</span>                    <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">subparams</span><span class="p">:</span>
+<span class="linenos">1452</span>                        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">TypeVarTuple</span><span class="p">):</span>
+<span class="linenos">1453</span>                            <span class="n">subargs</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">new_arg_by_param</span><span class="p">[</span><span class="n">x</span><span class="p">])</span>
+<span class="linenos">1454</span>                        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1455</span>                            <span class="n">subargs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_arg_by_param</span><span class="p">[</span><span class="n">x</span><span class="p">])</span>
+<span class="linenos">1456</span>                    <span class="n">new_arg</span> <span class="o">=</span> <span class="n">old_arg</span><span class="p">[</span><span class="nb">tuple</span><span class="p">(</span><span class="n">subargs</span><span class="p">)]</span>
+<span class="linenos">1457</span>
+<span class="linenos">1458</span>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Callable</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">new_arg</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos">1459</span>                <span class="c1"># Consider the following `Callable`.</span>
+<span class="linenos">1460</span>                <span class="c1">#   C = Callable[[int], str]</span>
+<span class="linenos">1461</span>                <span class="c1"># Here, `C.__args__` should be (int, str) - NOT ([int], str).</span>
+<span class="linenos">1462</span>                <span class="c1"># That means that if we had something like...</span>
+<span class="linenos">1463</span>                <span class="c1">#   P = ParamSpec(&#39;P&#39;)</span>
+<span class="linenos">1464</span>                <span class="c1">#   T = TypeVar(&#39;T&#39;)</span>
+<span class="linenos">1465</span>                <span class="c1">#   C = Callable[P, T]</span>
+<span class="linenos">1466</span>                <span class="c1">#   D = C[[int, str], float]</span>
+<span class="linenos">1467</span>                <span class="c1"># ...we need to be careful; `new_args` should end up as</span>
+<span class="linenos">1468</span>                <span class="c1"># `(int, str, float)` rather than `([int, str], float)`.</span>
+<span class="linenos">1469</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
+<span class="linenos">1470</span>            <span class="k">elif</span> <span class="n">_is_unpacked_typevartuple</span><span class="p">(</span><span class="n">old_arg</span><span class="p">):</span>
+<span class="linenos">1471</span>                <span class="c1"># Consider the following `_GenericAlias`, `B`:</span>
+<span class="linenos">1472</span>                <span class="c1">#   class A(Generic[*Ts]): ...</span>
+<span class="linenos">1473</span>                <span class="c1">#   B = A[T, *Ts]</span>
+<span class="linenos">1474</span>                <span class="c1"># If we then do:</span>
+<span class="linenos">1475</span>                <span class="c1">#   B[float, int, str]</span>
+<span class="linenos">1476</span>                <span class="c1"># The `new_arg` corresponding to `T` will be `float`, and the</span>
+<span class="linenos">1477</span>                <span class="c1"># `new_arg` corresponding to `*Ts` will be `(int, str)`. We</span>
+<span class="linenos">1478</span>                <span class="c1"># should join all these types together in a flat list</span>
+<span class="linenos">1479</span>                <span class="c1"># `(float, int, str)` - so again, we should `extend`.</span>
+<span class="linenos">1480</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
+<span class="linenos">1481</span>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos">1482</span>                <span class="c1"># Corner case:</span>
+<span class="linenos">1483</span>                <span class="c1">#    P = ParamSpec(&#39;P&#39;)</span>
+<span class="linenos">1484</span>                <span class="c1">#    T = TypeVar(&#39;T&#39;)</span>
+<span class="linenos">1485</span>                <span class="c1">#    class Base(Generic[P]): ...</span>
+<span class="linenos">1486</span>                <span class="c1"># Can be substituted like this:</span>
+<span class="linenos">1487</span>                <span class="c1">#    X = Base[[int, T]]</span>
+<span class="linenos">1488</span>                <span class="c1"># In this case, `old_arg` will be a tuple:</span>
+<span class="linenos">1489</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
+<span class="linenos">1490</span>                    <span class="nb">tuple</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_make_substitution</span><span class="p">(</span><span class="n">old_arg</span><span class="p">,</span> <span class="n">new_arg_by_param</span><span class="p">)),</span>
+<span class="linenos">1491</span>                <span class="p">)</span>
+<span class="linenos">1492</span>            <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1493</span>                <span class="n">new_args</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
+<span class="linenos">1494</span>        <span class="k">return</span> <span class="n">new_args</span>
+<span class="linenos">1495</span>
+<span class="linenos">1496</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
+<span class="linenos">1497</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__class__</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_inst</span><span class="p">,</span>
+<span class="linenos">1498</span>                              <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_paramspec_tvars</span><span class="p">)</span>
+<span class="linenos">1499</span>
+<span class="linenos">1500</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1501</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">:</span>
+<span class="linenos">1502</span>            <span class="n">name</span> <span class="o">=</span> <span class="s1">&#39;typing.&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
+<span class="linenos">1503</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1504</span>            <span class="n">name</span> <span class="o">=</span> <span class="n">_type_repr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
+<span class="linenos">1505</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
+<span class="linenos">1506</span>            <span class="n">args</span> <span class="o">=</span> <span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">])</span>
+<span class="linenos">1507</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1508</span>            <span class="c1"># To ensure the repr is eval-able.</span>
+<span class="linenos">1509</span>            <span class="n">args</span> <span class="o">=</span> <span class="s2">&quot;()&quot;</span>
+<span class="linenos">1510</span>        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="s1">[</span><span class="si">{</span><span class="n">args</span><span class="si">}</span><span class="s1">]&#39;</span>
+<span class="linenos">1511</span>
+<span class="linenos">1512</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1513</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">:</span>
+<span class="linenos">1514</span>            <span class="n">origin</span> <span class="o">=</span> <span class="nb">globals</span><span class="p">()[</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">]</span>
+<span class="linenos">1515</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1516</span>            <span class="n">origin</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span>
+<span class="linenos">1517</span>        <span class="n">args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
+<span class="linenos">1518</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">and</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos">1519</span>            <span class="n">args</span><span class="p">,</span> <span class="o">=</span> <span class="n">args</span>
+<span class="linenos">1520</span>        <span class="k">return</span> <span class="n">operator</span><span class="o">.</span><span class="n">getitem</span><span class="p">,</span> <span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span>
+<span class="linenos">1521</span>
+<span class="linenos">1522</span>    <span class="k">def</span> <span class="nf">__mro_entries__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bases</span><span class="p">):</span>
+<span class="linenos">1523</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">_SpecialForm</span><span class="p">):</span>
+<span class="linenos">1524</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Cannot subclass </span><span class="si">{</span><span class="bp">self</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos">1525</span>
+<span class="linenos">1526</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">:</span>  <span class="c1"># generic version of an ABC or built-in class</span>
+<span class="linenos">1527</span>            <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">__mro_entries__</span><span class="p">(</span><span class="n">bases</span><span class="p">)</span>
+<span class="linenos">1528</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Generic</span><span class="p">:</span>
+<span class="linenos">1529</span>            <span class="k">if</span> <span class="n">Protocol</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
+<span class="linenos">1530</span>                <span class="k">return</span> <span class="p">()</span>
+<span class="linenos">1531</span>            <span class="n">i</span> <span class="o">=</span> <span class="n">bases</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+<span class="linenos">1532</span>            <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">:]:</span>
+<span class="linenos">1533</span>                <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">_BaseGenericAlias</span><span class="p">)</span> <span class="ow">and</span> <span class="n">b</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">self</span><span class="p">:</span>
+<span class="linenos">1534</span>                    <span class="k">return</span> <span class="p">()</span>
+<span class="linenos">1535</span>        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,)</span>
+<span class="linenos">1536</span>
+<span class="linenos">1537</span>    <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1538</span>        <span class="k">yield</span> <span class="n">Unpack</span><span class="p">[</span><span class="bp">self</span><span class="p">]</span>
+<span class="linenos">1539</span>
+<span class="linenos">1540</span>
+<span class="linenos">1541</span><span class="c1"># _nparams is the number of accepted parameters, e.g. 0 for Hashable,</span>
+<span class="linenos">1542</span><span class="c1"># 1 for List and 2 for Dict.  It may be -1 if variable number of</span>
+<span class="linenos">1543</span><span class="c1"># parameters are accepted (needs custom __getitem__).</span>
+<span class="linenos">1544</span>
+<span class="linenos">1545</span><span class="k">class</span> <span class="nc">_SpecialGenericAlias</span><span class="p">(</span><span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_BaseGenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1546</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">,</span> <span class="n">nparams</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="linenos">1547</span>        <span class="k">if</span> <span class="n">name</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">1548</span>            <span class="n">name</span> <span class="o">=</span> <span class="n">origin</span><span class="o">.</span><span class="vm">__name__</span>
+<span class="linenos">1549</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="n">inst</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="n">name</span><span class="p">)</span>
+<span class="linenos">1550</span>        <span class="bp">self</span><span class="o">.</span><span class="n">_nparams</span> <span class="o">=</span> <span class="n">nparams</span>
+<span class="linenos">1551</span>        <span class="k">if</span> <span class="n">origin</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">==</span> <span class="s1">&#39;builtins&#39;</span><span class="p">:</span>
+<span class="linenos">1552</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;A generic version of </span><span class="si">{</span><span class="n">origin</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">.&#39;</span>
+<span class="linenos">1553</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1554</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="sa">f</span><span class="s1">&#39;A generic version of </span><span class="si">{</span><span class="n">origin</span><span class="o">.</span><span class="vm">__module__</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="n">origin</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">.&#39;</span>
+<span class="linenos">1555</span>
+<span class="linenos">1556</span>    <span class="nd">@_tp_cache</span>
+<span class="linenos">1557</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1558</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos">1559</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="n">params</span><span class="p">,)</span>
+<span class="linenos">1560</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Parameters to generic types must be types.&quot;</span>
+<span class="linenos">1561</span>        <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">)</span>
+<span class="linenos">1562</span>        <span class="n">_check_generic</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nparams</span><span class="p">)</span>
+<span class="linenos">1563</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos">1564</span>
+<span class="linenos">1565</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1566</span>        <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span>
+<span class="linenos">1567</span>                             <span class="n">name</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_inst</span><span class="p">)</span>
+<span class="linenos">1568</span>
+<span class="linenos">1569</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1570</span>        <span class="k">return</span> <span class="s1">&#39;typing.&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
 <span class="linenos">1571</span>
-<span class="linenos">1572</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1573</span>        <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span>
-<span class="linenos">1574</span>                             <span class="n">name</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_inst</span><span class="p">)</span>
-<span class="linenos">1575</span>
-<span class="linenos">1576</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1577</span>        <span class="k">return</span> <span class="s1">&#39;typing.&#39;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
+<span class="linenos">1572</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="bp">cls</span><span class="p">):</span>
+<span class="linenos">1573</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">_SpecialGenericAlias</span><span class="p">):</span>
+<span class="linenos">1574</span>            <span class="k">return</span> <span class="nb">issubclass</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
+<span class="linenos">1575</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">):</span>
+<span class="linenos">1576</span>            <span class="k">return</span> <span class="nb">issubclass</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
+<span class="linenos">1577</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">cls</span><span class="p">)</span>
 <span class="linenos">1578</span>
-<span class="linenos">1579</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="bp">cls</span><span class="p">):</span>
-<span class="linenos">1580</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">_SpecialGenericAlias</span><span class="p">):</span>
-<span class="linenos">1581</span>            <span class="k">return</span> <span class="nb">issubclass</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
-<span class="linenos">1582</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">):</span>
-<span class="linenos">1583</span>            <span class="k">return</span> <span class="nb">issubclass</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
-<span class="linenos">1584</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">cls</span><span class="p">)</span>
-<span class="linenos">1585</span>
-<span class="linenos">1586</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1587</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
-<span class="linenos">1588</span>
-<span class="linenos">1589</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
-<span class="linenos">1590</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">]</span>
-<span class="linenos">1591</span>
-<span class="linenos">1592</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">left</span><span class="p">):</span>
-<span class="linenos">1593</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
-<span class="linenos">1594</span>
-<span class="linenos">1595</span><span class="k">class</span> <span class="nc">_CallableGenericAlias</span><span class="p">(</span><span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1596</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1597</span>        <span class="k">assert</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="o">==</span> <span class="s1">&#39;Callable&#39;</span>
-<span class="linenos">1598</span>        <span class="n">args</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span>
-<span class="linenos">1599</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
-<span class="linenos">1600</span>            <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__repr__</span><span class="p">()</span>
-<span class="linenos">1601</span>        <span class="k">return</span> <span class="p">(</span><span class="sa">f</span><span class="s1">&#39;typing.Callable&#39;</span>
-<span class="linenos">1602</span>                <span class="sa">f</span><span class="s1">&#39;[[</span><span class="si">{</span><span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="ow">in</span><span class="w"> </span><span class="n">args</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]])</span><span class="si">}</span><span class="s1">], &#39;</span>
-<span class="linenos">1603</span>                <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="si">}</span><span class="s1">]&#39;</span><span class="p">)</span>
+<span class="linenos">1579</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1580</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span>
+<span class="linenos">1581</span>
+<span class="linenos">1582</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
+<span class="linenos">1583</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">right</span><span class="p">]</span>
+<span class="linenos">1584</span>
+<span class="linenos">1585</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">left</span><span class="p">):</span>
+<span class="linenos">1586</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">left</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
+<span class="linenos">1587</span>
+<span class="linenos">1588</span><span class="k">class</span> <span class="nc">_CallableGenericAlias</span><span class="p">(</span><span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1589</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1590</span>        <span class="k">assert</span> <span class="bp">self</span><span class="o">.</span><span class="n">_name</span> <span class="o">==</span> <span class="s1">&#39;Callable&#39;</span>
+<span class="linenos">1591</span>        <span class="n">args</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span>
+<span class="linenos">1592</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
+<span class="linenos">1593</span>            <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__repr__</span><span class="p">()</span>
+<span class="linenos">1594</span>        <span class="k">return</span> <span class="p">(</span><span class="sa">f</span><span class="s1">&#39;typing.Callable&#39;</span>
+<span class="linenos">1595</span>                <span class="sa">f</span><span class="s1">&#39;[[</span><span class="si">{</span><span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="ow">in</span><span class="w"> </span><span class="n">args</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]])</span><span class="si">}</span><span class="s1">], &#39;</span>
+<span class="linenos">1596</span>                <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span><span class="si">}</span><span class="s1">]&#39;</span><span class="p">)</span>
+<span class="linenos">1597</span>
+<span class="linenos">1598</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1599</span>        <span class="n">args</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span>
+<span class="linenos">1600</span>        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">])):</span>
+<span class="linenos">1601</span>            <span class="n">args</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">args</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span> <span class="n">args</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="linenos">1602</span>        <span class="k">return</span> <span class="n">operator</span><span class="o">.</span><span class="n">getitem</span><span class="p">,</span> <span class="p">(</span><span class="n">Callable</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span>
+<span class="linenos">1603</span>
 <span class="linenos">1604</span>
-<span class="linenos">1605</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1606</span>        <span class="n">args</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span>
-<span class="linenos">1607</span>        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">_is_param_expr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">])):</span>
-<span class="linenos">1608</span>            <span class="n">args</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">args</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span> <span class="n">args</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-<span class="linenos">1609</span>        <span class="k">return</span> <span class="n">operator</span><span class="o">.</span><span class="n">getitem</span><span class="p">,</span> <span class="p">(</span><span class="n">Callable</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span>
+<span class="linenos">1605</span><span class="k">class</span> <span class="nc">_CallableType</span><span class="p">(</span><span class="n">_SpecialGenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1606</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1607</span>        <span class="k">return</span> <span class="n">_CallableGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span>
+<span class="linenos">1608</span>                                     <span class="n">name</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_inst</span><span class="p">,</span>
+<span class="linenos">1609</span>                                     <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 <span class="linenos">1610</span>
-<span class="linenos">1611</span>
-<span class="linenos">1612</span><span class="k">class</span> <span class="nc">_CallableType</span><span class="p">(</span><span class="n">_SpecialGenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1613</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1614</span>        <span class="k">return</span> <span class="n">_CallableGenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span>
-<span class="linenos">1615</span>                                     <span class="n">name</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_inst</span><span class="p">,</span>
-<span class="linenos">1616</span>                                     <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="linenos">1617</span>
-<span class="linenos">1618</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1619</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">:</span>
-<span class="linenos">1620</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Callable must be used as &quot;</span>
-<span class="linenos">1621</span>                            <span class="s2">&quot;Callable[[arg, ...], result].&quot;</span><span class="p">)</span>
-<span class="linenos">1622</span>        <span class="n">args</span><span class="p">,</span> <span class="n">result</span> <span class="o">=</span> <span class="n">params</span>
-<span class="linenos">1623</span>        <span class="c1"># This relaxes what args can be on purpose to allow things like</span>
-<span class="linenos">1624</span>        <span class="c1"># PEP 612 ParamSpec.  Responsibility for whether a user is using</span>
-<span class="linenos">1625</span>        <span class="c1"># Callable[...] properly is deferred to static type checkers.</span>
-<span class="linenos">1626</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
-<span class="linenos">1627</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">),</span> <span class="n">result</span><span class="p">)</span>
-<span class="linenos">1628</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1629</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
-<span class="linenos">1630</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__getitem_inner__</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
-<span class="linenos">1631</span>
-<span class="linenos">1632</span>    <span class="nd">@_tp_cache</span>
-<span class="linenos">1633</span>    <span class="k">def</span> <span class="nf">__getitem_inner__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1634</span>        <span class="n">args</span><span class="p">,</span> <span class="n">result</span> <span class="o">=</span> <span class="n">params</span>
-<span class="linenos">1635</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Callable[args, result]: result must be a type.&quot;</span>
-<span class="linenos">1636</span>        <span class="n">result</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span>
-<span class="linenos">1637</span>        <span class="k">if</span> <span class="n">args</span> <span class="ow">is</span> <span class="bp">Ellipsis</span><span class="p">:</span>
-<span class="linenos">1638</span>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">((</span><span class="n">_TypingEllipsis</span><span class="p">,</span> <span class="n">result</span><span class="p">))</span>
-<span class="linenos">1639</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos">1640</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,)</span>
-<span class="linenos">1641</span>        <span class="n">args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_convert</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span> <span class="k">for</span> <span class="n">arg</span> <span class="ow">in</span> <span class="n">args</span><span class="p">)</span>
-<span class="linenos">1642</span>        <span class="n">params</span> <span class="o">=</span> <span class="n">args</span> <span class="o">+</span> <span class="p">(</span><span class="n">result</span><span class="p">,)</span>
-<span class="linenos">1643</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
-<span class="linenos">1644</span>
-<span class="linenos">1645</span>
-<span class="linenos">1646</span><span class="k">class</span> <span class="nc">_TupleType</span><span class="p">(</span><span class="n">_SpecialGenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1647</span>    <span class="nd">@_tp_cache</span>
-<span class="linenos">1648</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1649</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos">1650</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="n">params</span><span class="p">,)</span>
-<span class="linenos">1651</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">&gt;=</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="o">...</span><span class="p">:</span>
-<span class="linenos">1652</span>            <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Tuple[t, ...]: t must be a type.&quot;</span>
-<span class="linenos">1653</span>            <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
-<span class="linenos">1654</span>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">((</span><span class="o">*</span><span class="n">params</span><span class="p">,</span> <span class="n">_TypingEllipsis</span><span class="p">))</span>
-<span class="linenos">1655</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Tuple[t0, t1, ...]: each t must be a type.&quot;</span>
-<span class="linenos">1656</span>        <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">)</span>
-<span class="linenos">1657</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
-<span class="linenos">1658</span>
-<span class="linenos">1659</span>
-<span class="linenos">1660</span><span class="k">class</span> <span class="nc">_UnionGenericAlias</span><span class="p">(</span><span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1661</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1662</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">params</span><span class="p">]</span>
-<span class="linenos">1663</span>
-<span class="linenos">1664</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos">1665</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="p">(</span><span class="n">_UnionGenericAlias</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">)):</span>
-<span class="linenos">1666</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">1667</span>        <span class="k">return</span> <span class="nb">set</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span> <span class="o">==</span> <span class="nb">set</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
-<span class="linenos">1668</span>
-<span class="linenos">1669</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1670</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">frozenset</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">))</span>
-<span class="linenos">1671</span>
-<span class="linenos">1672</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1673</span>        <span class="n">args</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span>
-<span class="linenos">1674</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
-<span class="linenos">1675</span>            <span class="k">if</span> <span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="ow">is</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">):</span>
-<span class="linenos">1676</span>                <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;typing.Optional[</span><span class="si">{</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="si">}</span><span class="s1">]&#39;</span>
-<span class="linenos">1677</span>            <span class="k">elif</span> <span class="n">args</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">):</span>
-<span class="linenos">1678</span>                <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;typing.Optional[</span><span class="si">{</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="si">}</span><span class="s1">]&#39;</span>
-<span class="linenos">1679</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__repr__</span><span class="p">()</span>
-<span class="linenos">1680</span>
-<span class="linenos">1681</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">):</span>
-<span class="linenos">1682</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__subclasscheck__</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">obj</span><span class="p">))</span>
-<span class="linenos">1683</span>
-<span class="linenos">1684</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="bp">cls</span><span class="p">):</span>
-<span class="linenos">1685</span>        <span class="k">for</span> <span class="n">arg</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
-<span class="linenos">1686</span>            <span class="k">if</span> <span class="nb">issubclass</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">arg</span><span class="p">):</span>
-<span class="linenos">1687</span>                <span class="k">return</span> <span class="kc">True</span>
-<span class="linenos">1688</span>
-<span class="linenos">1689</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1690</span>        <span class="n">func</span><span class="p">,</span> <span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">__reduce__</span><span class="p">()</span>
-<span class="linenos">1691</span>        <span class="k">return</span> <span class="n">func</span><span class="p">,</span> <span class="p">(</span><span class="n">Union</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span>
-<span class="linenos">1692</span>
-<span class="linenos">1693</span>
-<span class="linenos">1694</span><span class="k">def</span> <span class="nf">_value_and_type_iter</span><span class="p">(</span><span class="n">parameters</span><span class="p">):</span>
-<span class="linenos">1695</span>    <span class="k">return</span> <span class="p">((</span><span class="n">p</span><span class="p">,</span> <span class="nb">type</span><span class="p">(</span><span class="n">p</span><span class="p">))</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">)</span>
-<span class="linenos">1696</span>
+<span class="linenos">1611</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1612</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">2</span><span class="p">:</span>
+<span class="linenos">1613</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Callable must be used as &quot;</span>
+<span class="linenos">1614</span>                            <span class="s2">&quot;Callable[[arg, ...], result].&quot;</span><span class="p">)</span>
+<span class="linenos">1615</span>        <span class="n">args</span><span class="p">,</span> <span class="n">result</span> <span class="o">=</span> <span class="n">params</span>
+<span class="linenos">1616</span>        <span class="c1"># This relaxes what args can be on purpose to allow things like</span>
+<span class="linenos">1617</span>        <span class="c1"># PEP 612 ParamSpec.  Responsibility for whether a user is using</span>
+<span class="linenos">1618</span>        <span class="c1"># Callable[...] properly is deferred to static type checkers.</span>
+<span class="linenos">1619</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+<span class="linenos">1620</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">),</span> <span class="n">result</span><span class="p">)</span>
+<span class="linenos">1621</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1622</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
+<span class="linenos">1623</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__getitem_inner__</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos">1624</span>
+<span class="linenos">1625</span>    <span class="nd">@_tp_cache</span>
+<span class="linenos">1626</span>    <span class="k">def</span> <span class="nf">__getitem_inner__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1627</span>        <span class="n">args</span><span class="p">,</span> <span class="n">result</span> <span class="o">=</span> <span class="n">params</span>
+<span class="linenos">1628</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Callable[args, result]: result must be a type.&quot;</span>
+<span class="linenos">1629</span>        <span class="n">result</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span>
+<span class="linenos">1630</span>        <span class="k">if</span> <span class="n">args</span> <span class="ow">is</span> <span class="bp">Ellipsis</span><span class="p">:</span>
+<span class="linenos">1631</span>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">((</span><span class="n">_TypingEllipsis</span><span class="p">,</span> <span class="n">result</span><span class="p">))</span>
+<span class="linenos">1632</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos">1633</span>            <span class="n">args</span> <span class="o">=</span> <span class="p">(</span><span class="n">args</span><span class="p">,)</span>
+<span class="linenos">1634</span>        <span class="n">args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_convert</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span> <span class="k">for</span> <span class="n">arg</span> <span class="ow">in</span> <span class="n">args</span><span class="p">)</span>
+<span class="linenos">1635</span>        <span class="n">params</span> <span class="o">=</span> <span class="n">args</span> <span class="o">+</span> <span class="p">(</span><span class="n">result</span><span class="p">,)</span>
+<span class="linenos">1636</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos">1637</span>
+<span class="linenos">1638</span>
+<span class="linenos">1639</span><span class="k">class</span> <span class="nc">_TupleType</span><span class="p">(</span><span class="n">_SpecialGenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1640</span>    <span class="nd">@_tp_cache</span>
+<span class="linenos">1641</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1642</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos">1643</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="n">params</span><span class="p">,)</span>
+<span class="linenos">1644</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">&gt;=</span> <span class="mi">2</span> <span class="ow">and</span> <span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="o">...</span><span class="p">:</span>
+<span class="linenos">1645</span>            <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Tuple[t, ...]: t must be a type.&quot;</span>
+<span class="linenos">1646</span>            <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
+<span class="linenos">1647</span>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">((</span><span class="o">*</span><span class="n">params</span><span class="p">,</span> <span class="n">_TypingEllipsis</span><span class="p">))</span>
+<span class="linenos">1648</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Tuple[t0, t1, ...]: each t must be a type.&quot;</span>
+<span class="linenos">1649</span>        <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_check</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">msg</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">)</span>
+<span class="linenos">1650</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos">1651</span>
+<span class="linenos">1652</span>
+<span class="linenos">1653</span><span class="k">class</span> <span class="nc">_UnionGenericAlias</span><span class="p">(</span><span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1654</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1655</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">params</span><span class="p">]</span>
+<span class="linenos">1656</span>
+<span class="linenos">1657</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos">1658</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="p">(</span><span class="n">_UnionGenericAlias</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">)):</span>
+<span class="linenos">1659</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">1660</span>        <span class="k">return</span> <span class="nb">set</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span> <span class="o">==</span> <span class="nb">set</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
+<span class="linenos">1661</span>
+<span class="linenos">1662</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1663</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">frozenset</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">))</span>
+<span class="linenos">1664</span>
+<span class="linenos">1665</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1666</span>        <span class="n">args</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span>
+<span class="linenos">1667</span>        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<span class="linenos">1668</span>            <span class="k">if</span> <span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="ow">is</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">):</span>
+<span class="linenos">1669</span>                <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;typing.Optional[</span><span class="si">{</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="si">}</span><span class="s1">]&#39;</span>
+<span class="linenos">1670</span>            <span class="k">elif</span> <span class="n">args</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">):</span>
+<span class="linenos">1671</span>                <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;typing.Optional[</span><span class="si">{</span><span class="n">_type_repr</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="si">}</span><span class="s1">]&#39;</span>
+<span class="linenos">1672</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__repr__</span><span class="p">()</span>
+<span class="linenos">1673</span>
+<span class="linenos">1674</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">obj</span><span class="p">):</span>
+<span class="linenos">1675</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__subclasscheck__</span><span class="p">(</span><span class="nb">type</span><span class="p">(</span><span class="n">obj</span><span class="p">))</span>
+<span class="linenos">1676</span>
+<span class="linenos">1677</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="bp">cls</span><span class="p">):</span>
+<span class="linenos">1678</span>        <span class="k">for</span> <span class="n">arg</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
+<span class="linenos">1679</span>            <span class="k">if</span> <span class="nb">issubclass</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">arg</span><span class="p">):</span>
+<span class="linenos">1680</span>                <span class="k">return</span> <span class="kc">True</span>
+<span class="linenos">1681</span>
+<span class="linenos">1682</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1683</span>        <span class="n">func</span><span class="p">,</span> <span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">__reduce__</span><span class="p">()</span>
+<span class="linenos">1684</span>        <span class="k">return</span> <span class="n">func</span><span class="p">,</span> <span class="p">(</span><span class="n">Union</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span>
+<span class="linenos">1685</span>
+<span class="linenos">1686</span>
+<span class="linenos">1687</span><span class="k">def</span> <span class="nf">_value_and_type_iter</span><span class="p">(</span><span class="n">parameters</span><span class="p">):</span>
+<span class="linenos">1688</span>    <span class="k">return</span> <span class="p">((</span><span class="n">p</span><span class="p">,</span> <span class="nb">type</span><span class="p">(</span><span class="n">p</span><span class="p">))</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">parameters</span><span class="p">)</span>
+<span class="linenos">1689</span>
+<span class="linenos">1690</span>
+<span class="linenos">1691</span><span class="k">class</span> <span class="nc">_LiteralGenericAlias</span><span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1692</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos">1693</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">_LiteralGenericAlias</span><span class="p">):</span>
+<span class="linenos">1694</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">1695</span>
+<span class="linenos">1696</span>        <span class="k">return</span> <span class="nb">set</span><span class="p">(</span><span class="n">_value_and_type_iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">))</span> <span class="o">==</span> <span class="nb">set</span><span class="p">(</span><span class="n">_value_and_type_iter</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="n">__args__</span><span class="p">))</span>
 <span class="linenos">1697</span>
-<span class="linenos">1698</span><span class="k">class</span> <span class="nc">_LiteralGenericAlias</span><span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1699</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos">1700</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">_LiteralGenericAlias</span><span class="p">):</span>
-<span class="linenos">1701</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">1702</span>
-<span class="linenos">1703</span>        <span class="k">return</span> <span class="nb">set</span><span class="p">(</span><span class="n">_value_and_type_iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">))</span> <span class="o">==</span> <span class="nb">set</span><span class="p">(</span><span class="n">_value_and_type_iter</span><span class="p">(</span><span class="n">other</span><span class="o">.</span><span class="n">__args__</span><span class="p">))</span>
-<span class="linenos">1704</span>
-<span class="linenos">1705</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1706</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">frozenset</span><span class="p">(</span><span class="n">_value_and_type_iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)))</span>
-<span class="linenos">1707</span>
-<span class="linenos">1708</span>
-<span class="linenos">1709</span><span class="k">class</span> <span class="nc">_ConcatenateGenericAlias</span><span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1710</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1711</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)):</span>
-<span class="linenos">1712</span>            <span class="k">return</span> <span class="p">(</span><span class="o">*</span><span class="n">params</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="o">*</span><span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
-<span class="linenos">1713</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">_ConcatenateGenericAlias</span><span class="p">):</span>
-<span class="linenos">1714</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="o">*</span><span class="n">params</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="o">*</span><span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
-<span class="linenos">1715</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
-<span class="linenos">1716</span>
-<span class="linenos">1717</span>
-<span class="linenos">1718</span><span class="nd">@_SpecialForm</span>
-<span class="linenos">1719</span><span class="k">def</span> <span class="nf">Unpack</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos">1720</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Type unpack operator.</span>
+<span class="linenos">1698</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1699</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">frozenset</span><span class="p">(</span><span class="n">_value_and_type_iter</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)))</span>
+<span class="linenos">1700</span>
+<span class="linenos">1701</span>
+<span class="linenos">1702</span><span class="k">class</span> <span class="nc">_ConcatenateGenericAlias</span><span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1703</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1704</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)):</span>
+<span class="linenos">1705</span>            <span class="k">return</span> <span class="p">(</span><span class="o">*</span><span class="n">params</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="o">*</span><span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
+<span class="linenos">1706</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">_ConcatenateGenericAlias</span><span class="p">):</span>
+<span class="linenos">1707</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="o">*</span><span class="n">params</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="o">*</span><span class="n">params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
+<span class="linenos">1708</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">params</span><span class="p">)</span>
+<span class="linenos">1709</span>
+<span class="linenos">1710</span>
+<span class="linenos">1711</span><span class="nd">@_SpecialForm</span>
+<span class="linenos">1712</span><span class="k">def</span> <span class="nf">Unpack</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos">1713</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Type unpack operator.</span>
+<span class="linenos">1714</span>
+<span class="linenos">1715</span><span class="sd">    The type unpack operator takes the child types from some container type,</span>
+<span class="linenos">1716</span><span class="sd">    such as `tuple[int, str]` or a `TypeVarTuple`, and &#39;pulls them out&#39;. For</span>
+<span class="linenos">1717</span><span class="sd">    example::</span>
+<span class="linenos">1718</span>
+<span class="linenos">1719</span><span class="sd">        # For some generic class `Foo`:</span>
+<span class="linenos">1720</span><span class="sd">        Foo[Unpack[tuple[int, str]]]  # Equivalent to Foo[int, str]</span>
 <span class="linenos">1721</span>
-<span class="linenos">1722</span><span class="sd">    The type unpack operator takes the child types from some container type,</span>
-<span class="linenos">1723</span><span class="sd">    such as `tuple[int, str]` or a `TypeVarTuple`, and &#39;pulls them out&#39;.</span>
-<span class="linenos">1724</span>
-<span class="linenos">1725</span><span class="sd">    For example::</span>
-<span class="linenos">1726</span>
-<span class="linenos">1727</span><span class="sd">        # For some generic class `Foo`:</span>
-<span class="linenos">1728</span><span class="sd">        Foo[Unpack[tuple[int, str]]]  # Equivalent to Foo[int, str]</span>
-<span class="linenos">1729</span>
-<span class="linenos">1730</span><span class="sd">        Ts = TypeVarTuple(&#39;Ts&#39;)</span>
-<span class="linenos">1731</span><span class="sd">        # Specifies that `Bar` is generic in an arbitrary number of types.</span>
-<span class="linenos">1732</span><span class="sd">        # (Think of `Ts` as a tuple of an arbitrary number of individual</span>
-<span class="linenos">1733</span><span class="sd">        #  `TypeVar`s, which the `Unpack` is &#39;pulling out&#39; directly into the</span>
-<span class="linenos">1734</span><span class="sd">        #  `Generic[]`.)</span>
-<span class="linenos">1735</span><span class="sd">        class Bar(Generic[Unpack[Ts]]): ...</span>
-<span class="linenos">1736</span><span class="sd">        Bar[int]  # Valid</span>
-<span class="linenos">1737</span><span class="sd">        Bar[int, str]  # Also valid</span>
+<span class="linenos">1722</span><span class="sd">        Ts = TypeVarTuple(&#39;Ts&#39;)</span>
+<span class="linenos">1723</span><span class="sd">        # Specifies that `Bar` is generic in an arbitrary number of types.</span>
+<span class="linenos">1724</span><span class="sd">        # (Think of `Ts` as a tuple of an arbitrary number of individual</span>
+<span class="linenos">1725</span><span class="sd">        #  `TypeVar`s, which the `Unpack` is &#39;pulling out&#39; directly into the</span>
+<span class="linenos">1726</span><span class="sd">        #  `Generic[]`.)</span>
+<span class="linenos">1727</span><span class="sd">        class Bar(Generic[Unpack[Ts]]): ...</span>
+<span class="linenos">1728</span><span class="sd">        Bar[int]  # Valid</span>
+<span class="linenos">1729</span><span class="sd">        Bar[int, str]  # Also valid</span>
+<span class="linenos">1730</span>
+<span class="linenos">1731</span><span class="sd">    From Python 3.11, this can also be done using the `*` operator::</span>
+<span class="linenos">1732</span>
+<span class="linenos">1733</span><span class="sd">        Foo[*tuple[int, str]]</span>
+<span class="linenos">1734</span><span class="sd">        class Bar(Generic[*Ts]): ...</span>
+<span class="linenos">1735</span>
+<span class="linenos">1736</span><span class="sd">    Note that there is only some runtime checking of this operator. Not</span>
+<span class="linenos">1737</span><span class="sd">    everything the runtime allows may be accepted by static type checkers.</span>
 <span class="linenos">1738</span>
-<span class="linenos">1739</span><span class="sd">    From Python 3.11, this can also be done using the `*` operator::</span>
-<span class="linenos">1740</span>
-<span class="linenos">1741</span><span class="sd">        Foo[*tuple[int, str]]</span>
-<span class="linenos">1742</span><span class="sd">        class Bar(Generic[*Ts]): ...</span>
+<span class="linenos">1739</span><span class="sd">    For more information, see PEP 646.</span>
+<span class="linenos">1740</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">1741</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s1"> accepts only single type.&#39;</span><span class="p">)</span>
+<span class="linenos">1742</span>    <span class="k">return</span> <span class="n">_UnpackGenericAlias</span><span class="p">(</span><span class="n">origin</span><span class="o">=</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="o">=</span><span class="p">(</span><span class="n">item</span><span class="p">,))</span>
 <span class="linenos">1743</span>
-<span class="linenos">1744</span><span class="sd">    Note that there is only some runtime checking of this operator. Not</span>
-<span class="linenos">1745</span><span class="sd">    everything the runtime allows may be accepted by static type checkers.</span>
-<span class="linenos">1746</span>
-<span class="linenos">1747</span><span class="sd">    For more information, see PEP 646.</span>
-<span class="linenos">1748</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1749</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="si">}</span><span class="s1"> accepts only single type.&#39;</span><span class="p">)</span>
-<span class="linenos">1750</span>    <span class="k">return</span> <span class="n">_UnpackGenericAlias</span><span class="p">(</span><span class="n">origin</span><span class="o">=</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="o">=</span><span class="p">(</span><span class="n">item</span><span class="p">,))</span>
-<span class="linenos">1751</span>
-<span class="linenos">1752</span>
-<span class="linenos">1753</span><span class="k">class</span> <span class="nc">_UnpackGenericAlias</span><span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">1754</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1755</span>        <span class="c1"># `Unpack` only takes one argument, so __args__ should contain only</span>
-<span class="linenos">1756</span>        <span class="c1"># a single item.</span>
-<span class="linenos">1757</span>        <span class="k">return</span> <span class="s1">&#39;*&#39;</span> <span class="o">+</span> <span class="nb">repr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="linenos">1758</span>
-<span class="linenos">1759</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
-<span class="linenos">1760</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__typing_is_unpacked_typevartuple__</span><span class="p">:</span>
-<span class="linenos">1761</span>            <span class="k">return</span> <span class="n">args</span>
-<span class="linenos">1762</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
-<span class="linenos">1763</span>
-<span class="linenos">1764</span>    <span class="nd">@property</span>
-<span class="linenos">1765</span>    <span class="k">def</span> <span class="nf">__typing_unpacked_tuple_args__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1766</span>        <span class="k">assert</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Unpack</span>
-<span class="linenos">1767</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span>
-<span class="linenos">1768</span>        <span class="n">arg</span><span class="p">,</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span>
-<span class="linenos">1769</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">):</span>
-<span class="linenos">1770</span>            <span class="k">assert</span> <span class="n">arg</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="nb">tuple</span>
-<span class="linenos">1771</span>            <span class="k">return</span> <span class="n">arg</span><span class="o">.</span><span class="n">__args__</span>
-<span class="linenos">1772</span>        <span class="k">return</span> <span class="kc">None</span>
-<span class="linenos">1773</span>
-<span class="linenos">1774</span>    <span class="nd">@property</span>
-<span class="linenos">1775</span>    <span class="k">def</span> <span class="nf">__typing_is_unpacked_typevartuple__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">1776</span>        <span class="k">assert</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Unpack</span>
-<span class="linenos">1777</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span>
-<span class="linenos">1778</span>        <span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">TypeVarTuple</span><span class="p">)</span>
+<span class="linenos">1744</span>
+<span class="linenos">1745</span><span class="k">class</span> <span class="nc">_UnpackGenericAlias</span><span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">1746</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1747</span>        <span class="c1"># `Unpack` only takes one argument, so __args__ should contain only</span>
+<span class="linenos">1748</span>        <span class="c1"># a single item.</span>
+<span class="linenos">1749</span>        <span class="k">return</span> <span class="s1">&#39;*&#39;</span> <span class="o">+</span> <span class="nb">repr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<span class="linenos">1750</span>
+<span class="linenos">1751</span>    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">args</span><span class="p">):</span>
+<span class="linenos">1752</span>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">__typing_is_unpacked_typevartuple__</span><span class="p">:</span>
+<span class="linenos">1753</span>            <span class="k">return</span> <span class="n">args</span>
+<span class="linenos">1754</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">args</span><span class="p">)</span>
+<span class="linenos">1755</span>
+<span class="linenos">1756</span>    <span class="nd">@property</span>
+<span class="linenos">1757</span>    <span class="k">def</span> <span class="nf">__typing_unpacked_tuple_args__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1758</span>        <span class="k">assert</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Unpack</span>
+<span class="linenos">1759</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span>
+<span class="linenos">1760</span>        <span class="n">arg</span><span class="p">,</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__args__</span>
+<span class="linenos">1761</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">):</span>
+<span class="linenos">1762</span>            <span class="k">assert</span> <span class="n">arg</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="nb">tuple</span>
+<span class="linenos">1763</span>            <span class="k">return</span> <span class="n">arg</span><span class="o">.</span><span class="n">__args__</span>
+<span class="linenos">1764</span>        <span class="k">return</span> <span class="kc">None</span>
+<span class="linenos">1765</span>
+<span class="linenos">1766</span>    <span class="nd">@property</span>
+<span class="linenos">1767</span>    <span class="k">def</span> <span class="nf">__typing_is_unpacked_typevartuple__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">1768</span>        <span class="k">assert</span> <span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Unpack</span>
+<span class="linenos">1769</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span>
+<span class="linenos">1770</span>        <span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__args__</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">TypeVarTuple</span><span class="p">)</span>
+<span class="linenos">1771</span>
+<span class="linenos">1772</span>
+<span class="linenos">1773</span><span class="k">class</span> <span class="nc">Generic</span><span class="p">:</span>
+<span class="linenos">1774</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Abstract base class for generic types.</span>
+<span class="linenos">1775</span>
+<span class="linenos">1776</span><span class="sd">    A generic type is typically declared by inheriting from</span>
+<span class="linenos">1777</span><span class="sd">    this class parameterized with one or more type variables.</span>
+<span class="linenos">1778</span><span class="sd">    For example, a generic mapping type might be defined as::</span>
 <span class="linenos">1779</span>
-<span class="linenos">1780</span>
-<span class="linenos">1781</span><span class="k">class</span> <span class="nc">Generic</span><span class="p">:</span>
-<span class="linenos">1782</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Abstract base class for generic types.</span>
-<span class="linenos">1783</span>
-<span class="linenos">1784</span><span class="sd">    A generic type is typically declared by inheriting from</span>
-<span class="linenos">1785</span><span class="sd">    this class parameterized with one or more type variables.</span>
-<span class="linenos">1786</span><span class="sd">    For example, a generic mapping type might be defined as::</span>
-<span class="linenos">1787</span>
-<span class="linenos">1788</span><span class="sd">      class Mapping(Generic[KT, VT]):</span>
-<span class="linenos">1789</span><span class="sd">          def __getitem__(self, key: KT) -&gt; VT:</span>
-<span class="linenos">1790</span><span class="sd">              ...</span>
-<span class="linenos">1791</span><span class="sd">          # Etc.</span>
-<span class="linenos">1792</span>
-<span class="linenos">1793</span><span class="sd">    This class can then be used as follows::</span>
-<span class="linenos">1794</span>
-<span class="linenos">1795</span><span class="sd">      def lookup_name(mapping: Mapping[KT, VT], key: KT, default: VT) -&gt; VT:</span>
-<span class="linenos">1796</span><span class="sd">          try:</span>
-<span class="linenos">1797</span><span class="sd">              return mapping[key]</span>
-<span class="linenos">1798</span><span class="sd">          except KeyError:</span>
-<span class="linenos">1799</span><span class="sd">              return default</span>
-<span class="linenos">1800</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1801</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
-<span class="linenos">1802</span>    <span class="n">_is_protocol</span> <span class="o">=</span> <span class="kc">False</span>
+<span class="linenos">1780</span><span class="sd">      class Mapping(Generic[KT, VT]):</span>
+<span class="linenos">1781</span><span class="sd">          def __getitem__(self, key: KT) -&gt; VT:</span>
+<span class="linenos">1782</span><span class="sd">              ...</span>
+<span class="linenos">1783</span><span class="sd">          # Etc.</span>
+<span class="linenos">1784</span>
+<span class="linenos">1785</span><span class="sd">    This class can then be used as follows::</span>
+<span class="linenos">1786</span>
+<span class="linenos">1787</span><span class="sd">      def lookup_name(mapping: Mapping[KT, VT], key: KT, default: VT) -&gt; VT:</span>
+<span class="linenos">1788</span><span class="sd">          try:</span>
+<span class="linenos">1789</span><span class="sd">              return mapping[key]</span>
+<span class="linenos">1790</span><span class="sd">          except KeyError:</span>
+<span class="linenos">1791</span><span class="sd">              return default</span>
+<span class="linenos">1792</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">1793</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">1794</span>    <span class="n">_is_protocol</span> <span class="o">=</span> <span class="kc">False</span>
+<span class="linenos">1795</span>
+<span class="linenos">1796</span>    <span class="nd">@_tp_cache</span>
+<span class="linenos">1797</span>    <span class="k">def</span> <span class="nf">__class_getitem__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1798</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Parameterizes a generic class.</span>
+<span class="linenos">1799</span>
+<span class="linenos">1800</span><span class="sd">        At least, parameterizing a generic class is the *main* thing this method</span>
+<span class="linenos">1801</span><span class="sd">        does. For example, for some generic class `Foo`, this is called when we</span>
+<span class="linenos">1802</span><span class="sd">        do `Foo[int]` - there, with `cls=Foo` and `params=int`.</span>
 <span class="linenos">1803</span>
-<span class="linenos">1804</span>    <span class="nd">@_tp_cache</span>
-<span class="linenos">1805</span>    <span class="k">def</span> <span class="nf">__class_getitem__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1806</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Parameterizes a generic class.</span>
-<span class="linenos">1807</span>
-<span class="linenos">1808</span><span class="sd">        At least, parameterizing a generic class is the *main* thing this method</span>
-<span class="linenos">1809</span><span class="sd">        does. For example, for some generic class `Foo`, this is called when we</span>
-<span class="linenos">1810</span><span class="sd">        do `Foo[int]` - there, with `cls=Foo` and `params=int`.</span>
-<span class="linenos">1811</span>
-<span class="linenos">1812</span><span class="sd">        However, note that this method is also called when defining generic</span>
-<span class="linenos">1813</span><span class="sd">        classes in the first place with `class Foo(Generic[T]): ...`.</span>
-<span class="linenos">1814</span><span class="sd">        &quot;&quot;&quot;</span>
-<span class="linenos">1815</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
-<span class="linenos">1816</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="n">params</span><span class="p">,)</span>
-<span class="linenos">1817</span>
-<span class="linenos">1818</span>        <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_convert</span><span class="p">(</span><span class="n">p</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">)</span>
-<span class="linenos">1819</span>        <span class="k">if</span> <span class="bp">cls</span> <span class="ow">in</span> <span class="p">(</span><span class="n">Generic</span><span class="p">,</span> <span class="n">Protocol</span><span class="p">):</span>
-<span class="linenos">1820</span>            <span class="c1"># Generic and Protocol can only be subscripted with unique type variables.</span>
-<span class="linenos">1821</span>            <span class="k">if</span> <span class="ow">not</span> <span class="n">params</span><span class="p">:</span>
+<span class="linenos">1804</span><span class="sd">        However, note that this method is also called when defining generic</span>
+<span class="linenos">1805</span><span class="sd">        classes in the first place with `class Foo(Generic[T]): ...`.</span>
+<span class="linenos">1806</span><span class="sd">        &quot;&quot;&quot;</span>
+<span class="linenos">1807</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">):</span>
+<span class="linenos">1808</span>            <span class="n">params</span> <span class="o">=</span> <span class="p">(</span><span class="n">params</span><span class="p">,)</span>
+<span class="linenos">1809</span>
+<span class="linenos">1810</span>        <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_type_convert</span><span class="p">(</span><span class="n">p</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">)</span>
+<span class="linenos">1811</span>        <span class="k">if</span> <span class="bp">cls</span> <span class="ow">in</span> <span class="p">(</span><span class="n">Generic</span><span class="p">,</span> <span class="n">Protocol</span><span class="p">):</span>
+<span class="linenos">1812</span>            <span class="c1"># Generic and Protocol can only be subscripted with unique type variables.</span>
+<span class="linenos">1813</span>            <span class="k">if</span> <span class="ow">not</span> <span class="n">params</span><span class="p">:</span>
+<span class="linenos">1814</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
+<span class="linenos">1815</span>                    <span class="sa">f</span><span class="s2">&quot;Parameter list to </span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s2">[...] cannot be empty&quot;</span>
+<span class="linenos">1816</span>                <span class="p">)</span>
+<span class="linenos">1817</span>            <span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">(</span><span class="n">_is_typevar_like</span><span class="p">(</span><span class="n">p</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1818</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
+<span class="linenos">1819</span>                    <span class="sa">f</span><span class="s2">&quot;Parameters to </span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">[...] must all be type variables &quot;</span>
+<span class="linenos">1820</span>                    <span class="sa">f</span><span class="s2">&quot;or parameter specification variables.&quot;</span><span class="p">)</span>
+<span class="linenos">1821</span>            <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">params</span><span class="p">))</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">):</span>
 <span class="linenos">1822</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
-<span class="linenos">1823</span>                    <span class="sa">f</span><span class="s2">&quot;Parameter list to </span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s2">[...] cannot be empty&quot;</span>
-<span class="linenos">1824</span>                <span class="p">)</span>
-<span class="linenos">1825</span>            <span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">(</span><span class="n">_is_typevar_like</span><span class="p">(</span><span class="n">p</span><span class="p">)</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1826</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
-<span class="linenos">1827</span>                    <span class="sa">f</span><span class="s2">&quot;Parameters to </span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">[...] must all be type variables &quot;</span>
-<span class="linenos">1828</span>                    <span class="sa">f</span><span class="s2">&quot;or parameter specification variables.&quot;</span><span class="p">)</span>
-<span class="linenos">1829</span>            <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">params</span><span class="p">))</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">):</span>
-<span class="linenos">1830</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
-<span class="linenos">1831</span>                    <span class="sa">f</span><span class="s2">&quot;Parameters to </span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">[...] must all be unique&quot;</span><span class="p">)</span>
-<span class="linenos">1832</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1833</span>            <span class="c1"># Subscripting a regular Generic subclass.</span>
-<span class="linenos">1834</span>            <span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="n">__parameters__</span><span class="p">:</span>
-<span class="linenos">1835</span>                <span class="n">prepare</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="s1">&#39;__typing_prepare_subst__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
-<span class="linenos">1836</span>                <span class="k">if</span> <span class="n">prepare</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">1837</span>                    <span class="n">params</span> <span class="o">=</span> <span class="n">prepare</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">)</span>
-<span class="linenos">1838</span>            <span class="n">_check_generic</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="n">__parameters__</span><span class="p">))</span>
+<span class="linenos">1823</span>                    <span class="sa">f</span><span class="s2">&quot;Parameters to </span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2">[...] must all be unique&quot;</span><span class="p">)</span>
+<span class="linenos">1824</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1825</span>            <span class="c1"># Subscripting a regular Generic subclass.</span>
+<span class="linenos">1826</span>            <span class="k">for</span> <span class="n">param</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="n">__parameters__</span><span class="p">:</span>
+<span class="linenos">1827</span>                <span class="n">prepare</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="s1">&#39;__typing_prepare_subst__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
+<span class="linenos">1828</span>                <span class="k">if</span> <span class="n">prepare</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">1829</span>                    <span class="n">params</span> <span class="o">=</span> <span class="n">prepare</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">)</span>
+<span class="linenos">1830</span>            <span class="n">_check_generic</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="n">__parameters__</span><span class="p">))</span>
+<span class="linenos">1831</span>
+<span class="linenos">1832</span>            <span class="n">new_args</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos">1833</span>            <span class="k">for</span> <span class="n">param</span><span class="p">,</span> <span class="n">new_arg</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="n">__parameters__</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">1834</span>                <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">TypeVarTuple</span><span class="p">):</span>
+<span class="linenos">1835</span>                    <span class="n">new_args</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
+<span class="linenos">1836</span>                <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1837</span>                    <span class="n">new_args</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
+<span class="linenos">1838</span>            <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">new_args</span><span class="p">)</span>
 <span class="linenos">1839</span>
-<span class="linenos">1840</span>            <span class="n">new_args</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos">1841</span>            <span class="k">for</span> <span class="n">param</span><span class="p">,</span> <span class="n">new_arg</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="n">__parameters__</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">1842</span>                <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">param</span><span class="p">,</span> <span class="n">TypeVarTuple</span><span class="p">):</span>
-<span class="linenos">1843</span>                    <span class="n">new_args</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
-<span class="linenos">1844</span>                <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1845</span>                    <span class="n">new_args</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_arg</span><span class="p">)</span>
-<span class="linenos">1846</span>            <span class="n">params</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">new_args</span><span class="p">)</span>
-<span class="linenos">1847</span>
-<span class="linenos">1848</span>        <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span>
-<span class="linenos">1849</span>                             <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="linenos">1850</span>
-<span class="linenos">1851</span>    <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos">1852</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">__init_subclass__</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos">1853</span>        <span class="n">tvars</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos">1840</span>        <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">,</span>
+<span class="linenos">1841</span>                             <span class="n">_paramspec_tvars</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<span class="linenos">1842</span>
+<span class="linenos">1843</span>    <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos">1844</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">__init_subclass__</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos">1845</span>        <span class="n">tvars</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos">1846</span>        <span class="k">if</span> <span class="s1">&#39;__orig_bases__&#39;</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
+<span class="linenos">1847</span>            <span class="n">error</span> <span class="o">=</span> <span class="n">Generic</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="n">__orig_bases__</span>
+<span class="linenos">1848</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1849</span>            <span class="n">error</span> <span class="o">=</span> <span class="p">(</span><span class="n">Generic</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__bases__</span> <span class="ow">and</span>
+<span class="linenos">1850</span>                        <span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">!=</span> <span class="s1">&#39;Protocol&#39;</span> <span class="ow">and</span>
+<span class="linenos">1851</span>                        <span class="nb">type</span><span class="p">(</span><span class="bp">cls</span><span class="p">)</span> <span class="o">!=</span> <span class="n">_TypedDictMeta</span><span class="p">)</span>
+<span class="linenos">1852</span>        <span class="k">if</span> <span class="n">error</span><span class="p">:</span>
+<span class="linenos">1853</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Cannot inherit from plain Generic&quot;</span><span class="p">)</span>
 <span class="linenos">1854</span>        <span class="k">if</span> <span class="s1">&#39;__orig_bases__&#39;</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
-<span class="linenos">1855</span>            <span class="n">error</span> <span class="o">=</span> <span class="n">Generic</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="n">__orig_bases__</span>
-<span class="linenos">1856</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1857</span>            <span class="n">error</span> <span class="o">=</span> <span class="p">(</span><span class="n">Generic</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__bases__</span> <span class="ow">and</span>
-<span class="linenos">1858</span>                        <span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">!=</span> <span class="s1">&#39;Protocol&#39;</span> <span class="ow">and</span>
-<span class="linenos">1859</span>                        <span class="nb">type</span><span class="p">(</span><span class="bp">cls</span><span class="p">)</span> <span class="o">!=</span> <span class="n">_TypedDictMeta</span><span class="p">)</span>
-<span class="linenos">1860</span>        <span class="k">if</span> <span class="n">error</span><span class="p">:</span>
-<span class="linenos">1861</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Cannot inherit from plain Generic&quot;</span><span class="p">)</span>
-<span class="linenos">1862</span>        <span class="k">if</span> <span class="s1">&#39;__orig_bases__&#39;</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
-<span class="linenos">1863</span>            <span class="n">tvars</span> <span class="o">=</span> <span class="n">_collect_parameters</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="n">__orig_bases__</span><span class="p">)</span>
-<span class="linenos">1864</span>            <span class="c1"># Look for Generic[T1, ..., Tn].</span>
-<span class="linenos">1865</span>            <span class="c1"># If found, tvars must be a subset of it.</span>
-<span class="linenos">1866</span>            <span class="c1"># If not found, tvars is it.</span>
-<span class="linenos">1867</span>            <span class="c1"># Also check for and reject plain Generic,</span>
-<span class="linenos">1868</span>            <span class="c1"># and reject multiple Generic[...].</span>
-<span class="linenos">1869</span>            <span class="n">gvars</span> <span class="o">=</span> <span class="kc">None</span>
-<span class="linenos">1870</span>            <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="n">__orig_bases__</span><span class="p">:</span>
-<span class="linenos">1871</span>                <span class="k">if</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">)</span> <span class="ow">and</span>
-<span class="linenos">1872</span>                        <span class="n">base</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Generic</span><span class="p">):</span>
-<span class="linenos">1873</span>                    <span class="k">if</span> <span class="n">gvars</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">1874</span>                        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
-<span class="linenos">1875</span>                            <span class="s2">&quot;Cannot inherit from Generic[...] multiple times.&quot;</span><span class="p">)</span>
-<span class="linenos">1876</span>                    <span class="n">gvars</span> <span class="o">=</span> <span class="n">base</span><span class="o">.</span><span class="n">__parameters__</span>
-<span class="linenos">1877</span>            <span class="k">if</span> <span class="n">gvars</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">1878</span>                <span class="n">tvarset</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">tvars</span><span class="p">)</span>
-<span class="linenos">1879</span>                <span class="n">gvarset</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">gvars</span><span class="p">)</span>
-<span class="linenos">1880</span>                <span class="k">if</span> <span class="ow">not</span> <span class="n">tvarset</span> <span class="o">&lt;=</span> <span class="n">gvarset</span><span class="p">:</span>
-<span class="linenos">1881</span>                    <span class="n">s_vars</span> <span class="o">=</span> <span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">tvars</span> <span class="k">if</span> <span class="n">t</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">gvarset</span><span class="p">)</span>
-<span class="linenos">1882</span>                    <span class="n">s_args</span> <span class="o">=</span> <span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">g</span><span class="p">)</span> <span class="k">for</span> <span class="n">g</span> <span class="ow">in</span> <span class="n">gvars</span><span class="p">)</span>
-<span class="linenos">1883</span>                    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Some type variables (</span><span class="si">{</span><span class="n">s_vars</span><span class="si">}</span><span class="s2">) are&quot;</span>
-<span class="linenos">1884</span>                                    <span class="sa">f</span><span class="s2">&quot; not listed in Generic[</span><span class="si">{</span><span class="n">s_args</span><span class="si">}</span><span class="s2">]&quot;</span><span class="p">)</span>
-<span class="linenos">1885</span>                <span class="n">tvars</span> <span class="o">=</span> <span class="n">gvars</span>
-<span class="linenos">1886</span>        <span class="bp">cls</span><span class="o">.</span><span class="n">__parameters__</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">tvars</span><span class="p">)</span>
+<span class="linenos">1855</span>            <span class="n">tvars</span> <span class="o">=</span> <span class="n">_collect_parameters</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="n">__orig_bases__</span><span class="p">)</span>
+<span class="linenos">1856</span>            <span class="c1"># Look for Generic[T1, ..., Tn].</span>
+<span class="linenos">1857</span>            <span class="c1"># If found, tvars must be a subset of it.</span>
+<span class="linenos">1858</span>            <span class="c1"># If not found, tvars is it.</span>
+<span class="linenos">1859</span>            <span class="c1"># Also check for and reject plain Generic,</span>
+<span class="linenos">1860</span>            <span class="c1"># and reject multiple Generic[...].</span>
+<span class="linenos">1861</span>            <span class="n">gvars</span> <span class="o">=</span> <span class="kc">None</span>
+<span class="linenos">1862</span>            <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="n">__orig_bases__</span><span class="p">:</span>
+<span class="linenos">1863</span>                <span class="k">if</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">)</span> <span class="ow">and</span>
+<span class="linenos">1864</span>                        <span class="n">base</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">is</span> <span class="n">Generic</span><span class="p">):</span>
+<span class="linenos">1865</span>                    <span class="k">if</span> <span class="n">gvars</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">1866</span>                        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
+<span class="linenos">1867</span>                            <span class="s2">&quot;Cannot inherit from Generic[...] multiple times.&quot;</span><span class="p">)</span>
+<span class="linenos">1868</span>                    <span class="n">gvars</span> <span class="o">=</span> <span class="n">base</span><span class="o">.</span><span class="n">__parameters__</span>
+<span class="linenos">1869</span>            <span class="k">if</span> <span class="n">gvars</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">1870</span>                <span class="n">tvarset</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">tvars</span><span class="p">)</span>
+<span class="linenos">1871</span>                <span class="n">gvarset</span> <span class="o">=</span> <span class="nb">set</span><span class="p">(</span><span class="n">gvars</span><span class="p">)</span>
+<span class="linenos">1872</span>                <span class="k">if</span> <span class="ow">not</span> <span class="n">tvarset</span> <span class="o">&lt;=</span> <span class="n">gvarset</span><span class="p">:</span>
+<span class="linenos">1873</span>                    <span class="n">s_vars</span> <span class="o">=</span> <span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">tvars</span> <span class="k">if</span> <span class="n">t</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">gvarset</span><span class="p">)</span>
+<span class="linenos">1874</span>                    <span class="n">s_args</span> <span class="o">=</span> <span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">g</span><span class="p">)</span> <span class="k">for</span> <span class="n">g</span> <span class="ow">in</span> <span class="n">gvars</span><span class="p">)</span>
+<span class="linenos">1875</span>                    <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Some type variables (</span><span class="si">{</span><span class="n">s_vars</span><span class="si">}</span><span class="s2">) are&quot;</span>
+<span class="linenos">1876</span>                                    <span class="sa">f</span><span class="s2">&quot; not listed in Generic[</span><span class="si">{</span><span class="n">s_args</span><span class="si">}</span><span class="s2">]&quot;</span><span class="p">)</span>
+<span class="linenos">1877</span>                <span class="n">tvars</span> <span class="o">=</span> <span class="n">gvars</span>
+<span class="linenos">1878</span>        <span class="bp">cls</span><span class="o">.</span><span class="n">__parameters__</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">tvars</span><span class="p">)</span>
+<span class="linenos">1879</span>
+<span class="linenos">1880</span>
+<span class="linenos">1881</span><span class="k">class</span> <span class="nc">_TypingEllipsis</span><span class="p">:</span>
+<span class="linenos">1882</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal placeholder for ... (ellipsis).&quot;&quot;&quot;</span>
+<span class="linenos">1883</span>
+<span class="linenos">1884</span>
+<span class="linenos">1885</span><span class="n">_TYPING_INTERNALS</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;__parameters__&#39;</span><span class="p">,</span> <span class="s1">&#39;__orig_bases__&#39;</span><span class="p">,</span>  <span class="s1">&#39;__orig_class__&#39;</span><span class="p">,</span>
+<span class="linenos">1886</span>                     <span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="s1">&#39;_is_runtime_protocol&#39;</span><span class="p">]</span>
 <span class="linenos">1887</span>
-<span class="linenos">1888</span>
-<span class="linenos">1889</span><span class="k">class</span> <span class="nc">_TypingEllipsis</span><span class="p">:</span>
-<span class="linenos">1890</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Internal placeholder for ... (ellipsis).&quot;&quot;&quot;</span>
+<span class="linenos">1888</span><span class="n">_SPECIAL_NAMES</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;__abstractmethods__&#39;</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="s1">&#39;__dict__&#39;</span><span class="p">,</span> <span class="s1">&#39;__doc__&#39;</span><span class="p">,</span>
+<span class="linenos">1889</span>                  <span class="s1">&#39;__init__&#39;</span><span class="p">,</span> <span class="s1">&#39;__module__&#39;</span><span class="p">,</span> <span class="s1">&#39;__new__&#39;</span><span class="p">,</span> <span class="s1">&#39;__slots__&#39;</span><span class="p">,</span>
+<span class="linenos">1890</span>                  <span class="s1">&#39;__subclasshook__&#39;</span><span class="p">,</span> <span class="s1">&#39;__weakref__&#39;</span><span class="p">,</span> <span class="s1">&#39;__class_getitem__&#39;</span><span class="p">]</span>
 <span class="linenos">1891</span>
-<span class="linenos">1892</span>
-<span class="linenos">1893</span><span class="n">_TYPING_INTERNALS</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;__parameters__&#39;</span><span class="p">,</span> <span class="s1">&#39;__orig_bases__&#39;</span><span class="p">,</span>  <span class="s1">&#39;__orig_class__&#39;</span><span class="p">,</span>
-<span class="linenos">1894</span>                     <span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="s1">&#39;_is_runtime_protocol&#39;</span><span class="p">,</span> <span class="s1">&#39;__final__&#39;</span><span class="p">]</span>
+<span class="linenos">1892</span><span class="c1"># These special attributes will be not collected as protocol members.</span>
+<span class="linenos">1893</span><span class="n">EXCLUDED_ATTRIBUTES</span> <span class="o">=</span> <span class="n">_TYPING_INTERNALS</span> <span class="o">+</span> <span class="n">_SPECIAL_NAMES</span> <span class="o">+</span> <span class="p">[</span><span class="s1">&#39;_MutableMapping__marker&#39;</span><span class="p">]</span>
+<span class="linenos">1894</span>
 <span class="linenos">1895</span>
-<span class="linenos">1896</span><span class="n">_SPECIAL_NAMES</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;__abstractmethods__&#39;</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="s1">&#39;__dict__&#39;</span><span class="p">,</span> <span class="s1">&#39;__doc__&#39;</span><span class="p">,</span>
-<span class="linenos">1897</span>                  <span class="s1">&#39;__init__&#39;</span><span class="p">,</span> <span class="s1">&#39;__module__&#39;</span><span class="p">,</span> <span class="s1">&#39;__new__&#39;</span><span class="p">,</span> <span class="s1">&#39;__slots__&#39;</span><span class="p">,</span>
-<span class="linenos">1898</span>                  <span class="s1">&#39;__subclasshook__&#39;</span><span class="p">,</span> <span class="s1">&#39;__weakref__&#39;</span><span class="p">,</span> <span class="s1">&#39;__class_getitem__&#39;</span><span class="p">]</span>
-<span class="linenos">1899</span>
-<span class="linenos">1900</span><span class="c1"># These special attributes will be not collected as protocol members.</span>
-<span class="linenos">1901</span><span class="n">EXCLUDED_ATTRIBUTES</span> <span class="o">=</span> <span class="n">_TYPING_INTERNALS</span> <span class="o">+</span> <span class="n">_SPECIAL_NAMES</span> <span class="o">+</span> <span class="p">[</span><span class="s1">&#39;_MutableMapping__marker&#39;</span><span class="p">]</span>
-<span class="linenos">1902</span>
-<span class="linenos">1903</span>
-<span class="linenos">1904</span><span class="k">def</span> <span class="nf">_get_protocol_attrs</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
-<span class="linenos">1905</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Collect protocol members from a protocol class objects.</span>
-<span class="linenos">1906</span>
-<span class="linenos">1907</span><span class="sd">    This includes names actually defined in the class dictionary, as well</span>
-<span class="linenos">1908</span><span class="sd">    as names that appear in annotations. Special names (above) are skipped.</span>
-<span class="linenos">1909</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1910</span>    <span class="n">attrs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
-<span class="linenos">1911</span>    <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__mro__</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>  <span class="c1"># without object</span>
-<span class="linenos">1912</span>        <span class="k">if</span> <span class="n">base</span><span class="o">.</span><span class="vm">__name__</span> <span class="ow">in</span> <span class="p">(</span><span class="s1">&#39;Protocol&#39;</span><span class="p">,</span> <span class="s1">&#39;Generic&#39;</span><span class="p">):</span>
-<span class="linenos">1913</span>            <span class="k">continue</span>
-<span class="linenos">1914</span>        <span class="n">annotations</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
-<span class="linenos">1915</span>        <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">annotations</span><span class="o">.</span><span class="n">keys</span><span class="p">()):</span>
-<span class="linenos">1916</span>            <span class="k">if</span> <span class="ow">not</span> <span class="n">attr</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">&#39;_abc_&#39;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">attr</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">EXCLUDED_ATTRIBUTES</span><span class="p">:</span>
-<span class="linenos">1917</span>                <span class="n">attrs</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span>
-<span class="linenos">1918</span>    <span class="k">return</span> <span class="n">attrs</span>
-<span class="linenos">1919</span>
+<span class="linenos">1896</span><span class="k">def</span> <span class="nf">_get_protocol_attrs</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
+<span class="linenos">1897</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Collect protocol members from a protocol class objects.</span>
+<span class="linenos">1898</span>
+<span class="linenos">1899</span><span class="sd">    This includes names actually defined in the class dictionary, as well</span>
+<span class="linenos">1900</span><span class="sd">    as names that appear in annotations. Special names (above) are skipped.</span>
+<span class="linenos">1901</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">1902</span>    <span class="n">attrs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
+<span class="linenos">1903</span>    <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__mro__</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>  <span class="c1"># without object</span>
+<span class="linenos">1904</span>        <span class="k">if</span> <span class="n">base</span><span class="o">.</span><span class="vm">__name__</span> <span class="ow">in</span> <span class="p">(</span><span class="s1">&#39;Protocol&#39;</span><span class="p">,</span> <span class="s1">&#39;Generic&#39;</span><span class="p">):</span>
+<span class="linenos">1905</span>            <span class="k">continue</span>
+<span class="linenos">1906</span>        <span class="n">annotations</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
+<span class="linenos">1907</span>        <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">keys</span><span class="p">())</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">annotations</span><span class="o">.</span><span class="n">keys</span><span class="p">()):</span>
+<span class="linenos">1908</span>            <span class="k">if</span> <span class="ow">not</span> <span class="n">attr</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">&#39;_abc_&#39;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">attr</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">EXCLUDED_ATTRIBUTES</span><span class="p">:</span>
+<span class="linenos">1909</span>                <span class="n">attrs</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span>
+<span class="linenos">1910</span>    <span class="k">return</span> <span class="n">attrs</span>
+<span class="linenos">1911</span>
+<span class="linenos">1912</span>
+<span class="linenos">1913</span><span class="k">def</span> <span class="nf">_is_callable_members_only</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
+<span class="linenos">1914</span>    <span class="c1"># PEP 544 prohibits using issubclass() with protocols that have non-method members.</span>
+<span class="linenos">1915</span>    <span class="k">return</span> <span class="nb">all</span><span class="p">(</span><span class="nb">callable</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">attr</span><span class="p">,</span> <span class="kc">None</span><span class="p">))</span> <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">_get_protocol_attrs</span><span class="p">(</span><span class="bp">cls</span><span class="p">))</span>
+<span class="linenos">1916</span>
+<span class="linenos">1917</span>
+<span class="linenos">1918</span><span class="k">def</span> <span class="nf">_no_init_or_replace_init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos">1919</span>    <span class="bp">cls</span> <span class="o">=</span> <span class="nb">type</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
 <span class="linenos">1920</span>
-<span class="linenos">1921</span><span class="k">def</span> <span class="nf">_is_callable_members_only</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
-<span class="linenos">1922</span>    <span class="c1"># PEP 544 prohibits using issubclass() with protocols that have non-method members.</span>
-<span class="linenos">1923</span>    <span class="k">return</span> <span class="nb">all</span><span class="p">(</span><span class="nb">callable</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">attr</span><span class="p">,</span> <span class="kc">None</span><span class="p">))</span> <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">_get_protocol_attrs</span><span class="p">(</span><span class="bp">cls</span><span class="p">))</span>
-<span class="linenos">1924</span>
-<span class="linenos">1925</span>
-<span class="linenos">1926</span><span class="k">def</span> <span class="nf">_no_init_or_replace_init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos">1927</span>    <span class="bp">cls</span> <span class="o">=</span> <span class="nb">type</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+<span class="linenos">1921</span>    <span class="k">if</span> <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">:</span>
+<span class="linenos">1922</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Protocols cannot be instantiated&#39;</span><span class="p">)</span>
+<span class="linenos">1923</span>
+<span class="linenos">1924</span>    <span class="c1"># Already using a custom `__init__`. No need to calculate correct</span>
+<span class="linenos">1925</span>    <span class="c1"># `__init__` to call. This can lead to RecursionError. See bpo-45121.</span>
+<span class="linenos">1926</span>    <span class="k">if</span> <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">_no_init_or_replace_init</span><span class="p">:</span>
+<span class="linenos">1927</span>        <span class="k">return</span>
 <span class="linenos">1928</span>
-<span class="linenos">1929</span>    <span class="k">if</span> <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">:</span>
-<span class="linenos">1930</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Protocols cannot be instantiated&#39;</span><span class="p">)</span>
-<span class="linenos">1931</span>
-<span class="linenos">1932</span>    <span class="c1"># Already using a custom `__init__`. No need to calculate correct</span>
-<span class="linenos">1933</span>    <span class="c1"># `__init__` to call. This can lead to RecursionError. See bpo-45121.</span>
-<span class="linenos">1934</span>    <span class="k">if</span> <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">_no_init_or_replace_init</span><span class="p">:</span>
-<span class="linenos">1935</span>        <span class="k">return</span>
-<span class="linenos">1936</span>
-<span class="linenos">1937</span>    <span class="c1"># Initially, `__init__` of a protocol subclass is set to `_no_init_or_replace_init`.</span>
-<span class="linenos">1938</span>    <span class="c1"># The first instantiation of the subclass will call `_no_init_or_replace_init` which</span>
-<span class="linenos">1939</span>    <span class="c1"># searches for a proper new `__init__` in the MRO. The new `__init__`</span>
-<span class="linenos">1940</span>    <span class="c1"># replaces the subclass&#39; old `__init__` (ie `_no_init_or_replace_init`). Subsequent</span>
-<span class="linenos">1941</span>    <span class="c1"># instantiation of the protocol subclass will thus use the new</span>
-<span class="linenos">1942</span>    <span class="c1"># `__init__` and no longer call `_no_init_or_replace_init`.</span>
-<span class="linenos">1943</span>    <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__mro__</span><span class="p">:</span>
-<span class="linenos">1944</span>        <span class="n">init</span> <span class="o">=</span> <span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__init__&#39;</span><span class="p">,</span> <span class="n">_no_init_or_replace_init</span><span class="p">)</span>
-<span class="linenos">1945</span>        <span class="k">if</span> <span class="n">init</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">_no_init_or_replace_init</span><span class="p">:</span>
-<span class="linenos">1946</span>            <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="o">=</span> <span class="n">init</span>
-<span class="linenos">1947</span>            <span class="k">break</span>
-<span class="linenos">1948</span>    <span class="k">else</span><span class="p">:</span>
-<span class="linenos">1949</span>        <span class="c1"># should not happen</span>
-<span class="linenos">1950</span>        <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="o">=</span> <span class="nb">object</span><span class="o">.</span><span class="fm">__init__</span>
-<span class="linenos">1951</span>
-<span class="linenos">1952</span>    <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos">1929</span>    <span class="c1"># Initially, `__init__` of a protocol subclass is set to `_no_init_or_replace_init`.</span>
+<span class="linenos">1930</span>    <span class="c1"># The first instantiation of the subclass will call `_no_init_or_replace_init` which</span>
+<span class="linenos">1931</span>    <span class="c1"># searches for a proper new `__init__` in the MRO. The new `__init__`</span>
+<span class="linenos">1932</span>    <span class="c1"># replaces the subclass&#39; old `__init__` (ie `_no_init_or_replace_init`). Subsequent</span>
+<span class="linenos">1933</span>    <span class="c1"># instantiation of the protocol subclass will thus use the new</span>
+<span class="linenos">1934</span>    <span class="c1"># `__init__` and no longer call `_no_init_or_replace_init`.</span>
+<span class="linenos">1935</span>    <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__mro__</span><span class="p">:</span>
+<span class="linenos">1936</span>        <span class="n">init</span> <span class="o">=</span> <span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__init__&#39;</span><span class="p">,</span> <span class="n">_no_init_or_replace_init</span><span class="p">)</span>
+<span class="linenos">1937</span>        <span class="k">if</span> <span class="n">init</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">_no_init_or_replace_init</span><span class="p">:</span>
+<span class="linenos">1938</span>            <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="o">=</span> <span class="n">init</span>
+<span class="linenos">1939</span>            <span class="k">break</span>
+<span class="linenos">1940</span>    <span class="k">else</span><span class="p">:</span>
+<span class="linenos">1941</span>        <span class="c1"># should not happen</span>
+<span class="linenos">1942</span>        <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="o">=</span> <span class="nb">object</span><span class="o">.</span><span class="fm">__init__</span>
+<span class="linenos">1943</span>
+<span class="linenos">1944</span>    <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos">1945</span>
+<span class="linenos">1946</span>
+<span class="linenos">1947</span><span class="k">def</span> <span class="nf">_caller</span><span class="p">(</span><span class="n">depth</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="s1">&#39;__main__&#39;</span><span class="p">):</span>
+<span class="linenos">1948</span>    <span class="k">try</span><span class="p">:</span>
+<span class="linenos">1949</span>        <span class="k">return</span> <span class="n">sys</span><span class="o">.</span><span class="n">_getframe</span><span class="p">(</span><span class="n">depth</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">f_globals</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="n">default</span><span class="p">)</span>
+<span class="linenos">1950</span>    <span class="k">except</span> <span class="p">(</span><span class="ne">AttributeError</span><span class="p">,</span> <span class="ne">ValueError</span><span class="p">):</span>  <span class="c1"># For platforms without _getframe()</span>
+<span class="linenos">1951</span>        <span class="k">return</span> <span class="kc">None</span>
+<span class="linenos">1952</span>
 <span class="linenos">1953</span>
-<span class="linenos">1954</span>
-<span class="linenos">1955</span><span class="k">def</span> <span class="nf">_caller</span><span class="p">(</span><span class="n">depth</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">default</span><span class="o">=</span><span class="s1">&#39;__main__&#39;</span><span class="p">):</span>
-<span class="linenos">1956</span>    <span class="k">try</span><span class="p">:</span>
-<span class="linenos">1957</span>        <span class="k">return</span> <span class="n">sys</span><span class="o">.</span><span class="n">_getframe</span><span class="p">(</span><span class="n">depth</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">f_globals</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="n">default</span><span class="p">)</span>
-<span class="linenos">1958</span>    <span class="k">except</span> <span class="p">(</span><span class="ne">AttributeError</span><span class="p">,</span> <span class="ne">ValueError</span><span class="p">):</span>  <span class="c1"># For platforms without _getframe()</span>
-<span class="linenos">1959</span>        <span class="k">return</span> <span class="kc">None</span>
-<span class="linenos">1960</span>
+<span class="linenos">1954</span><span class="k">def</span> <span class="nf">_allow_reckless_class_checks</span><span class="p">(</span><span class="n">depth</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
+<span class="linenos">1955</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Allow instance and class checks for special stdlib modules.</span>
+<span class="linenos">1956</span>
+<span class="linenos">1957</span><span class="sd">    The abc and functools modules indiscriminately call isinstance() and</span>
+<span class="linenos">1958</span><span class="sd">    issubclass() on the whole MRO of a user class, which may contain protocols.</span>
+<span class="linenos">1959</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">1960</span>    <span class="k">return</span> <span class="n">_caller</span><span class="p">(</span><span class="n">depth</span><span class="p">)</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;abc&#39;</span><span class="p">,</span> <span class="s1">&#39;functools&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">}</span>
 <span class="linenos">1961</span>
-<span class="linenos">1962</span><span class="k">def</span> <span class="nf">_allow_reckless_class_checks</span><span class="p">(</span><span class="n">depth</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
-<span class="linenos">1963</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Allow instance and class checks for special stdlib modules.</span>
-<span class="linenos">1964</span>
-<span class="linenos">1965</span><span class="sd">    The abc and functools modules indiscriminately call isinstance() and</span>
-<span class="linenos">1966</span><span class="sd">    issubclass() on the whole MRO of a user class, which may contain protocols.</span>
-<span class="linenos">1967</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">1968</span>    <span class="k">return</span> <span class="n">_caller</span><span class="p">(</span><span class="n">depth</span><span class="p">)</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;abc&#39;</span><span class="p">,</span> <span class="s1">&#39;functools&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">}</span>
-<span class="linenos">1969</span>
+<span class="linenos">1962</span>
+<span class="linenos">1963</span><span class="n">_PROTO_ALLOWLIST</span> <span class="o">=</span> <span class="p">{</span>
+<span class="linenos">1964</span>    <span class="s1">&#39;collections.abc&#39;</span><span class="p">:</span> <span class="p">[</span>
+<span class="linenos">1965</span>        <span class="s1">&#39;Callable&#39;</span><span class="p">,</span> <span class="s1">&#39;Awaitable&#39;</span><span class="p">,</span> <span class="s1">&#39;Iterable&#39;</span><span class="p">,</span> <span class="s1">&#39;Iterator&#39;</span><span class="p">,</span> <span class="s1">&#39;AsyncIterable&#39;</span><span class="p">,</span>
+<span class="linenos">1966</span>        <span class="s1">&#39;Hashable&#39;</span><span class="p">,</span> <span class="s1">&#39;Sized&#39;</span><span class="p">,</span> <span class="s1">&#39;Container&#39;</span><span class="p">,</span> <span class="s1">&#39;Collection&#39;</span><span class="p">,</span> <span class="s1">&#39;Reversible&#39;</span><span class="p">,</span>
+<span class="linenos">1967</span>    <span class="p">],</span>
+<span class="linenos">1968</span>    <span class="s1">&#39;contextlib&#39;</span><span class="p">:</span> <span class="p">[</span><span class="s1">&#39;AbstractContextManager&#39;</span><span class="p">,</span> <span class="s1">&#39;AbstractAsyncContextManager&#39;</span><span class="p">],</span>
+<span class="linenos">1969</span><span class="p">}</span>
 <span class="linenos">1970</span>
-<span class="linenos">1971</span><span class="n">_PROTO_ALLOWLIST</span> <span class="o">=</span> <span class="p">{</span>
-<span class="linenos">1972</span>    <span class="s1">&#39;collections.abc&#39;</span><span class="p">:</span> <span class="p">[</span>
-<span class="linenos">1973</span>        <span class="s1">&#39;Callable&#39;</span><span class="p">,</span> <span class="s1">&#39;Awaitable&#39;</span><span class="p">,</span> <span class="s1">&#39;Iterable&#39;</span><span class="p">,</span> <span class="s1">&#39;Iterator&#39;</span><span class="p">,</span> <span class="s1">&#39;AsyncIterable&#39;</span><span class="p">,</span>
-<span class="linenos">1974</span>        <span class="s1">&#39;Hashable&#39;</span><span class="p">,</span> <span class="s1">&#39;Sized&#39;</span><span class="p">,</span> <span class="s1">&#39;Container&#39;</span><span class="p">,</span> <span class="s1">&#39;Collection&#39;</span><span class="p">,</span> <span class="s1">&#39;Reversible&#39;</span><span class="p">,</span>
-<span class="linenos">1975</span>    <span class="p">],</span>
-<span class="linenos">1976</span>    <span class="s1">&#39;contextlib&#39;</span><span class="p">:</span> <span class="p">[</span><span class="s1">&#39;AbstractContextManager&#39;</span><span class="p">,</span> <span class="s1">&#39;AbstractAsyncContextManager&#39;</span><span class="p">],</span>
-<span class="linenos">1977</span><span class="p">}</span>
-<span class="linenos">1978</span>
-<span class="linenos">1979</span>
-<span class="linenos">1980</span><span class="k">class</span> <span class="nc">_ProtocolMeta</span><span class="p">(</span><span class="n">ABCMeta</span><span class="p">):</span>
-<span class="linenos">1981</span>    <span class="c1"># This metaclass is really unfortunate and exists only because of</span>
-<span class="linenos">1982</span>    <span class="c1"># the lack of __instancehook__.</span>
-<span class="linenos">1983</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">instance</span><span class="p">):</span>
-<span class="linenos">1984</span>        <span class="c1"># We need this method for situations where attributes are</span>
-<span class="linenos">1985</span>        <span class="c1"># assigned in __init__.</span>
-<span class="linenos">1986</span>        <span class="k">if</span> <span class="p">(</span>
-<span class="linenos">1987</span>            <span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">and</span>
-<span class="linenos">1988</span>            <span class="ow">not</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;_is_runtime_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">and</span>
-<span class="linenos">1989</span>            <span class="ow">not</span> <span class="n">_allow_reckless_class_checks</span><span class="p">(</span><span class="n">depth</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
-<span class="linenos">1990</span>        <span class="p">):</span>
-<span class="linenos">1991</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Instance and class checks can only be used with&quot;</span>
-<span class="linenos">1992</span>                            <span class="s2">&quot; @runtime_checkable protocols&quot;</span><span class="p">)</span>
-<span class="linenos">1993</span>
-<span class="linenos">1994</span>        <span class="k">if</span> <span class="p">((</span><span class="ow">not</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">or</span>
-<span class="linenos">1995</span>                <span class="n">_is_callable_members_only</span><span class="p">(</span><span class="bp">cls</span><span class="p">))</span> <span class="ow">and</span>
-<span class="linenos">1996</span>                <span class="nb">issubclass</span><span class="p">(</span><span class="n">instance</span><span class="o">.</span><span class="vm">__class__</span><span class="p">,</span> <span class="bp">cls</span><span class="p">)):</span>
-<span class="linenos">1997</span>            <span class="k">return</span> <span class="kc">True</span>
-<span class="linenos">1998</span>        <span class="k">if</span> <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">:</span>
-<span class="linenos">1999</span>            <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="nb">hasattr</span><span class="p">(</span><span class="n">instance</span><span class="p">,</span> <span class="n">attr</span><span class="p">)</span> <span class="ow">and</span>
-<span class="linenos">2000</span>                    <span class="c1"># All *methods* can be blocked by setting them to None.</span>
-<span class="linenos">2001</span>                    <span class="p">(</span><span class="ow">not</span> <span class="nb">callable</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">attr</span><span class="p">,</span> <span class="kc">None</span><span class="p">))</span> <span class="ow">or</span>
-<span class="linenos">2002</span>                     <span class="nb">getattr</span><span class="p">(</span><span class="n">instance</span><span class="p">,</span> <span class="n">attr</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span>
-<span class="linenos">2003</span>                    <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">_get_protocol_attrs</span><span class="p">(</span><span class="bp">cls</span><span class="p">)):</span>
-<span class="linenos">2004</span>                <span class="k">return</span> <span class="kc">True</span>
-<span class="linenos">2005</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__instancecheck__</span><span class="p">(</span><span class="n">instance</span><span class="p">)</span>
-<span class="linenos">2006</span>
-<span class="linenos">2007</span>
-<span class="linenos">2008</span><span class="k">class</span> <span class="nc">Protocol</span><span class="p">(</span><span class="n">Generic</span><span class="p">,</span> <span class="n">metaclass</span><span class="o">=</span><span class="n">_ProtocolMeta</span><span class="p">):</span>
-<span class="linenos">2009</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Base class for protocol classes.</span>
-<span class="linenos">2010</span>
-<span class="linenos">2011</span><span class="sd">    Protocol classes are defined as::</span>
-<span class="linenos">2012</span>
-<span class="linenos">2013</span><span class="sd">        class Proto(Protocol):</span>
-<span class="linenos">2014</span><span class="sd">            def meth(self) -&gt; int:</span>
-<span class="linenos">2015</span><span class="sd">                ...</span>
-<span class="linenos">2016</span>
-<span class="linenos">2017</span><span class="sd">    Such classes are primarily used with static type checkers that recognize</span>
-<span class="linenos">2018</span><span class="sd">    structural subtyping (static duck-typing).</span>
-<span class="linenos">2019</span>
-<span class="linenos">2020</span><span class="sd">    For example::</span>
-<span class="linenos">2021</span>
-<span class="linenos">2022</span><span class="sd">        class C:</span>
-<span class="linenos">2023</span><span class="sd">            def meth(self) -&gt; int:</span>
-<span class="linenos">2024</span><span class="sd">                return 0</span>
+<span class="linenos">1971</span>
+<span class="linenos">1972</span><span class="k">class</span> <span class="nc">_ProtocolMeta</span><span class="p">(</span><span class="n">ABCMeta</span><span class="p">):</span>
+<span class="linenos">1973</span>    <span class="c1"># This metaclass is really unfortunate and exists only because of</span>
+<span class="linenos">1974</span>    <span class="c1"># the lack of __instancehook__.</span>
+<span class="linenos">1975</span>    <span class="k">def</span> <span class="fm">__instancecheck__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">instance</span><span class="p">):</span>
+<span class="linenos">1976</span>        <span class="c1"># We need this method for situations where attributes are</span>
+<span class="linenos">1977</span>        <span class="c1"># assigned in __init__.</span>
+<span class="linenos">1978</span>        <span class="k">if</span> <span class="p">(</span>
+<span class="linenos">1979</span>            <span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">and</span>
+<span class="linenos">1980</span>            <span class="ow">not</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;_is_runtime_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">and</span>
+<span class="linenos">1981</span>            <span class="ow">not</span> <span class="n">_allow_reckless_class_checks</span><span class="p">(</span><span class="n">depth</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+<span class="linenos">1982</span>        <span class="p">):</span>
+<span class="linenos">1983</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Instance and class checks can only be used with&quot;</span>
+<span class="linenos">1984</span>                            <span class="s2">&quot; @runtime_checkable protocols&quot;</span><span class="p">)</span>
+<span class="linenos">1985</span>
+<span class="linenos">1986</span>        <span class="k">if</span> <span class="p">((</span><span class="ow">not</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">or</span>
+<span class="linenos">1987</span>                <span class="n">_is_callable_members_only</span><span class="p">(</span><span class="bp">cls</span><span class="p">))</span> <span class="ow">and</span>
+<span class="linenos">1988</span>                <span class="nb">issubclass</span><span class="p">(</span><span class="n">instance</span><span class="o">.</span><span class="vm">__class__</span><span class="p">,</span> <span class="bp">cls</span><span class="p">)):</span>
+<span class="linenos">1989</span>            <span class="k">return</span> <span class="kc">True</span>
+<span class="linenos">1990</span>        <span class="k">if</span> <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">:</span>
+<span class="linenos">1991</span>            <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="nb">hasattr</span><span class="p">(</span><span class="n">instance</span><span class="p">,</span> <span class="n">attr</span><span class="p">)</span> <span class="ow">and</span>
+<span class="linenos">1992</span>                    <span class="c1"># All *methods* can be blocked by setting them to None.</span>
+<span class="linenos">1993</span>                    <span class="p">(</span><span class="ow">not</span> <span class="nb">callable</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">attr</span><span class="p">,</span> <span class="kc">None</span><span class="p">))</span> <span class="ow">or</span>
+<span class="linenos">1994</span>                     <span class="nb">getattr</span><span class="p">(</span><span class="n">instance</span><span class="p">,</span> <span class="n">attr</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span>
+<span class="linenos">1995</span>                    <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">_get_protocol_attrs</span><span class="p">(</span><span class="bp">cls</span><span class="p">)):</span>
+<span class="linenos">1996</span>                <span class="k">return</span> <span class="kc">True</span>
+<span class="linenos">1997</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__instancecheck__</span><span class="p">(</span><span class="n">instance</span><span class="p">)</span>
+<span class="linenos">1998</span>
+<span class="linenos">1999</span>
+<span class="linenos">2000</span><span class="k">class</span> <span class="nc">Protocol</span><span class="p">(</span><span class="n">Generic</span><span class="p">,</span> <span class="n">metaclass</span><span class="o">=</span><span class="n">_ProtocolMeta</span><span class="p">):</span>
+<span class="linenos">2001</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Base class for protocol classes.</span>
+<span class="linenos">2002</span>
+<span class="linenos">2003</span><span class="sd">    Protocol classes are defined as::</span>
+<span class="linenos">2004</span>
+<span class="linenos">2005</span><span class="sd">        class Proto(Protocol):</span>
+<span class="linenos">2006</span><span class="sd">            def meth(self) -&gt; int:</span>
+<span class="linenos">2007</span><span class="sd">                ...</span>
+<span class="linenos">2008</span>
+<span class="linenos">2009</span><span class="sd">    Such classes are primarily used with static type checkers that recognize</span>
+<span class="linenos">2010</span><span class="sd">    structural subtyping (static duck-typing), for example::</span>
+<span class="linenos">2011</span>
+<span class="linenos">2012</span><span class="sd">        class C:</span>
+<span class="linenos">2013</span><span class="sd">            def meth(self) -&gt; int:</span>
+<span class="linenos">2014</span><span class="sd">                return 0</span>
+<span class="linenos">2015</span>
+<span class="linenos">2016</span><span class="sd">        def func(x: Proto) -&gt; int:</span>
+<span class="linenos">2017</span><span class="sd">            return x.meth()</span>
+<span class="linenos">2018</span>
+<span class="linenos">2019</span><span class="sd">        func(C())  # Passes static type check</span>
+<span class="linenos">2020</span>
+<span class="linenos">2021</span><span class="sd">    See PEP 544 for details. Protocol classes decorated with</span>
+<span class="linenos">2022</span><span class="sd">    @typing.runtime_checkable act as simple-minded runtime protocols that check</span>
+<span class="linenos">2023</span><span class="sd">    only the presence of given attributes, ignoring their type signatures.</span>
+<span class="linenos">2024</span><span class="sd">    Protocol classes can be generic, they are defined as::</span>
 <span class="linenos">2025</span>
-<span class="linenos">2026</span><span class="sd">        def func(x: Proto) -&gt; int:</span>
-<span class="linenos">2027</span><span class="sd">            return x.meth()</span>
-<span class="linenos">2028</span>
-<span class="linenos">2029</span><span class="sd">        func(C())  # Passes static type check</span>
+<span class="linenos">2026</span><span class="sd">        class GenProto(Protocol[T]):</span>
+<span class="linenos">2027</span><span class="sd">            def meth(self) -&gt; T:</span>
+<span class="linenos">2028</span><span class="sd">                ...</span>
+<span class="linenos">2029</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">2030</span>
-<span class="linenos">2031</span><span class="sd">    See PEP 544 for details. Protocol classes decorated with</span>
-<span class="linenos">2032</span><span class="sd">    @typing.runtime_checkable act as simple-minded runtime protocols that check</span>
-<span class="linenos">2033</span><span class="sd">    only the presence of given attributes, ignoring their type signatures.</span>
-<span class="linenos">2034</span><span class="sd">    Protocol classes can be generic, they are defined as::</span>
-<span class="linenos">2035</span>
-<span class="linenos">2036</span><span class="sd">        class GenProto(Protocol[T]):</span>
-<span class="linenos">2037</span><span class="sd">            def meth(self) -&gt; T:</span>
-<span class="linenos">2038</span><span class="sd">                ...</span>
-<span class="linenos">2039</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2040</span>
-<span class="linenos">2041</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
-<span class="linenos">2042</span>    <span class="n">_is_protocol</span> <span class="o">=</span> <span class="kc">True</span>
-<span class="linenos">2043</span>    <span class="n">_is_runtime_protocol</span> <span class="o">=</span> <span class="kc">False</span>
-<span class="linenos">2044</span>
-<span class="linenos">2045</span>    <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos">2046</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">__init_subclass__</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="linenos">2047</span>
-<span class="linenos">2048</span>        <span class="c1"># Determine if this is a protocol or a concrete subclass.</span>
-<span class="linenos">2049</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
-<span class="linenos">2050</span>            <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span> <span class="o">=</span> <span class="nb">any</span><span class="p">(</span><span class="n">b</span> <span class="ow">is</span> <span class="n">Protocol</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__bases__</span><span class="p">)</span>
-<span class="linenos">2051</span>
-<span class="linenos">2052</span>        <span class="c1"># Set (or override) the protocol subclass hook.</span>
-<span class="linenos">2053</span>        <span class="k">def</span> <span class="nf">_proto_hook</span><span class="p">(</span><span class="n">other</span><span class="p">):</span>
-<span class="linenos">2054</span>            <span class="k">if</span> <span class="ow">not</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
-<span class="linenos">2055</span>                <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">2056</span>
-<span class="linenos">2057</span>            <span class="c1"># First, perform various sanity checks.</span>
-<span class="linenos">2058</span>            <span class="k">if</span> <span class="ow">not</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;_is_runtime_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
-<span class="linenos">2059</span>                <span class="k">if</span> <span class="n">_allow_reckless_class_checks</span><span class="p">():</span>
-<span class="linenos">2060</span>                    <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">2061</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Instance and class checks can only be used with&quot;</span>
-<span class="linenos">2062</span>                                <span class="s2">&quot; @runtime_checkable protocols&quot;</span><span class="p">)</span>
-<span class="linenos">2063</span>            <span class="k">if</span> <span class="ow">not</span> <span class="n">_is_callable_members_only</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
-<span class="linenos">2064</span>                <span class="k">if</span> <span class="n">_allow_reckless_class_checks</span><span class="p">():</span>
-<span class="linenos">2065</span>                    <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">2066</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Protocols with non-method members&quot;</span>
-<span class="linenos">2067</span>                                <span class="s2">&quot; don&#39;t support issubclass()&quot;</span><span class="p">)</span>
-<span class="linenos">2068</span>            <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
-<span class="linenos">2069</span>                <span class="c1"># Same error message as for issubclass(1, int).</span>
-<span class="linenos">2070</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;issubclass() arg 1 must be a class&#39;</span><span class="p">)</span>
-<span class="linenos">2071</span>
-<span class="linenos">2072</span>            <span class="c1"># Second, perform the actual structural compatibility check.</span>
-<span class="linenos">2073</span>            <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">_get_protocol_attrs</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
-<span class="linenos">2074</span>                <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">other</span><span class="o">.</span><span class="vm">__mro__</span><span class="p">:</span>
-<span class="linenos">2075</span>                    <span class="c1"># Check if the members appears in the class dictionary...</span>
-<span class="linenos">2076</span>                    <span class="k">if</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
-<span class="linenos">2077</span>                        <span class="k">if</span> <span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">[</span><span class="n">attr</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2078</span>                            <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">2079</span>                        <span class="k">break</span>
+<span class="linenos">2031</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2032</span>    <span class="n">_is_protocol</span> <span class="o">=</span> <span class="kc">True</span>
+<span class="linenos">2033</span>    <span class="n">_is_runtime_protocol</span> <span class="o">=</span> <span class="kc">False</span>
+<span class="linenos">2034</span>
+<span class="linenos">2035</span>    <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos">2036</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">__init_subclass__</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="linenos">2037</span>
+<span class="linenos">2038</span>        <span class="c1"># Determine if this is a protocol or a concrete subclass.</span>
+<span class="linenos">2039</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+<span class="linenos">2040</span>            <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span> <span class="o">=</span> <span class="nb">any</span><span class="p">(</span><span class="n">b</span> <span class="ow">is</span> <span class="n">Protocol</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__bases__</span><span class="p">)</span>
+<span class="linenos">2041</span>
+<span class="linenos">2042</span>        <span class="c1"># Set (or override) the protocol subclass hook.</span>
+<span class="linenos">2043</span>        <span class="k">def</span> <span class="nf">_proto_hook</span><span class="p">(</span><span class="n">other</span><span class="p">):</span>
+<span class="linenos">2044</span>            <span class="k">if</span> <span class="ow">not</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;_is_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+<span class="linenos">2045</span>                <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">2046</span>
+<span class="linenos">2047</span>            <span class="c1"># First, perform various sanity checks.</span>
+<span class="linenos">2048</span>            <span class="k">if</span> <span class="ow">not</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="s1">&#39;_is_runtime_protocol&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+<span class="linenos">2049</span>                <span class="k">if</span> <span class="n">_allow_reckless_class_checks</span><span class="p">():</span>
+<span class="linenos">2050</span>                    <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">2051</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Instance and class checks can only be used with&quot;</span>
+<span class="linenos">2052</span>                                <span class="s2">&quot; @runtime_checkable protocols&quot;</span><span class="p">)</span>
+<span class="linenos">2053</span>            <span class="k">if</span> <span class="ow">not</span> <span class="n">_is_callable_members_only</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
+<span class="linenos">2054</span>                <span class="k">if</span> <span class="n">_allow_reckless_class_checks</span><span class="p">():</span>
+<span class="linenos">2055</span>                    <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">2056</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Protocols with non-method members&quot;</span>
+<span class="linenos">2057</span>                                <span class="s2">&quot; don&#39;t support issubclass()&quot;</span><span class="p">)</span>
+<span class="linenos">2058</span>            <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
+<span class="linenos">2059</span>                <span class="c1"># Same error message as for issubclass(1, int).</span>
+<span class="linenos">2060</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;issubclass() arg 1 must be a class&#39;</span><span class="p">)</span>
+<span class="linenos">2061</span>
+<span class="linenos">2062</span>            <span class="c1"># Second, perform the actual structural compatibility check.</span>
+<span class="linenos">2063</span>            <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">_get_protocol_attrs</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
+<span class="linenos">2064</span>                <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">other</span><span class="o">.</span><span class="vm">__mro__</span><span class="p">:</span>
+<span class="linenos">2065</span>                    <span class="c1"># Check if the members appears in the class dictionary...</span>
+<span class="linenos">2066</span>                    <span class="k">if</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
+<span class="linenos">2067</span>                        <span class="k">if</span> <span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">[</span><span class="n">attr</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2068</span>                            <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">2069</span>                        <span class="k">break</span>
+<span class="linenos">2070</span>
+<span class="linenos">2071</span>                    <span class="c1"># ...or in annotations, if it is a sub-protocol.</span>
+<span class="linenos">2072</span>                    <span class="n">annotations</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
+<span class="linenos">2073</span>                    <span class="k">if</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">annotations</span><span class="p">,</span> <span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Mapping</span><span class="p">)</span> <span class="ow">and</span>
+<span class="linenos">2074</span>                            <span class="n">attr</span> <span class="ow">in</span> <span class="n">annotations</span> <span class="ow">and</span>
+<span class="linenos">2075</span>                            <span class="nb">issubclass</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="ow">and</span> <span class="n">other</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">):</span>
+<span class="linenos">2076</span>                        <span class="k">break</span>
+<span class="linenos">2077</span>                <span class="k">else</span><span class="p">:</span>
+<span class="linenos">2078</span>                    <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">2079</span>            <span class="k">return</span> <span class="kc">True</span>
 <span class="linenos">2080</span>
-<span class="linenos">2081</span>                    <span class="c1"># ...or in annotations, if it is a sub-protocol.</span>
-<span class="linenos">2082</span>                    <span class="n">annotations</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
-<span class="linenos">2083</span>                    <span class="k">if</span> <span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">annotations</span><span class="p">,</span> <span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Mapping</span><span class="p">)</span> <span class="ow">and</span>
-<span class="linenos">2084</span>                            <span class="n">attr</span> <span class="ow">in</span> <span class="n">annotations</span> <span class="ow">and</span>
-<span class="linenos">2085</span>                            <span class="nb">issubclass</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="ow">and</span> <span class="n">other</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">):</span>
-<span class="linenos">2086</span>                        <span class="k">break</span>
-<span class="linenos">2087</span>                <span class="k">else</span><span class="p">:</span>
-<span class="linenos">2088</span>                    <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">2089</span>            <span class="k">return</span> <span class="kc">True</span>
-<span class="linenos">2090</span>
-<span class="linenos">2091</span>        <span class="k">if</span> <span class="s1">&#39;__subclasshook__&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
-<span class="linenos">2092</span>            <span class="bp">cls</span><span class="o">.</span><span class="n">__subclasshook__</span> <span class="o">=</span> <span class="n">_proto_hook</span>
-<span class="linenos">2093</span>
-<span class="linenos">2094</span>        <span class="c1"># We have nothing more to do for non-protocols...</span>
-<span class="linenos">2095</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">:</span>
-<span class="linenos">2096</span>            <span class="k">return</span>
-<span class="linenos">2097</span>
-<span class="linenos">2098</span>        <span class="c1"># ... otherwise check consistency of bases, and prohibit instantiation.</span>
-<span class="linenos">2099</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__bases__</span><span class="p">:</span>
-<span class="linenos">2100</span>            <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">base</span> <span class="ow">in</span> <span class="p">(</span><span class="nb">object</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="ow">or</span>
-<span class="linenos">2101</span>                    <span class="n">base</span><span class="o">.</span><span class="vm">__module__</span> <span class="ow">in</span> <span class="n">_PROTO_ALLOWLIST</span> <span class="ow">and</span>
-<span class="linenos">2102</span>                    <span class="n">base</span><span class="o">.</span><span class="vm">__name__</span> <span class="ow">in</span> <span class="n">_PROTO_ALLOWLIST</span><span class="p">[</span><span class="n">base</span><span class="o">.</span><span class="vm">__module__</span><span class="p">]</span> <span class="ow">or</span>
-<span class="linenos">2103</span>                    <span class="nb">issubclass</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="ow">and</span> <span class="n">base</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">):</span>
-<span class="linenos">2104</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Protocols can only inherit from other&#39;</span>
-<span class="linenos">2105</span>                                <span class="s1">&#39; protocols, got </span><span class="si">%r</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">base</span><span class="p">)</span>
-<span class="linenos">2106</span>        <span class="k">if</span> <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="ow">is</span> <span class="n">Protocol</span><span class="o">.</span><span class="fm">__init__</span><span class="p">:</span>
-<span class="linenos">2107</span>            <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="o">=</span> <span class="n">_no_init_or_replace_init</span>
-<span class="linenos">2108</span>
-<span class="linenos">2109</span>
-<span class="linenos">2110</span><span class="k">class</span> <span class="nc">_AnnotatedAlias</span><span class="p">(</span><span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">2111</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Runtime representation of an annotated type.</span>
-<span class="linenos">2112</span>
-<span class="linenos">2113</span><span class="sd">    At its core &#39;Annotated[t, dec1, dec2, ...]&#39; is an alias for the type &#39;t&#39;</span>
-<span class="linenos">2114</span><span class="sd">    with extra annotations. The alias behaves like a normal typing alias.</span>
-<span class="linenos">2115</span><span class="sd">    Instantiating is the same as instantiating the underlying type; binding</span>
-<span class="linenos">2116</span><span class="sd">    it to types is also the same.</span>
+<span class="linenos">2081</span>        <span class="k">if</span> <span class="s1">&#39;__subclasshook__&#39;</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
+<span class="linenos">2082</span>            <span class="bp">cls</span><span class="o">.</span><span class="n">__subclasshook__</span> <span class="o">=</span> <span class="n">_proto_hook</span>
+<span class="linenos">2083</span>
+<span class="linenos">2084</span>        <span class="c1"># We have nothing more to do for non-protocols...</span>
+<span class="linenos">2085</span>        <span class="k">if</span> <span class="ow">not</span> <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">:</span>
+<span class="linenos">2086</span>            <span class="k">return</span>
+<span class="linenos">2087</span>
+<span class="linenos">2088</span>        <span class="c1"># ... otherwise check consistency of bases, and prohibit instantiation.</span>
+<span class="linenos">2089</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__bases__</span><span class="p">:</span>
+<span class="linenos">2090</span>            <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">base</span> <span class="ow">in</span> <span class="p">(</span><span class="nb">object</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="ow">or</span>
+<span class="linenos">2091</span>                    <span class="n">base</span><span class="o">.</span><span class="vm">__module__</span> <span class="ow">in</span> <span class="n">_PROTO_ALLOWLIST</span> <span class="ow">and</span>
+<span class="linenos">2092</span>                    <span class="n">base</span><span class="o">.</span><span class="vm">__name__</span> <span class="ow">in</span> <span class="n">_PROTO_ALLOWLIST</span><span class="p">[</span><span class="n">base</span><span class="o">.</span><span class="vm">__module__</span><span class="p">]</span> <span class="ow">or</span>
+<span class="linenos">2093</span>                    <span class="nb">issubclass</span><span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="ow">and</span> <span class="n">base</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">):</span>
+<span class="linenos">2094</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;Protocols can only inherit from other&#39;</span>
+<span class="linenos">2095</span>                                <span class="s1">&#39; protocols, got </span><span class="si">%r</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="n">base</span><span class="p">)</span>
+<span class="linenos">2096</span>        <span class="k">if</span> <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="ow">is</span> <span class="n">Protocol</span><span class="o">.</span><span class="fm">__init__</span><span class="p">:</span>
+<span class="linenos">2097</span>            <span class="bp">cls</span><span class="o">.</span><span class="fm">__init__</span> <span class="o">=</span> <span class="n">_no_init_or_replace_init</span>
+<span class="linenos">2098</span>
+<span class="linenos">2099</span>
+<span class="linenos">2100</span><span class="k">class</span> <span class="nc">_AnnotatedAlias</span><span class="p">(</span><span class="n">_NotIterable</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">_root</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">2101</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Runtime representation of an annotated type.</span>
+<span class="linenos">2102</span>
+<span class="linenos">2103</span><span class="sd">    At its core &#39;Annotated[t, dec1, dec2, ...]&#39; is an alias for the type &#39;t&#39;</span>
+<span class="linenos">2104</span><span class="sd">    with extra annotations. The alias behaves like a normal typing alias.</span>
+<span class="linenos">2105</span><span class="sd">    Instantiating is the same as instantiating the underlying type; binding</span>
+<span class="linenos">2106</span><span class="sd">    it to types is also the same.</span>
+<span class="linenos">2107</span>
+<span class="linenos">2108</span><span class="sd">    The metadata itself is stored in a &#39;__metadata__&#39; attribute as a tuple.</span>
+<span class="linenos">2109</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2110</span>
+<span class="linenos">2111</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">,</span> <span class="n">metadata</span><span class="p">):</span>
+<span class="linenos">2112</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
+<span class="linenos">2113</span>            <span class="n">metadata</span> <span class="o">=</span> <span class="n">origin</span><span class="o">.</span><span class="n">__metadata__</span> <span class="o">+</span> <span class="n">metadata</span>
+<span class="linenos">2114</span>            <span class="n">origin</span> <span class="o">=</span> <span class="n">origin</span><span class="o">.</span><span class="n">__origin__</span>
+<span class="linenos">2115</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">origin</span><span class="p">)</span>
+<span class="linenos">2116</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span> <span class="o">=</span> <span class="n">metadata</span>
 <span class="linenos">2117</span>
-<span class="linenos">2118</span><span class="sd">    The metadata itself is stored in a &#39;__metadata__&#39; attribute as a tuple.</span>
-<span class="linenos">2119</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2120</span>
-<span class="linenos">2121</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">origin</span><span class="p">,</span> <span class="n">metadata</span><span class="p">):</span>
-<span class="linenos">2122</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
-<span class="linenos">2123</span>            <span class="n">metadata</span> <span class="o">=</span> <span class="n">origin</span><span class="o">.</span><span class="n">__metadata__</span> <span class="o">+</span> <span class="n">metadata</span>
-<span class="linenos">2124</span>            <span class="n">origin</span> <span class="o">=</span> <span class="n">origin</span><span class="o">.</span><span class="n">__origin__</span>
-<span class="linenos">2125</span>        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">origin</span><span class="p">)</span>
-<span class="linenos">2126</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span> <span class="o">=</span> <span class="n">metadata</span>
-<span class="linenos">2127</span>
-<span class="linenos">2128</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">2129</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span>
-<span class="linenos">2130</span>        <span class="n">new_type</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-<span class="linenos">2131</span>        <span class="k">return</span> <span class="n">_AnnotatedAlias</span><span class="p">(</span><span class="n">new_type</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span><span class="p">)</span>
-<span class="linenos">2132</span>
-<span class="linenos">2133</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">2134</span>        <span class="k">return</span> <span class="s2">&quot;typing.Annotated[</span><span class="si">{}</span><span class="s2">, </span><span class="si">{}</span><span class="s2">]&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
-<span class="linenos">2135</span>            <span class="n">_type_repr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">),</span>
-<span class="linenos">2136</span>            <span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span><span class="p">)</span>
-<span class="linenos">2137</span>        <span class="p">)</span>
-<span class="linenos">2138</span>
-<span class="linenos">2139</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">2140</span>        <span class="k">return</span> <span class="n">operator</span><span class="o">.</span><span class="n">getitem</span><span class="p">,</span> <span class="p">(</span>
-<span class="linenos">2141</span>            <span class="n">Annotated</span><span class="p">,</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span>
-<span class="linenos">2142</span>        <span class="p">)</span>
-<span class="linenos">2143</span>
-<span class="linenos">2144</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos">2145</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
-<span class="linenos">2146</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
-<span class="linenos">2147</span>        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__origin__</span>
-<span class="linenos">2148</span>                <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__metadata__</span><span class="p">)</span>
-<span class="linenos">2149</span>
-<span class="linenos">2150</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">2151</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span><span class="p">))</span>
-<span class="linenos">2152</span>
-<span class="linenos">2153</span>    <span class="k">def</span> <span class="fm">__getattr__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">):</span>
-<span class="linenos">2154</span>        <span class="k">if</span> <span class="n">attr</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="s1">&#39;__qualname__&#39;</span><span class="p">}:</span>
-<span class="linenos">2155</span>            <span class="k">return</span> <span class="s1">&#39;Annotated&#39;</span>
-<span class="linenos">2156</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getattr__</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span>
-<span class="linenos">2157</span>
+<span class="linenos">2118</span>    <span class="k">def</span> <span class="nf">copy_with</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">2119</span>        <span class="k">assert</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span>
+<span class="linenos">2120</span>        <span class="n">new_type</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<span class="linenos">2121</span>        <span class="k">return</span> <span class="n">_AnnotatedAlias</span><span class="p">(</span><span class="n">new_type</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span><span class="p">)</span>
+<span class="linenos">2122</span>
+<span class="linenos">2123</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">2124</span>        <span class="k">return</span> <span class="s2">&quot;typing.Annotated[</span><span class="si">{}</span><span class="s2">, </span><span class="si">{}</span><span class="s2">]&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
+<span class="linenos">2125</span>            <span class="n">_type_repr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">),</span>
+<span class="linenos">2126</span>            <span class="s2">&quot;, &quot;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">repr</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span><span class="p">)</span>
+<span class="linenos">2127</span>        <span class="p">)</span>
+<span class="linenos">2128</span>
+<span class="linenos">2129</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">2130</span>        <span class="k">return</span> <span class="n">operator</span><span class="o">.</span><span class="n">getitem</span><span class="p">,</span> <span class="p">(</span>
+<span class="linenos">2131</span>            <span class="n">Annotated</span><span class="p">,</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span>
+<span class="linenos">2132</span>        <span class="p">)</span>
+<span class="linenos">2133</span>
+<span class="linenos">2134</span>    <span class="k">def</span> <span class="fm">__eq__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos">2135</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">other</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
+<span class="linenos">2136</span>            <span class="k">return</span> <span class="bp">NotImplemented</span>
+<span class="linenos">2137</span>        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__origin__</span>
+<span class="linenos">2138</span>                <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span> <span class="o">==</span> <span class="n">other</span><span class="o">.</span><span class="n">__metadata__</span><span class="p">)</span>
+<span class="linenos">2139</span>
+<span class="linenos">2140</span>    <span class="k">def</span> <span class="fm">__hash__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">2141</span>        <span class="k">return</span> <span class="nb">hash</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">__metadata__</span><span class="p">))</span>
+<span class="linenos">2142</span>
+<span class="linenos">2143</span>    <span class="k">def</span> <span class="fm">__getattr__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">):</span>
+<span class="linenos">2144</span>        <span class="k">if</span> <span class="n">attr</span> <span class="ow">in</span> <span class="p">{</span><span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="s1">&#39;__qualname__&#39;</span><span class="p">}:</span>
+<span class="linenos">2145</span>            <span class="k">return</span> <span class="s1">&#39;Annotated&#39;</span>
+<span class="linenos">2146</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getattr__</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span>
+<span class="linenos">2147</span>
+<span class="linenos">2148</span>
+<span class="linenos">2149</span><span class="k">class</span> <span class="nc">Annotated</span><span class="p">:</span>
+<span class="linenos">2150</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Add context-specific metadata to a type.</span>
+<span class="linenos">2151</span>
+<span class="linenos">2152</span><span class="sd">    Example: Annotated[int, runtime_check.Unsigned] indicates to the</span>
+<span class="linenos">2153</span><span class="sd">    hypothetical runtime_check module that this type is an unsigned int.</span>
+<span class="linenos">2154</span><span class="sd">    Every other consumer of this type can ignore this metadata and treat</span>
+<span class="linenos">2155</span><span class="sd">    this type as int.</span>
+<span class="linenos">2156</span>
+<span class="linenos">2157</span><span class="sd">    The first argument to Annotated must be a valid type.</span>
 <span class="linenos">2158</span>
-<span class="linenos">2159</span><span class="k">class</span> <span class="nc">Annotated</span><span class="p">:</span>
-<span class="linenos">2160</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Add context-specific metadata to a type.</span>
-<span class="linenos">2161</span>
-<span class="linenos">2162</span><span class="sd">    Example: Annotated[int, runtime_check.Unsigned] indicates to the</span>
-<span class="linenos">2163</span><span class="sd">    hypothetical runtime_check module that this type is an unsigned int.</span>
-<span class="linenos">2164</span><span class="sd">    Every other consumer of this type can ignore this metadata and treat</span>
-<span class="linenos">2165</span><span class="sd">    this type as int.</span>
-<span class="linenos">2166</span>
-<span class="linenos">2167</span><span class="sd">    The first argument to Annotated must be a valid type.</span>
-<span class="linenos">2168</span>
-<span class="linenos">2169</span><span class="sd">    Details:</span>
-<span class="linenos">2170</span>
-<span class="linenos">2171</span><span class="sd">    - It&#39;s an error to call `Annotated` with less than two arguments.</span>
-<span class="linenos">2172</span><span class="sd">    - Access the metadata via the ``__metadata__`` attribute::</span>
-<span class="linenos">2173</span>
-<span class="linenos">2174</span><span class="sd">        assert Annotated[int, &#39;$&#39;].__metadata__ == (&#39;$&#39;,)</span>
-<span class="linenos">2175</span>
-<span class="linenos">2176</span><span class="sd">    - Nested Annotated types are flattened::</span>
-<span class="linenos">2177</span>
-<span class="linenos">2178</span><span class="sd">        assert Annotated[Annotated[T, Ann1, Ann2], Ann3] == Annotated[T, Ann1, Ann2, Ann3]</span>
+<span class="linenos">2159</span><span class="sd">    Details:</span>
+<span class="linenos">2160</span>
+<span class="linenos">2161</span><span class="sd">    - It&#39;s an error to call `Annotated` with less than two arguments.</span>
+<span class="linenos">2162</span><span class="sd">    - Access the metadata via the ``__metadata__`` attribute::</span>
+<span class="linenos">2163</span>
+<span class="linenos">2164</span><span class="sd">        assert Annotated[int, &#39;$&#39;].__metadata__ == (&#39;$&#39;,)</span>
+<span class="linenos">2165</span>
+<span class="linenos">2166</span><span class="sd">    - Nested Annotated are flattened::</span>
+<span class="linenos">2167</span>
+<span class="linenos">2168</span><span class="sd">        assert Annotated[Annotated[T, Ann1, Ann2], Ann3] == Annotated[T, Ann1, Ann2, Ann3]</span>
+<span class="linenos">2169</span>
+<span class="linenos">2170</span><span class="sd">    - Instantiating an annotated type is equivalent to instantiating the</span>
+<span class="linenos">2171</span><span class="sd">    underlying type::</span>
+<span class="linenos">2172</span>
+<span class="linenos">2173</span><span class="sd">        assert Annotated[C, Ann1](5) == C(5)</span>
+<span class="linenos">2174</span>
+<span class="linenos">2175</span><span class="sd">    - Annotated can be used as a generic type alias::</span>
+<span class="linenos">2176</span>
+<span class="linenos">2177</span><span class="sd">        Optimized = Annotated[T, runtime.Optimize()]</span>
+<span class="linenos">2178</span><span class="sd">        assert Optimized[int] == Annotated[int, runtime.Optimize()]</span>
 <span class="linenos">2179</span>
-<span class="linenos">2180</span><span class="sd">    - Instantiating an annotated type is equivalent to instantiating the</span>
-<span class="linenos">2181</span><span class="sd">    underlying type::</span>
+<span class="linenos">2180</span><span class="sd">        OptimizedList = Annotated[List[T], runtime.Optimize()]</span>
+<span class="linenos">2181</span><span class="sd">        assert OptimizedList[int] == Annotated[List[int], runtime.Optimize()]</span>
 <span class="linenos">2182</span>
-<span class="linenos">2183</span><span class="sd">        assert Annotated[C, Ann1](5) == C(5)</span>
+<span class="linenos">2183</span><span class="sd">    - Annotated cannot be used with an unpacked TypeVarTuple::</span>
 <span class="linenos">2184</span>
-<span class="linenos">2185</span><span class="sd">    - Annotated can be used as a generic type alias::</span>
+<span class="linenos">2185</span><span class="sd">        Annotated[*Ts, Ann1]  # NOT valid</span>
 <span class="linenos">2186</span>
-<span class="linenos">2187</span><span class="sd">        Optimized: TypeAlias = Annotated[T, runtime.Optimize()]</span>
-<span class="linenos">2188</span><span class="sd">        assert Optimized[int] == Annotated[int, runtime.Optimize()]</span>
-<span class="linenos">2189</span>
-<span class="linenos">2190</span><span class="sd">        OptimizedList: TypeAlias = Annotated[list[T], runtime.Optimize()]</span>
-<span class="linenos">2191</span><span class="sd">        assert OptimizedList[int] == Annotated[list[int], runtime.Optimize()]</span>
-<span class="linenos">2192</span>
-<span class="linenos">2193</span><span class="sd">    - Annotated cannot be used with an unpacked TypeVarTuple::</span>
+<span class="linenos">2187</span><span class="sd">      This would be equivalent to</span>
+<span class="linenos">2188</span>
+<span class="linenos">2189</span><span class="sd">        Annotated[T1, T2, T3, ..., Ann1]</span>
+<span class="linenos">2190</span>
+<span class="linenos">2191</span><span class="sd">      where T1, T2 etc. are TypeVars, which would be invalid, because</span>
+<span class="linenos">2192</span><span class="sd">      only one type should be passed to Annotated.</span>
+<span class="linenos">2193</span><span class="sd">    &quot;&quot;&quot;</span>
 <span class="linenos">2194</span>
-<span class="linenos">2195</span><span class="sd">        Variadic: TypeAlias = Annotated[*Ts, Ann1]  # NOT valid</span>
+<span class="linenos">2195</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
 <span class="linenos">2196</span>
-<span class="linenos">2197</span><span class="sd">      This would be equivalent to::</span>
-<span class="linenos">2198</span>
-<span class="linenos">2199</span><span class="sd">        Annotated[T1, T2, T3, ..., Ann1]</span>
-<span class="linenos">2200</span>
-<span class="linenos">2201</span><span class="sd">      where T1, T2 etc. are TypeVars, which would be invalid, because</span>
-<span class="linenos">2202</span><span class="sd">      only one type should be passed to Annotated.</span>
-<span class="linenos">2203</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2204</span>
-<span class="linenos">2205</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
-<span class="linenos">2206</span>
-<span class="linenos">2207</span>    <span class="k">def</span> <span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos">2208</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Type Annotated cannot be instantiated.&quot;</span><span class="p">)</span>
-<span class="linenos">2209</span>
-<span class="linenos">2210</span>    <span class="nd">@_tp_cache</span>
-<span class="linenos">2211</span>    <span class="k">def</span> <span class="nf">__class_getitem__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
-<span class="linenos">2212</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mi">2</span><span class="p">:</span>
-<span class="linenos">2213</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Annotated[...] should be used &quot;</span>
-<span class="linenos">2214</span>                            <span class="s2">&quot;with at least two arguments (a type and an &quot;</span>
-<span class="linenos">2215</span>                            <span class="s2">&quot;annotation).&quot;</span><span class="p">)</span>
-<span class="linenos">2216</span>        <span class="k">if</span> <span class="n">_is_unpacked_typevartuple</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
-<span class="linenos">2217</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Annotated[...] should not be used with an &quot;</span>
-<span class="linenos">2218</span>                            <span class="s2">&quot;unpacked TypeVarTuple&quot;</span><span class="p">)</span>
-<span class="linenos">2219</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Annotated[t, ...]: t must be a type.&quot;</span>
-<span class="linenos">2220</span>        <span class="n">origin</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">msg</span><span class="p">,</span> <span class="n">allow_special_forms</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="linenos">2221</span>        <span class="n">metadata</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
-<span class="linenos">2222</span>        <span class="k">return</span> <span class="n">_AnnotatedAlias</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">metadata</span><span class="p">)</span>
-<span class="linenos">2223</span>
-<span class="linenos">2224</span>    <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos">2225</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
-<span class="linenos">2226</span>            <span class="s2">&quot;Cannot subclass </span><span class="si">{}</span><span class="s2">.Annotated&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__module__</span><span class="p">)</span>
-<span class="linenos">2227</span>        <span class="p">)</span>
-<span class="linenos">2228</span>
+<span class="linenos">2197</span>    <span class="k">def</span> <span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos">2198</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Type Annotated cannot be instantiated.&quot;</span><span class="p">)</span>
+<span class="linenos">2199</span>
+<span class="linenos">2200</span>    <span class="nd">@_tp_cache</span>
+<span class="linenos">2201</span>    <span class="k">def</span> <span class="nf">__class_getitem__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">params</span><span class="p">):</span>
+<span class="linenos">2202</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="nb">tuple</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">params</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mi">2</span><span class="p">:</span>
+<span class="linenos">2203</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Annotated[...] should be used &quot;</span>
+<span class="linenos">2204</span>                            <span class="s2">&quot;with at least two arguments (a type and an &quot;</span>
+<span class="linenos">2205</span>                            <span class="s2">&quot;annotation).&quot;</span><span class="p">)</span>
+<span class="linenos">2206</span>        <span class="k">if</span> <span class="n">_is_unpacked_typevartuple</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
+<span class="linenos">2207</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Annotated[...] should not be used with an &quot;</span>
+<span class="linenos">2208</span>                            <span class="s2">&quot;unpacked TypeVarTuple&quot;</span><span class="p">)</span>
+<span class="linenos">2209</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;Annotated[t, ...]: t must be a type.&quot;</span>
+<span class="linenos">2210</span>        <span class="n">origin</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">msg</span><span class="p">,</span> <span class="n">allow_special_forms</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<span class="linenos">2211</span>        <span class="n">metadata</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">params</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
+<span class="linenos">2212</span>        <span class="k">return</span> <span class="n">_AnnotatedAlias</span><span class="p">(</span><span class="n">origin</span><span class="p">,</span> <span class="n">metadata</span><span class="p">)</span>
+<span class="linenos">2213</span>
+<span class="linenos">2214</span>    <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos">2215</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
+<span class="linenos">2216</span>            <span class="s2">&quot;Cannot subclass </span><span class="si">{}</span><span class="s2">.Annotated&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__module__</span><span class="p">)</span>
+<span class="linenos">2217</span>        <span class="p">)</span>
+<span class="linenos">2218</span>
+<span class="linenos">2219</span>
+<span class="linenos">2220</span><span class="k">def</span> <span class="nf">runtime_checkable</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
+<span class="linenos">2221</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mark a protocol class as a runtime protocol.</span>
+<span class="linenos">2222</span>
+<span class="linenos">2223</span><span class="sd">    Such protocol can be used with isinstance() and issubclass().</span>
+<span class="linenos">2224</span><span class="sd">    Raise TypeError if applied to a non-protocol class.</span>
+<span class="linenos">2225</span><span class="sd">    This allows a simple-minded structural check very similar to</span>
+<span class="linenos">2226</span><span class="sd">    one trick ponies in collections.abc such as Iterable.</span>
+<span class="linenos">2227</span>
+<span class="linenos">2228</span><span class="sd">    For example::</span>
 <span class="linenos">2229</span>
-<span class="linenos">2230</span><span class="k">def</span> <span class="nf">runtime_checkable</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
-<span class="linenos">2231</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Mark a protocol class as a runtime protocol.</span>
-<span class="linenos">2232</span>
-<span class="linenos">2233</span><span class="sd">    Such protocol can be used with isinstance() and issubclass().</span>
-<span class="linenos">2234</span><span class="sd">    Raise TypeError if applied to a non-protocol class.</span>
-<span class="linenos">2235</span><span class="sd">    This allows a simple-minded structural check very similar to</span>
-<span class="linenos">2236</span><span class="sd">    one trick ponies in collections.abc such as Iterable.</span>
-<span class="linenos">2237</span>
-<span class="linenos">2238</span><span class="sd">    For example::</span>
-<span class="linenos">2239</span>
-<span class="linenos">2240</span><span class="sd">        @runtime_checkable</span>
-<span class="linenos">2241</span><span class="sd">        class Closable(Protocol):</span>
-<span class="linenos">2242</span><span class="sd">            def close(self): ...</span>
-<span class="linenos">2243</span>
-<span class="linenos">2244</span><span class="sd">        assert isinstance(open(&#39;/some/file&#39;), Closable)</span>
+<span class="linenos">2230</span><span class="sd">        @runtime_checkable</span>
+<span class="linenos">2231</span><span class="sd">        class Closable(Protocol):</span>
+<span class="linenos">2232</span><span class="sd">            def close(self): ...</span>
+<span class="linenos">2233</span>
+<span class="linenos">2234</span><span class="sd">        assert isinstance(open(&#39;/some/file&#39;), Closable)</span>
+<span class="linenos">2235</span>
+<span class="linenos">2236</span><span class="sd">    Warning: this will check only the presence of the required methods,</span>
+<span class="linenos">2237</span><span class="sd">    not their type signatures!</span>
+<span class="linenos">2238</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2239</span>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">issubclass</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="ow">or</span> <span class="ow">not</span> <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">:</span>
+<span class="linenos">2240</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;@runtime_checkable can be only applied to protocol classes,&#39;</span>
+<span class="linenos">2241</span>                        <span class="s1">&#39; got </span><span class="si">%r</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="bp">cls</span><span class="p">)</span>
+<span class="linenos">2242</span>    <span class="bp">cls</span><span class="o">.</span><span class="n">_is_runtime_protocol</span> <span class="o">=</span> <span class="kc">True</span>
+<span class="linenos">2243</span>    <span class="k">return</span> <span class="bp">cls</span>
+<span class="linenos">2244</span>
 <span class="linenos">2245</span>
-<span class="linenos">2246</span><span class="sd">    Warning: this will check only the presence of the required methods,</span>
-<span class="linenos">2247</span><span class="sd">    not their type signatures!</span>
-<span class="linenos">2248</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2249</span>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">issubclass</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="ow">or</span> <span class="ow">not</span> <span class="bp">cls</span><span class="o">.</span><span class="n">_is_protocol</span><span class="p">:</span>
-<span class="linenos">2250</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;@runtime_checkable can be only applied to protocol classes,&#39;</span>
-<span class="linenos">2251</span>                        <span class="s1">&#39; got </span><span class="si">%r</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="bp">cls</span><span class="p">)</span>
-<span class="linenos">2252</span>    <span class="bp">cls</span><span class="o">.</span><span class="n">_is_runtime_protocol</span> <span class="o">=</span> <span class="kc">True</span>
-<span class="linenos">2253</span>    <span class="k">return</span> <span class="bp">cls</span>
-<span class="linenos">2254</span>
+<span class="linenos">2246</span><span class="k">def</span> <span class="nf">cast</span><span class="p">(</span><span class="n">typ</span><span class="p">,</span> <span class="n">val</span><span class="p">):</span>
+<span class="linenos">2247</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Cast a value to a type.</span>
+<span class="linenos">2248</span>
+<span class="linenos">2249</span><span class="sd">    This returns the value unchanged.  To the type checker this</span>
+<span class="linenos">2250</span><span class="sd">    signals that the return value has the designated type, but at</span>
+<span class="linenos">2251</span><span class="sd">    runtime we intentionally don&#39;t check anything (we want this</span>
+<span class="linenos">2252</span><span class="sd">    to be as fast as possible).</span>
+<span class="linenos">2253</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2254</span>    <span class="k">return</span> <span class="n">val</span>
 <span class="linenos">2255</span>
-<span class="linenos">2256</span><span class="k">def</span> <span class="nf">cast</span><span class="p">(</span><span class="n">typ</span><span class="p">,</span> <span class="n">val</span><span class="p">):</span>
-<span class="linenos">2257</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Cast a value to a type.</span>
-<span class="linenos">2258</span>
-<span class="linenos">2259</span><span class="sd">    This returns the value unchanged.  To the type checker this</span>
-<span class="linenos">2260</span><span class="sd">    signals that the return value has the designated type, but at</span>
-<span class="linenos">2261</span><span class="sd">    runtime we intentionally don&#39;t check anything (we want this</span>
-<span class="linenos">2262</span><span class="sd">    to be as fast as possible).</span>
-<span class="linenos">2263</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2264</span>    <span class="k">return</span> <span class="n">val</span>
+<span class="linenos">2256</span>
+<span class="linenos">2257</span><span class="k">def</span> <span class="nf">assert_type</span><span class="p">(</span><span class="n">val</span><span class="p">,</span> <span class="n">typ</span><span class="p">,</span> <span class="o">/</span><span class="p">):</span>
+<span class="linenos">2258</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Ask a static type checker to confirm that the value is of the given type.</span>
+<span class="linenos">2259</span>
+<span class="linenos">2260</span><span class="sd">    At runtime this does nothing: it returns the first argument unchanged with no</span>
+<span class="linenos">2261</span><span class="sd">    checks or side effects, no matter the actual type of the argument.</span>
+<span class="linenos">2262</span>
+<span class="linenos">2263</span><span class="sd">    When a static type checker encounters a call to assert_type(), it</span>
+<span class="linenos">2264</span><span class="sd">    emits an error if the value is not of the specified type::</span>
 <span class="linenos">2265</span>
-<span class="linenos">2266</span>
-<span class="linenos">2267</span><span class="k">def</span> <span class="nf">assert_type</span><span class="p">(</span><span class="n">val</span><span class="p">,</span> <span class="n">typ</span><span class="p">,</span> <span class="o">/</span><span class="p">):</span>
-<span class="linenos">2268</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Ask a static type checker to confirm that the value is of the given type.</span>
-<span class="linenos">2269</span>
-<span class="linenos">2270</span><span class="sd">    At runtime this does nothing: it returns the first argument unchanged with no</span>
-<span class="linenos">2271</span><span class="sd">    checks or side effects, no matter the actual type of the argument.</span>
+<span class="linenos">2266</span><span class="sd">        def greet(name: str) -&gt; None:</span>
+<span class="linenos">2267</span><span class="sd">            assert_type(name, str)  # ok</span>
+<span class="linenos">2268</span><span class="sd">            assert_type(name, int)  # type checker error</span>
+<span class="linenos">2269</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2270</span>    <span class="k">return</span> <span class="n">val</span>
+<span class="linenos">2271</span>
 <span class="linenos">2272</span>
-<span class="linenos">2273</span><span class="sd">    When a static type checker encounters a call to assert_type(), it</span>
-<span class="linenos">2274</span><span class="sd">    emits an error if the value is not of the specified type::</span>
-<span class="linenos">2275</span>
-<span class="linenos">2276</span><span class="sd">        def greet(name: str) -&gt; None:</span>
-<span class="linenos">2277</span><span class="sd">            assert_type(name, str)  # OK</span>
-<span class="linenos">2278</span><span class="sd">            assert_type(name, int)  # type checker error</span>
-<span class="linenos">2279</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2280</span>    <span class="k">return</span> <span class="n">val</span>
-<span class="linenos">2281</span>
-<span class="linenos">2282</span>
-<span class="linenos">2283</span><span class="n">_allowed_types</span> <span class="o">=</span> <span class="p">(</span><span class="n">types</span><span class="o">.</span><span class="n">FunctionType</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">BuiltinFunctionType</span><span class="p">,</span>
-<span class="linenos">2284</span>                  <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">,</span>
-<span class="linenos">2285</span>                  <span class="n">WrapperDescriptorType</span><span class="p">,</span> <span class="n">MethodWrapperType</span><span class="p">,</span> <span class="n">MethodDescriptorType</span><span class="p">)</span>
-<span class="linenos">2286</span>
-<span class="linenos">2287</span>
-<span class="linenos">2288</span><span class="k">def</span> <span class="nf">get_type_hints</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">globalns</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">localns</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">include_extras</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
-<span class="linenos">2289</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Return type hints for an object.</span>
-<span class="linenos">2290</span>
-<span class="linenos">2291</span><span class="sd">    This is often the same as obj.__annotations__, but it handles</span>
-<span class="linenos">2292</span><span class="sd">    forward references encoded as string literals and recursively replaces all</span>
-<span class="linenos">2293</span><span class="sd">    &#39;Annotated[T, ...]&#39; with &#39;T&#39; (unless &#39;include_extras=True&#39;).</span>
-<span class="linenos">2294</span>
-<span class="linenos">2295</span><span class="sd">    The argument may be a module, class, method, or function. The annotations</span>
-<span class="linenos">2296</span><span class="sd">    are returned as a dictionary. For classes, annotations include also</span>
-<span class="linenos">2297</span><span class="sd">    inherited members.</span>
-<span class="linenos">2298</span>
-<span class="linenos">2299</span><span class="sd">    TypeError is raised if the argument is not of a type that can contain</span>
-<span class="linenos">2300</span><span class="sd">    annotations, and an empty dictionary is returned if no annotations are</span>
-<span class="linenos">2301</span><span class="sd">    present.</span>
+<span class="linenos">2273</span><span class="n">_allowed_types</span> <span class="o">=</span> <span class="p">(</span><span class="n">types</span><span class="o">.</span><span class="n">FunctionType</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">BuiltinFunctionType</span><span class="p">,</span>
+<span class="linenos">2274</span>                  <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">,</span>
+<span class="linenos">2275</span>                  <span class="n">WrapperDescriptorType</span><span class="p">,</span> <span class="n">MethodWrapperType</span><span class="p">,</span> <span class="n">MethodDescriptorType</span><span class="p">)</span>
+<span class="linenos">2276</span>
+<span class="linenos">2277</span>
+<span class="linenos">2278</span><span class="k">def</span> <span class="nf">get_type_hints</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">globalns</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">localns</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">include_extras</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="linenos">2279</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Return type hints for an object.</span>
+<span class="linenos">2280</span>
+<span class="linenos">2281</span><span class="sd">    This is often the same as obj.__annotations__, but it handles</span>
+<span class="linenos">2282</span><span class="sd">    forward references encoded as string literals and recursively replaces all</span>
+<span class="linenos">2283</span><span class="sd">    &#39;Annotated[T, ...]&#39; with &#39;T&#39; (unless &#39;include_extras=True&#39;).</span>
+<span class="linenos">2284</span>
+<span class="linenos">2285</span><span class="sd">    The argument may be a module, class, method, or function. The annotations</span>
+<span class="linenos">2286</span><span class="sd">    are returned as a dictionary. For classes, annotations include also</span>
+<span class="linenos">2287</span><span class="sd">    inherited members.</span>
+<span class="linenos">2288</span>
+<span class="linenos">2289</span><span class="sd">    TypeError is raised if the argument is not of a type that can contain</span>
+<span class="linenos">2290</span><span class="sd">    annotations, and an empty dictionary is returned if no annotations are</span>
+<span class="linenos">2291</span><span class="sd">    present.</span>
+<span class="linenos">2292</span>
+<span class="linenos">2293</span><span class="sd">    BEWARE -- the behavior of globalns and localns is counterintuitive</span>
+<span class="linenos">2294</span><span class="sd">    (unless you are familiar with how eval() and exec() work).  The</span>
+<span class="linenos">2295</span><span class="sd">    search order is locals first, then globals.</span>
+<span class="linenos">2296</span>
+<span class="linenos">2297</span><span class="sd">    - If no dict arguments are passed, an attempt is made to use the</span>
+<span class="linenos">2298</span><span class="sd">      globals from obj (or the respective module&#39;s globals for classes),</span>
+<span class="linenos">2299</span><span class="sd">      and these are also used as the locals.  If the object does not appear</span>
+<span class="linenos">2300</span><span class="sd">      to have globals, an empty dictionary is used.  For classes, the search</span>
+<span class="linenos">2301</span><span class="sd">      order is globals first then locals.</span>
 <span class="linenos">2302</span>
-<span class="linenos">2303</span><span class="sd">    BEWARE -- the behavior of globalns and localns is counterintuitive</span>
-<span class="linenos">2304</span><span class="sd">    (unless you are familiar with how eval() and exec() work).  The</span>
-<span class="linenos">2305</span><span class="sd">    search order is locals first, then globals.</span>
-<span class="linenos">2306</span>
-<span class="linenos">2307</span><span class="sd">    - If no dict arguments are passed, an attempt is made to use the</span>
-<span class="linenos">2308</span><span class="sd">      globals from obj (or the respective module&#39;s globals for classes),</span>
-<span class="linenos">2309</span><span class="sd">      and these are also used as the locals.  If the object does not appear</span>
-<span class="linenos">2310</span><span class="sd">      to have globals, an empty dictionary is used.  For classes, the search</span>
-<span class="linenos">2311</span><span class="sd">      order is globals first then locals.</span>
-<span class="linenos">2312</span>
-<span class="linenos">2313</span><span class="sd">    - If one dict argument is passed, it is used for both globals and</span>
-<span class="linenos">2314</span><span class="sd">      locals.</span>
-<span class="linenos">2315</span>
-<span class="linenos">2316</span><span class="sd">    - If two dict arguments are passed, they specify globals and</span>
-<span class="linenos">2317</span><span class="sd">      locals, respectively.</span>
-<span class="linenos">2318</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2319</span>    <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="s1">&#39;__no_type_check__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">):</span>
-<span class="linenos">2320</span>        <span class="k">return</span> <span class="p">{}</span>
-<span class="linenos">2321</span>    <span class="c1"># Classes require a special treatment.</span>
-<span class="linenos">2322</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
-<span class="linenos">2323</span>        <span class="n">hints</span> <span class="o">=</span> <span class="p">{}</span>
-<span class="linenos">2324</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">obj</span><span class="o">.</span><span class="vm">__mro__</span><span class="p">):</span>
-<span class="linenos">2325</span>            <span class="k">if</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2326</span>                <span class="n">base_globals</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">sys</span><span class="o">.</span><span class="n">modules</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__module__</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span> <span class="s1">&#39;__dict__&#39;</span><span class="p">,</span> <span class="p">{})</span>
-<span class="linenos">2327</span>            <span class="k">else</span><span class="p">:</span>
-<span class="linenos">2328</span>                <span class="n">base_globals</span> <span class="o">=</span> <span class="n">globalns</span>
-<span class="linenos">2329</span>            <span class="n">ann</span> <span class="o">=</span> <span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
-<span class="linenos">2330</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">ann</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">GetSetDescriptorType</span><span class="p">):</span>
-<span class="linenos">2331</span>                <span class="n">ann</span> <span class="o">=</span> <span class="p">{}</span>
-<span class="linenos">2332</span>            <span class="n">base_locals</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">vars</span><span class="p">(</span><span class="n">base</span><span class="p">))</span> <span class="k">if</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">localns</span>
-<span class="linenos">2333</span>            <span class="k">if</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2334</span>                <span class="c1"># This is surprising, but required.  Before Python 3.10,</span>
-<span class="linenos">2335</span>                <span class="c1"># get_type_hints only evaluated the globalns of</span>
-<span class="linenos">2336</span>                <span class="c1"># a class.  To maintain backwards compatibility, we reverse</span>
-<span class="linenos">2337</span>                <span class="c1"># the globalns and localns order so that eval() looks into</span>
-<span class="linenos">2338</span>                <span class="c1"># *base_globals* first rather than *base_locals*.</span>
-<span class="linenos">2339</span>                <span class="c1"># This only affects ForwardRefs.</span>
-<span class="linenos">2340</span>                <span class="n">base_globals</span><span class="p">,</span> <span class="n">base_locals</span> <span class="o">=</span> <span class="n">base_locals</span><span class="p">,</span> <span class="n">base_globals</span>
-<span class="linenos">2341</span>            <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">ann</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos">2342</span>                <span class="k">if</span> <span class="n">value</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2343</span>                    <span class="n">value</span> <span class="o">=</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
-<span class="linenos">2344</span>                <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
-<span class="linenos">2345</span>                    <span class="n">value</span> <span class="o">=</span> <span class="n">ForwardRef</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="n">is_argument</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">is_class</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="linenos">2346</span>                <span class="n">value</span> <span class="o">=</span> <span class="n">_eval_type</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="n">base_globals</span><span class="p">,</span> <span class="n">base_locals</span><span class="p">)</span>
-<span class="linenos">2347</span>                <span class="n">hints</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">value</span>
-<span class="linenos">2348</span>        <span class="k">return</span> <span class="n">hints</span> <span class="k">if</span> <span class="n">include_extras</span> <span class="k">else</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="n">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">hints</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span>
-<span class="linenos">2349</span>
-<span class="linenos">2350</span>    <span class="k">if</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2351</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">):</span>
-<span class="linenos">2352</span>            <span class="n">globalns</span> <span class="o">=</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__dict__</span>
-<span class="linenos">2353</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">2354</span>            <span class="n">nsobj</span> <span class="o">=</span> <span class="n">obj</span>
-<span class="linenos">2355</span>            <span class="c1"># Find globalns for the unwrapped object.</span>
-<span class="linenos">2356</span>            <span class="k">while</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">nsobj</span><span class="p">,</span> <span class="s1">&#39;__wrapped__&#39;</span><span class="p">):</span>
-<span class="linenos">2357</span>                <span class="n">nsobj</span> <span class="o">=</span> <span class="n">nsobj</span><span class="o">.</span><span class="n">__wrapped__</span>
-<span class="linenos">2358</span>            <span class="n">globalns</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">nsobj</span><span class="p">,</span> <span class="s1">&#39;__globals__&#39;</span><span class="p">,</span> <span class="p">{})</span>
-<span class="linenos">2359</span>        <span class="k">if</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2360</span>            <span class="n">localns</span> <span class="o">=</span> <span class="n">globalns</span>
-<span class="linenos">2361</span>    <span class="k">elif</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2362</span>        <span class="n">localns</span> <span class="o">=</span> <span class="n">globalns</span>
-<span class="linenos">2363</span>    <span class="n">hints</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
-<span class="linenos">2364</span>    <span class="k">if</span> <span class="n">hints</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2365</span>        <span class="c1"># Return empty annotations for something that _could_ have them.</span>
-<span class="linenos">2366</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">_allowed_types</span><span class="p">):</span>
-<span class="linenos">2367</span>            <span class="k">return</span> <span class="p">{}</span>
-<span class="linenos">2368</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">2369</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">{!r}</span><span class="s1"> is not a module, class, method, &#39;</span>
-<span class="linenos">2370</span>                            <span class="s1">&#39;or function.&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">obj</span><span class="p">))</span>
-<span class="linenos">2371</span>    <span class="n">hints</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">hints</span><span class="p">)</span>
-<span class="linenos">2372</span>    <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hints</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos">2373</span>        <span class="k">if</span> <span class="n">value</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2374</span>            <span class="n">value</span> <span class="o">=</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
-<span class="linenos">2375</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
-<span class="linenos">2376</span>            <span class="c1"># class-level forward refs were handled above, this must be either</span>
-<span class="linenos">2377</span>            <span class="c1"># a module-level annotation or a function argument annotation</span>
-<span class="linenos">2378</span>            <span class="n">value</span> <span class="o">=</span> <span class="n">ForwardRef</span><span class="p">(</span>
-<span class="linenos">2379</span>                <span class="n">value</span><span class="p">,</span>
-<span class="linenos">2380</span>                <span class="n">is_argument</span><span class="o">=</span><span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">),</span>
-<span class="linenos">2381</span>                <span class="n">is_class</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
-<span class="linenos">2382</span>            <span class="p">)</span>
-<span class="linenos">2383</span>        <span class="n">hints</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">_eval_type</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">)</span>
-<span class="linenos">2384</span>    <span class="k">return</span> <span class="n">hints</span> <span class="k">if</span> <span class="n">include_extras</span> <span class="k">else</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="n">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">hints</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span>
-<span class="linenos">2385</span>
-<span class="linenos">2386</span>
-<span class="linenos">2387</span><span class="k">def</span> <span class="nf">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>
-<span class="linenos">2388</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Strip the annotations from a given type.&quot;&quot;&quot;</span>
-<span class="linenos">2389</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
-<span class="linenos">2390</span>        <span class="k">return</span> <span class="n">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
-<span class="linenos">2391</span>    <span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="s2">&quot;__origin__&quot;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">t</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">in</span> <span class="p">(</span><span class="n">Required</span><span class="p">,</span> <span class="n">NotRequired</span><span class="p">):</span>
-<span class="linenos">2392</span>        <span class="k">return</span> <span class="n">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="linenos">2393</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">):</span>
+<span class="linenos">2303</span><span class="sd">    - If one dict argument is passed, it is used for both globals and</span>
+<span class="linenos">2304</span><span class="sd">      locals.</span>
+<span class="linenos">2305</span>
+<span class="linenos">2306</span><span class="sd">    - If two dict arguments are passed, they specify globals and</span>
+<span class="linenos">2307</span><span class="sd">      locals, respectively.</span>
+<span class="linenos">2308</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2309</span>    <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="s1">&#39;__no_type_check__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">):</span>
+<span class="linenos">2310</span>        <span class="k">return</span> <span class="p">{}</span>
+<span class="linenos">2311</span>    <span class="c1"># Classes require a special treatment.</span>
+<span class="linenos">2312</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
+<span class="linenos">2313</span>        <span class="n">hints</span> <span class="o">=</span> <span class="p">{}</span>
+<span class="linenos">2314</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="nb">reversed</span><span class="p">(</span><span class="n">obj</span><span class="o">.</span><span class="vm">__mro__</span><span class="p">):</span>
+<span class="linenos">2315</span>            <span class="k">if</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2316</span>                <span class="n">base_globals</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">sys</span><span class="o">.</span><span class="n">modules</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__module__</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span> <span class="s1">&#39;__dict__&#39;</span><span class="p">,</span> <span class="p">{})</span>
+<span class="linenos">2317</span>            <span class="k">else</span><span class="p">:</span>
+<span class="linenos">2318</span>                <span class="n">base_globals</span> <span class="o">=</span> <span class="n">globalns</span>
+<span class="linenos">2319</span>            <span class="n">ann</span> <span class="o">=</span> <span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
+<span class="linenos">2320</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">ann</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">GetSetDescriptorType</span><span class="p">):</span>
+<span class="linenos">2321</span>                <span class="n">ann</span> <span class="o">=</span> <span class="p">{}</span>
+<span class="linenos">2322</span>            <span class="n">base_locals</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">vars</span><span class="p">(</span><span class="n">base</span><span class="p">))</span> <span class="k">if</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">localns</span>
+<span class="linenos">2323</span>            <span class="k">if</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2324</span>                <span class="c1"># This is surprising, but required.  Before Python 3.10,</span>
+<span class="linenos">2325</span>                <span class="c1"># get_type_hints only evaluated the globalns of</span>
+<span class="linenos">2326</span>                <span class="c1"># a class.  To maintain backwards compatibility, we reverse</span>
+<span class="linenos">2327</span>                <span class="c1"># the globalns and localns order so that eval() looks into</span>
+<span class="linenos">2328</span>                <span class="c1"># *base_globals* first rather than *base_locals*.</span>
+<span class="linenos">2329</span>                <span class="c1"># This only affects ForwardRefs.</span>
+<span class="linenos">2330</span>                <span class="n">base_globals</span><span class="p">,</span> <span class="n">base_locals</span> <span class="o">=</span> <span class="n">base_locals</span><span class="p">,</span> <span class="n">base_globals</span>
+<span class="linenos">2331</span>            <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">ann</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos">2332</span>                <span class="k">if</span> <span class="n">value</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2333</span>                    <span class="n">value</span> <span class="o">=</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
+<span class="linenos">2334</span>                <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+<span class="linenos">2335</span>                    <span class="n">value</span> <span class="o">=</span> <span class="n">ForwardRef</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="n">is_argument</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">is_class</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<span class="linenos">2336</span>                <span class="n">value</span> <span class="o">=</span> <span class="n">_eval_type</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="n">base_globals</span><span class="p">,</span> <span class="n">base_locals</span><span class="p">)</span>
+<span class="linenos">2337</span>                <span class="n">hints</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">value</span>
+<span class="linenos">2338</span>        <span class="k">return</span> <span class="n">hints</span> <span class="k">if</span> <span class="n">include_extras</span> <span class="k">else</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="n">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">hints</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span>
+<span class="linenos">2339</span>
+<span class="linenos">2340</span>    <span class="k">if</span> <span class="n">globalns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2341</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">):</span>
+<span class="linenos">2342</span>            <span class="n">globalns</span> <span class="o">=</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__dict__</span>
+<span class="linenos">2343</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">2344</span>            <span class="n">nsobj</span> <span class="o">=</span> <span class="n">obj</span>
+<span class="linenos">2345</span>            <span class="c1"># Find globalns for the unwrapped object.</span>
+<span class="linenos">2346</span>            <span class="k">while</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">nsobj</span><span class="p">,</span> <span class="s1">&#39;__wrapped__&#39;</span><span class="p">):</span>
+<span class="linenos">2347</span>                <span class="n">nsobj</span> <span class="o">=</span> <span class="n">nsobj</span><span class="o">.</span><span class="n">__wrapped__</span>
+<span class="linenos">2348</span>            <span class="n">globalns</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">nsobj</span><span class="p">,</span> <span class="s1">&#39;__globals__&#39;</span><span class="p">,</span> <span class="p">{})</span>
+<span class="linenos">2349</span>        <span class="k">if</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2350</span>            <span class="n">localns</span> <span class="o">=</span> <span class="n">globalns</span>
+<span class="linenos">2351</span>    <span class="k">elif</span> <span class="n">localns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2352</span>        <span class="n">localns</span> <span class="o">=</span> <span class="n">globalns</span>
+<span class="linenos">2353</span>    <span class="n">hints</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
+<span class="linenos">2354</span>    <span class="k">if</span> <span class="n">hints</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2355</span>        <span class="c1"># Return empty annotations for something that _could_ have them.</span>
+<span class="linenos">2356</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">_allowed_types</span><span class="p">):</span>
+<span class="linenos">2357</span>            <span class="k">return</span> <span class="p">{}</span>
+<span class="linenos">2358</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">2359</span>            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">{!r}</span><span class="s1"> is not a module, class, method, &#39;</span>
+<span class="linenos">2360</span>                            <span class="s1">&#39;or function.&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">obj</span><span class="p">))</span>
+<span class="linenos">2361</span>    <span class="n">hints</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="n">hints</span><span class="p">)</span>
+<span class="linenos">2362</span>    <span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hints</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos">2363</span>        <span class="k">if</span> <span class="n">value</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2364</span>            <span class="n">value</span> <span class="o">=</span> <span class="nb">type</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
+<span class="linenos">2365</span>        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+<span class="linenos">2366</span>            <span class="c1"># class-level forward refs were handled above, this must be either</span>
+<span class="linenos">2367</span>            <span class="c1"># a module-level annotation or a function argument annotation</span>
+<span class="linenos">2368</span>            <span class="n">value</span> <span class="o">=</span> <span class="n">ForwardRef</span><span class="p">(</span>
+<span class="linenos">2369</span>                <span class="n">value</span><span class="p">,</span>
+<span class="linenos">2370</span>                <span class="n">is_argument</span><span class="o">=</span><span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">ModuleType</span><span class="p">),</span>
+<span class="linenos">2371</span>                <span class="n">is_class</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+<span class="linenos">2372</span>            <span class="p">)</span>
+<span class="linenos">2373</span>        <span class="n">hints</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">_eval_type</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="n">globalns</span><span class="p">,</span> <span class="n">localns</span><span class="p">)</span>
+<span class="linenos">2374</span>    <span class="k">return</span> <span class="n">hints</span> <span class="k">if</span> <span class="n">include_extras</span> <span class="k">else</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="n">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">hints</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span>
+<span class="linenos">2375</span>
+<span class="linenos">2376</span>
+<span class="linenos">2377</span><span class="k">def</span> <span class="nf">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>
+<span class="linenos">2378</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Strip the annotations from a given type.&quot;&quot;&quot;</span>
+<span class="linenos">2379</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
+<span class="linenos">2380</span>        <span class="k">return</span> <span class="n">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">)</span>
+<span class="linenos">2381</span>    <span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="s2">&quot;__origin__&quot;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">t</span><span class="o">.</span><span class="n">__origin__</span> <span class="ow">in</span> <span class="p">(</span><span class="n">Required</span><span class="p">,</span> <span class="n">NotRequired</span><span class="p">):</span>
+<span class="linenos">2382</span>        <span class="k">return</span> <span class="n">_strip_annotations</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<span class="linenos">2383</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">_GenericAlias</span><span class="p">):</span>
+<span class="linenos">2384</span>        <span class="n">stripped_args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_strip_annotations</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
+<span class="linenos">2385</span>        <span class="k">if</span> <span class="n">stripped_args</span> <span class="o">==</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
+<span class="linenos">2386</span>            <span class="k">return</span> <span class="n">t</span>
+<span class="linenos">2387</span>        <span class="k">return</span> <span class="n">t</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">stripped_args</span><span class="p">)</span>
+<span class="linenos">2388</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">):</span>
+<span class="linenos">2389</span>        <span class="n">stripped_args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_strip_annotations</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
+<span class="linenos">2390</span>        <span class="k">if</span> <span class="n">stripped_args</span> <span class="o">==</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
+<span class="linenos">2391</span>            <span class="k">return</span> <span class="n">t</span>
+<span class="linenos">2392</span>        <span class="k">return</span> <span class="n">GenericAlias</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">stripped_args</span><span class="p">)</span>
+<span class="linenos">2393</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">):</span>
 <span class="linenos">2394</span>        <span class="n">stripped_args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_strip_annotations</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
 <span class="linenos">2395</span>        <span class="k">if</span> <span class="n">stripped_args</span> <span class="o">==</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
 <span class="linenos">2396</span>            <span class="k">return</span> <span class="n">t</span>
-<span class="linenos">2397</span>        <span class="k">return</span> <span class="n">t</span><span class="o">.</span><span class="n">copy_with</span><span class="p">(</span><span class="n">stripped_args</span><span class="p">)</span>
-<span class="linenos">2398</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">):</span>
-<span class="linenos">2399</span>        <span class="n">stripped_args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_strip_annotations</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
-<span class="linenos">2400</span>        <span class="k">if</span> <span class="n">stripped_args</span> <span class="o">==</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
-<span class="linenos">2401</span>            <span class="k">return</span> <span class="n">t</span>
-<span class="linenos">2402</span>        <span class="k">return</span> <span class="n">GenericAlias</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,</span> <span class="n">stripped_args</span><span class="p">)</span>
-<span class="linenos">2403</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">):</span>
-<span class="linenos">2404</span>        <span class="n">stripped_args</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">_strip_annotations</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">)</span>
-<span class="linenos">2405</span>        <span class="k">if</span> <span class="n">stripped_args</span> <span class="o">==</span> <span class="n">t</span><span class="o">.</span><span class="n">__args__</span><span class="p">:</span>
-<span class="linenos">2406</span>            <span class="k">return</span> <span class="n">t</span>
-<span class="linenos">2407</span>        <span class="k">return</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">or_</span><span class="p">,</span> <span class="n">stripped_args</span><span class="p">)</span>
-<span class="linenos">2408</span>
-<span class="linenos">2409</span>    <span class="k">return</span> <span class="n">t</span>
-<span class="linenos">2410</span>
-<span class="linenos">2411</span>
-<span class="linenos">2412</span><span class="k">def</span> <span class="nf">get_origin</span><span class="p">(</span><span class="n">tp</span><span class="p">):</span>
-<span class="linenos">2413</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Get the unsubscripted version of a type.</span>
-<span class="linenos">2414</span>
-<span class="linenos">2415</span><span class="sd">    This supports generic types, Callable, Tuple, Union, Literal, Final, ClassVar,</span>
-<span class="linenos">2416</span><span class="sd">    Annotated, and others. Return None for unsupported types.</span>
-<span class="linenos">2417</span>
-<span class="linenos">2418</span><span class="sd">    Examples::</span>
-<span class="linenos">2419</span>
-<span class="linenos">2420</span><span class="sd">        assert get_origin(Literal[42]) is Literal</span>
-<span class="linenos">2421</span><span class="sd">        assert get_origin(int) is None</span>
-<span class="linenos">2422</span><span class="sd">        assert get_origin(ClassVar[int]) is ClassVar</span>
-<span class="linenos">2423</span><span class="sd">        assert get_origin(Generic) is Generic</span>
-<span class="linenos">2424</span><span class="sd">        assert get_origin(Generic[T]) is Generic</span>
-<span class="linenos">2425</span><span class="sd">        assert get_origin(Union[T, int]) is Union</span>
-<span class="linenos">2426</span><span class="sd">        assert get_origin(List[Tuple[T, T]][int]) is list</span>
-<span class="linenos">2427</span><span class="sd">        assert get_origin(P.args) is P</span>
-<span class="linenos">2428</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2429</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
-<span class="linenos">2430</span>        <span class="k">return</span> <span class="n">Annotated</span>
-<span class="linenos">2431</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="p">(</span><span class="n">_BaseGenericAlias</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">,</span>
-<span class="linenos">2432</span>                       <span class="n">ParamSpecArgs</span><span class="p">,</span> <span class="n">ParamSpecKwargs</span><span class="p">)):</span>
-<span class="linenos">2433</span>        <span class="k">return</span> <span class="n">tp</span><span class="o">.</span><span class="n">__origin__</span>
-<span class="linenos">2434</span>    <span class="k">if</span> <span class="n">tp</span> <span class="ow">is</span> <span class="n">Generic</span><span class="p">:</span>
-<span class="linenos">2435</span>        <span class="k">return</span> <span class="n">Generic</span>
-<span class="linenos">2436</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">):</span>
-<span class="linenos">2437</span>        <span class="k">return</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span>
-<span class="linenos">2438</span>    <span class="k">return</span> <span class="kc">None</span>
-<span class="linenos">2439</span>
-<span class="linenos">2440</span>
-<span class="linenos">2441</span><span class="k">def</span> <span class="nf">get_args</span><span class="p">(</span><span class="n">tp</span><span class="p">):</span>
-<span class="linenos">2442</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Get type arguments with all substitutions performed.</span>
-<span class="linenos">2443</span>
-<span class="linenos">2444</span><span class="sd">    For unions, basic simplifications used by Union constructor are performed.</span>
-<span class="linenos">2445</span>
-<span class="linenos">2446</span><span class="sd">    Examples::</span>
-<span class="linenos">2447</span>
-<span class="linenos">2448</span><span class="sd">        assert get_args(Dict[str, int]) == (str, int)</span>
-<span class="linenos">2449</span><span class="sd">        assert get_args(int) == ()</span>
-<span class="linenos">2450</span><span class="sd">        assert get_args(Union[int, Union[T, int], str][int]) == (int, str)</span>
-<span class="linenos">2451</span><span class="sd">        assert get_args(Union[int, Tuple[T, int]][str]) == (int, Tuple[str, int])</span>
-<span class="linenos">2452</span><span class="sd">        assert get_args(Callable[[], T][int]) == ([], int)</span>
-<span class="linenos">2453</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2454</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
-<span class="linenos">2455</span>        <span class="k">return</span> <span class="p">(</span><span class="n">tp</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,)</span> <span class="o">+</span> <span class="n">tp</span><span class="o">.</span><span class="n">__metadata__</span>
-<span class="linenos">2456</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">)):</span>
-<span class="linenos">2457</span>        <span class="n">res</span> <span class="o">=</span> <span class="n">tp</span><span class="o">.</span><span class="n">__args__</span>
-<span class="linenos">2458</span>        <span class="k">if</span> <span class="n">_should_unflatten_callable_args</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">res</span><span class="p">):</span>
-<span class="linenos">2459</span>            <span class="n">res</span> <span class="o">=</span> <span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">res</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span> <span class="n">res</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
-<span class="linenos">2460</span>        <span class="k">return</span> <span class="n">res</span>
-<span class="linenos">2461</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">):</span>
-<span class="linenos">2462</span>        <span class="k">return</span> <span class="n">tp</span><span class="o">.</span><span class="n">__args__</span>
-<span class="linenos">2463</span>    <span class="k">return</span> <span class="p">()</span>
-<span class="linenos">2464</span>
-<span class="linenos">2465</span>
-<span class="linenos">2466</span><span class="k">def</span> <span class="nf">is_typeddict</span><span class="p">(</span><span class="n">tp</span><span class="p">):</span>
-<span class="linenos">2467</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Check if an annotation is a TypedDict class.</span>
+<span class="linenos">2397</span>        <span class="k">return</span> <span class="n">functools</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="n">operator</span><span class="o">.</span><span class="n">or_</span><span class="p">,</span> <span class="n">stripped_args</span><span class="p">)</span>
+<span class="linenos">2398</span>
+<span class="linenos">2399</span>    <span class="k">return</span> <span class="n">t</span>
+<span class="linenos">2400</span>
+<span class="linenos">2401</span>
+<span class="linenos">2402</span><span class="k">def</span> <span class="nf">get_origin</span><span class="p">(</span><span class="n">tp</span><span class="p">):</span>
+<span class="linenos">2403</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Get the unsubscripted version of a type.</span>
+<span class="linenos">2404</span>
+<span class="linenos">2405</span><span class="sd">    This supports generic types, Callable, Tuple, Union, Literal, Final, ClassVar</span>
+<span class="linenos">2406</span><span class="sd">    Annotated, and others. Return None for unsupported types. Examples::</span>
+<span class="linenos">2407</span>
+<span class="linenos">2408</span><span class="sd">        assert get_origin(Literal[42]) is Literal</span>
+<span class="linenos">2409</span><span class="sd">        assert get_origin(int) is None</span>
+<span class="linenos">2410</span><span class="sd">        assert get_origin(ClassVar[int]) is ClassVar</span>
+<span class="linenos">2411</span><span class="sd">        assert get_origin(Generic) is Generic</span>
+<span class="linenos">2412</span><span class="sd">        assert get_origin(Generic[T]) is Generic</span>
+<span class="linenos">2413</span><span class="sd">        assert get_origin(Union[T, int]) is Union</span>
+<span class="linenos">2414</span><span class="sd">        assert get_origin(List[Tuple[T, T]][int]) is list</span>
+<span class="linenos">2415</span><span class="sd">        assert get_origin(P.args) is P</span>
+<span class="linenos">2416</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2417</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
+<span class="linenos">2418</span>        <span class="k">return</span> <span class="n">Annotated</span>
+<span class="linenos">2419</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="p">(</span><span class="n">_BaseGenericAlias</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">,</span>
+<span class="linenos">2420</span>                       <span class="n">ParamSpecArgs</span><span class="p">,</span> <span class="n">ParamSpecKwargs</span><span class="p">)):</span>
+<span class="linenos">2421</span>        <span class="k">return</span> <span class="n">tp</span><span class="o">.</span><span class="n">__origin__</span>
+<span class="linenos">2422</span>    <span class="k">if</span> <span class="n">tp</span> <span class="ow">is</span> <span class="n">Generic</span><span class="p">:</span>
+<span class="linenos">2423</span>        <span class="k">return</span> <span class="n">Generic</span>
+<span class="linenos">2424</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">):</span>
+<span class="linenos">2425</span>        <span class="k">return</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span>
+<span class="linenos">2426</span>    <span class="k">return</span> <span class="kc">None</span>
+<span class="linenos">2427</span>
+<span class="linenos">2428</span>
+<span class="linenos">2429</span><span class="k">def</span> <span class="nf">get_args</span><span class="p">(</span><span class="n">tp</span><span class="p">):</span>
+<span class="linenos">2430</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Get type arguments with all substitutions performed.</span>
+<span class="linenos">2431</span>
+<span class="linenos">2432</span><span class="sd">    For unions, basic simplifications used by Union constructor are performed.</span>
+<span class="linenos">2433</span>
+<span class="linenos">2434</span><span class="sd">    Examples::</span>
+<span class="linenos">2435</span>
+<span class="linenos">2436</span><span class="sd">        assert get_args(Dict[str, int]) == (str, int)</span>
+<span class="linenos">2437</span><span class="sd">        assert get_args(int) == ()</span>
+<span class="linenos">2438</span><span class="sd">        assert get_args(Union[int, Union[T, int], str][int]) == (int, str)</span>
+<span class="linenos">2439</span><span class="sd">        assert get_args(Union[int, Tuple[T, int]][str]) == (int, Tuple[str, int])</span>
+<span class="linenos">2440</span><span class="sd">        assert get_args(Callable[[], T][int]) == ([], int)</span>
+<span class="linenos">2441</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2442</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">_AnnotatedAlias</span><span class="p">):</span>
+<span class="linenos">2443</span>        <span class="k">return</span> <span class="p">(</span><span class="n">tp</span><span class="o">.</span><span class="n">__origin__</span><span class="p">,)</span> <span class="o">+</span> <span class="n">tp</span><span class="o">.</span><span class="n">__metadata__</span>
+<span class="linenos">2444</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="p">(</span><span class="n">_GenericAlias</span><span class="p">,</span> <span class="n">GenericAlias</span><span class="p">)):</span>
+<span class="linenos">2445</span>        <span class="n">res</span> <span class="o">=</span> <span class="n">tp</span><span class="o">.</span><span class="n">__args__</span>
+<span class="linenos">2446</span>        <span class="k">if</span> <span class="n">_should_unflatten_callable_args</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">res</span><span class="p">):</span>
+<span class="linenos">2447</span>            <span class="n">res</span> <span class="o">=</span> <span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">res</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]),</span> <span class="n">res</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
+<span class="linenos">2448</span>        <span class="k">return</span> <span class="n">res</span>
+<span class="linenos">2449</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">UnionType</span><span class="p">):</span>
+<span class="linenos">2450</span>        <span class="k">return</span> <span class="n">tp</span><span class="o">.</span><span class="n">__args__</span>
+<span class="linenos">2451</span>    <span class="k">return</span> <span class="p">()</span>
+<span class="linenos">2452</span>
+<span class="linenos">2453</span>
+<span class="linenos">2454</span><span class="k">def</span> <span class="nf">is_typeddict</span><span class="p">(</span><span class="n">tp</span><span class="p">):</span>
+<span class="linenos">2455</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Check if an annotation is a TypedDict class.</span>
+<span class="linenos">2456</span>
+<span class="linenos">2457</span><span class="sd">    For example::</span>
+<span class="linenos">2458</span>
+<span class="linenos">2459</span><span class="sd">        class Film(TypedDict):</span>
+<span class="linenos">2460</span><span class="sd">            title: str</span>
+<span class="linenos">2461</span><span class="sd">            year: int</span>
+<span class="linenos">2462</span>
+<span class="linenos">2463</span><span class="sd">        is_typeddict(Film)              # =&gt; True</span>
+<span class="linenos">2464</span><span class="sd">        is_typeddict(Union[list, str])  # =&gt; False</span>
+<span class="linenos">2465</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2466</span>    <span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">_TypedDictMeta</span><span class="p">)</span>
+<span class="linenos">2467</span>
 <span class="linenos">2468</span>
-<span class="linenos">2469</span><span class="sd">    For example::</span>
+<span class="linenos">2469</span><span class="n">_ASSERT_NEVER_REPR_MAX_LENGTH</span> <span class="o">=</span> <span class="mi">100</span>
 <span class="linenos">2470</span>
-<span class="linenos">2471</span><span class="sd">        class Film(TypedDict):</span>
-<span class="linenos">2472</span><span class="sd">            title: str</span>
-<span class="linenos">2473</span><span class="sd">            year: int</span>
+<span class="linenos">2471</span>
+<span class="linenos">2472</span><span class="k">def</span> <span class="nf">assert_never</span><span class="p">(</span><span class="n">arg</span><span class="p">:</span> <span class="n">Never</span><span class="p">,</span> <span class="o">/</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Never</span><span class="p">:</span>
+<span class="linenos">2473</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Statically assert that a line of code is unreachable.</span>
 <span class="linenos">2474</span>
-<span class="linenos">2475</span><span class="sd">        is_typeddict(Film)              # =&gt; True</span>
-<span class="linenos">2476</span><span class="sd">        is_typeddict(Union[list, str])  # =&gt; False</span>
-<span class="linenos">2477</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2478</span>    <span class="k">return</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">_TypedDictMeta</span><span class="p">)</span>
-<span class="linenos">2479</span>
-<span class="linenos">2480</span>
-<span class="linenos">2481</span><span class="n">_ASSERT_NEVER_REPR_MAX_LENGTH</span> <span class="o">=</span> <span class="mi">100</span>
-<span class="linenos">2482</span>
-<span class="linenos">2483</span>
-<span class="linenos">2484</span><span class="k">def</span> <span class="nf">assert_never</span><span class="p">(</span><span class="n">arg</span><span class="p">:</span> <span class="n">Never</span><span class="p">,</span> <span class="o">/</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Never</span><span class="p">:</span>
-<span class="linenos">2485</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Statically assert that a line of code is unreachable.</span>
-<span class="linenos">2486</span>
-<span class="linenos">2487</span><span class="sd">    Example::</span>
+<span class="linenos">2475</span><span class="sd">    Example::</span>
+<span class="linenos">2476</span>
+<span class="linenos">2477</span><span class="sd">        def int_or_str(arg: int | str) -&gt; None:</span>
+<span class="linenos">2478</span><span class="sd">            match arg:</span>
+<span class="linenos">2479</span><span class="sd">                case int():</span>
+<span class="linenos">2480</span><span class="sd">                    print(&quot;It&#39;s an int&quot;)</span>
+<span class="linenos">2481</span><span class="sd">                case str():</span>
+<span class="linenos">2482</span><span class="sd">                    print(&quot;It&#39;s a str&quot;)</span>
+<span class="linenos">2483</span><span class="sd">                case _:</span>
+<span class="linenos">2484</span><span class="sd">                    assert_never(arg)</span>
+<span class="linenos">2485</span>
+<span class="linenos">2486</span><span class="sd">    If a type checker finds that a call to assert_never() is</span>
+<span class="linenos">2487</span><span class="sd">    reachable, it will emit an error.</span>
 <span class="linenos">2488</span>
-<span class="linenos">2489</span><span class="sd">        def int_or_str(arg: int | str) -&gt; None:</span>
-<span class="linenos">2490</span><span class="sd">            match arg:</span>
-<span class="linenos">2491</span><span class="sd">                case int():</span>
-<span class="linenos">2492</span><span class="sd">                    print(&quot;It&#39;s an int&quot;)</span>
-<span class="linenos">2493</span><span class="sd">                case str():</span>
-<span class="linenos">2494</span><span class="sd">                    print(&quot;It&#39;s a str&quot;)</span>
-<span class="linenos">2495</span><span class="sd">                case _:</span>
-<span class="linenos">2496</span><span class="sd">                    assert_never(arg)</span>
-<span class="linenos">2497</span>
-<span class="linenos">2498</span><span class="sd">    If a type checker finds that a call to assert_never() is</span>
-<span class="linenos">2499</span><span class="sd">    reachable, it will emit an error.</span>
-<span class="linenos">2500</span>
-<span class="linenos">2501</span><span class="sd">    At runtime, this throws an exception when called.</span>
-<span class="linenos">2502</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2503</span>    <span class="n">value</span> <span class="o">=</span> <span class="nb">repr</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span>
-<span class="linenos">2504</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">&gt;</span> <span class="n">_ASSERT_NEVER_REPR_MAX_LENGTH</span><span class="p">:</span>
-<span class="linenos">2505</span>        <span class="n">value</span> <span class="o">=</span> <span class="n">value</span><span class="p">[:</span><span class="n">_ASSERT_NEVER_REPR_MAX_LENGTH</span><span class="p">]</span> <span class="o">+</span> <span class="s1">&#39;...&#39;</span>
-<span class="linenos">2506</span>    <span class="k">raise</span> <span class="ne">AssertionError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Expected code to be unreachable, but got: </span><span class="si">{</span><span class="n">value</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos">2507</span>
-<span class="linenos">2508</span>
-<span class="linenos">2509</span><span class="k">def</span> <span class="nf">no_type_check</span><span class="p">(</span><span class="n">arg</span><span class="p">):</span>
-<span class="linenos">2510</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator to indicate that annotations are not type hints.</span>
-<span class="linenos">2511</span>
-<span class="linenos">2512</span><span class="sd">    The argument must be a class or function; if it is a class, it</span>
-<span class="linenos">2513</span><span class="sd">    applies recursively to all methods and classes defined in that class</span>
-<span class="linenos">2514</span><span class="sd">    (but not to methods defined in its superclasses or subclasses).</span>
-<span class="linenos">2515</span>
-<span class="linenos">2516</span><span class="sd">    This mutates the function(s) or class(es) in place.</span>
-<span class="linenos">2517</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2518</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
-<span class="linenos">2519</span>        <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="nb">dir</span><span class="p">(</span><span class="n">arg</span><span class="p">):</span>
-<span class="linenos">2520</span>            <span class="n">obj</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">key</span><span class="p">)</span>
-<span class="linenos">2521</span>            <span class="k">if</span> <span class="p">(</span>
-<span class="linenos">2522</span>                <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="s1">&#39;__qualname__&#39;</span><span class="p">)</span>
-<span class="linenos">2523</span>                <span class="ow">or</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__qualname__</span> <span class="o">!=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">arg</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="n">obj</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s1">&#39;</span>
-<span class="linenos">2524</span>                <span class="ow">or</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="s1">&#39;__module__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span> <span class="o">!=</span> <span class="n">arg</span><span class="o">.</span><span class="vm">__module__</span>
-<span class="linenos">2525</span>            <span class="p">):</span>
-<span class="linenos">2526</span>                <span class="c1"># We only modify objects that are defined in this type directly.</span>
-<span class="linenos">2527</span>                <span class="c1"># If classes / methods are nested in multiple layers,</span>
-<span class="linenos">2528</span>                <span class="c1"># we will modify them when processing their direct holders.</span>
-<span class="linenos">2529</span>                <span class="k">continue</span>
-<span class="linenos">2530</span>            <span class="c1"># Instance, class, and static methods:</span>
-<span class="linenos">2531</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">FunctionType</span><span class="p">):</span>
-<span class="linenos">2532</span>                <span class="n">obj</span><span class="o">.</span><span class="n">__no_type_check__</span> <span class="o">=</span> <span class="kc">True</span>
-<span class="linenos">2533</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">):</span>
-<span class="linenos">2534</span>                <span class="n">obj</span><span class="o">.</span><span class="vm">__func__</span><span class="o">.</span><span class="n">__no_type_check__</span> <span class="o">=</span> <span class="kc">True</span>
-<span class="linenos">2535</span>            <span class="c1"># Nested types:</span>
-<span class="linenos">2536</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
-<span class="linenos">2537</span>                <span class="n">no_type_check</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
-<span class="linenos">2538</span>    <span class="k">try</span><span class="p">:</span>
-<span class="linenos">2539</span>        <span class="n">arg</span><span class="o">.</span><span class="n">__no_type_check__</span> <span class="o">=</span> <span class="kc">True</span>
-<span class="linenos">2540</span>    <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>  <span class="c1"># built-in classes</span>
-<span class="linenos">2541</span>        <span class="k">pass</span>
-<span class="linenos">2542</span>    <span class="k">return</span> <span class="n">arg</span>
-<span class="linenos">2543</span>
+<span class="linenos">2489</span><span class="sd">    At runtime, this throws an exception when called.</span>
+<span class="linenos">2490</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2491</span>    <span class="n">value</span> <span class="o">=</span> <span class="nb">repr</span><span class="p">(</span><span class="n">arg</span><span class="p">)</span>
+<span class="linenos">2492</span>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">&gt;</span> <span class="n">_ASSERT_NEVER_REPR_MAX_LENGTH</span><span class="p">:</span>
+<span class="linenos">2493</span>        <span class="n">value</span> <span class="o">=</span> <span class="n">value</span><span class="p">[:</span><span class="n">_ASSERT_NEVER_REPR_MAX_LENGTH</span><span class="p">]</span> <span class="o">+</span> <span class="s1">&#39;...&#39;</span>
+<span class="linenos">2494</span>    <span class="k">raise</span> <span class="ne">AssertionError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Expected code to be unreachable, but got: </span><span class="si">{</span><span class="n">value</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos">2495</span>
+<span class="linenos">2496</span>
+<span class="linenos">2497</span><span class="k">def</span> <span class="nf">no_type_check</span><span class="p">(</span><span class="n">arg</span><span class="p">):</span>
+<span class="linenos">2498</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator to indicate that annotations are not type hints.</span>
+<span class="linenos">2499</span>
+<span class="linenos">2500</span><span class="sd">    The argument must be a class or function; if it is a class, it</span>
+<span class="linenos">2501</span><span class="sd">    applies recursively to all methods and classes defined in that class</span>
+<span class="linenos">2502</span><span class="sd">    (but not to methods defined in its superclasses or subclasses).</span>
+<span class="linenos">2503</span>
+<span class="linenos">2504</span><span class="sd">    This mutates the function(s) or class(es) in place.</span>
+<span class="linenos">2505</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2506</span>    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
+<span class="linenos">2507</span>        <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="nb">dir</span><span class="p">(</span><span class="n">arg</span><span class="p">):</span>
+<span class="linenos">2508</span>            <span class="n">obj</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">arg</span><span class="p">,</span> <span class="n">key</span><span class="p">)</span>
+<span class="linenos">2509</span>            <span class="k">if</span> <span class="p">(</span>
+<span class="linenos">2510</span>                <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="s1">&#39;__qualname__&#39;</span><span class="p">)</span>
+<span class="linenos">2511</span>                <span class="ow">or</span> <span class="n">obj</span><span class="o">.</span><span class="vm">__qualname__</span> <span class="o">!=</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="n">arg</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="n">obj</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s1">&#39;</span>
+<span class="linenos">2512</span>                <span class="ow">or</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="s1">&#39;__module__&#39;</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span> <span class="o">!=</span> <span class="n">arg</span><span class="o">.</span><span class="vm">__module__</span>
+<span class="linenos">2513</span>            <span class="p">):</span>
+<span class="linenos">2514</span>                <span class="c1"># We only modify objects that are defined in this type directly.</span>
+<span class="linenos">2515</span>                <span class="c1"># If classes / methods are nested in multiple layers,</span>
+<span class="linenos">2516</span>                <span class="c1"># we will modify them when processing their direct holders.</span>
+<span class="linenos">2517</span>                <span class="k">continue</span>
+<span class="linenos">2518</span>            <span class="c1"># Instance, class, and static methods:</span>
+<span class="linenos">2519</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">FunctionType</span><span class="p">):</span>
+<span class="linenos">2520</span>                <span class="n">obj</span><span class="o">.</span><span class="n">__no_type_check__</span> <span class="o">=</span> <span class="kc">True</span>
+<span class="linenos">2521</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">MethodType</span><span class="p">):</span>
+<span class="linenos">2522</span>                <span class="n">obj</span><span class="o">.</span><span class="vm">__func__</span><span class="o">.</span><span class="n">__no_type_check__</span> <span class="o">=</span> <span class="kc">True</span>
+<span class="linenos">2523</span>            <span class="c1"># Nested types:</span>
+<span class="linenos">2524</span>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="nb">type</span><span class="p">):</span>
+<span class="linenos">2525</span>                <span class="n">no_type_check</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
+<span class="linenos">2526</span>    <span class="k">try</span><span class="p">:</span>
+<span class="linenos">2527</span>        <span class="n">arg</span><span class="o">.</span><span class="n">__no_type_check__</span> <span class="o">=</span> <span class="kc">True</span>
+<span class="linenos">2528</span>    <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>  <span class="c1"># built-in classes</span>
+<span class="linenos">2529</span>        <span class="k">pass</span>
+<span class="linenos">2530</span>    <span class="k">return</span> <span class="n">arg</span>
+<span class="linenos">2531</span>
+<span class="linenos">2532</span>
+<span class="linenos">2533</span><span class="k">def</span> <span class="nf">no_type_check_decorator</span><span class="p">(</span><span class="n">decorator</span><span class="p">):</span>
+<span class="linenos">2534</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator to give another decorator the @no_type_check effect.</span>
+<span class="linenos">2535</span>
+<span class="linenos">2536</span><span class="sd">    This wraps the decorator with something that wraps the decorated</span>
+<span class="linenos">2537</span><span class="sd">    function in @no_type_check.</span>
+<span class="linenos">2538</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2539</span>    <span class="nd">@functools</span><span class="o">.</span><span class="n">wraps</span><span class="p">(</span><span class="n">decorator</span><span class="p">)</span>
+<span class="linenos">2540</span>    <span class="k">def</span> <span class="nf">wrapped_decorator</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
+<span class="linenos">2541</span>        <span class="n">func</span> <span class="o">=</span> <span class="n">decorator</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">)</span>
+<span class="linenos">2542</span>        <span class="n">func</span> <span class="o">=</span> <span class="n">no_type_check</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
+<span class="linenos">2543</span>        <span class="k">return</span> <span class="n">func</span>
 <span class="linenos">2544</span>
-<span class="linenos">2545</span><span class="k">def</span> <span class="nf">no_type_check_decorator</span><span class="p">(</span><span class="n">decorator</span><span class="p">):</span>
-<span class="linenos">2546</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator to give another decorator the @no_type_check effect.</span>
+<span class="linenos">2545</span>    <span class="k">return</span> <span class="n">wrapped_decorator</span>
+<span class="linenos">2546</span>
 <span class="linenos">2547</span>
-<span class="linenos">2548</span><span class="sd">    This wraps the decorator with something that wraps the decorated</span>
-<span class="linenos">2549</span><span class="sd">    function in @no_type_check.</span>
-<span class="linenos">2550</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2551</span>    <span class="nd">@functools</span><span class="o">.</span><span class="n">wraps</span><span class="p">(</span><span class="n">decorator</span><span class="p">)</span>
-<span class="linenos">2552</span>    <span class="k">def</span> <span class="nf">wrapped_decorator</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
-<span class="linenos">2553</span>        <span class="n">func</span> <span class="o">=</span> <span class="n">decorator</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">)</span>
-<span class="linenos">2554</span>        <span class="n">func</span> <span class="o">=</span> <span class="n">no_type_check</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
-<span class="linenos">2555</span>        <span class="k">return</span> <span class="n">func</span>
+<span class="linenos">2548</span><span class="k">def</span> <span class="nf">_overload_dummy</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
+<span class="linenos">2549</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Helper for @overload to raise when called.&quot;&quot;&quot;</span>
+<span class="linenos">2550</span>    <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span>
+<span class="linenos">2551</span>        <span class="s2">&quot;You should not call an overloaded function. &quot;</span>
+<span class="linenos">2552</span>        <span class="s2">&quot;A series of @overload-decorated functions &quot;</span>
+<span class="linenos">2553</span>        <span class="s2">&quot;outside a stub module should always be followed &quot;</span>
+<span class="linenos">2554</span>        <span class="s2">&quot;by an implementation that is not @overload-ed.&quot;</span><span class="p">)</span>
+<span class="linenos">2555</span>
 <span class="linenos">2556</span>
-<span class="linenos">2557</span>    <span class="k">return</span> <span class="n">wrapped_decorator</span>
-<span class="linenos">2558</span>
+<span class="linenos">2557</span><span class="c1"># {module: {qualname: {firstlineno: func}}}</span>
+<span class="linenos">2558</span><span class="n">_overload_registry</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="n">functools</span><span class="o">.</span><span class="n">partial</span><span class="p">(</span><span class="n">defaultdict</span><span class="p">,</span> <span class="nb">dict</span><span class="p">))</span>
 <span class="linenos">2559</span>
-<span class="linenos">2560</span><span class="k">def</span> <span class="nf">_overload_dummy</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwds</span><span class="p">):</span>
-<span class="linenos">2561</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Helper for @overload to raise when called.&quot;&quot;&quot;</span>
-<span class="linenos">2562</span>    <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span>
-<span class="linenos">2563</span>        <span class="s2">&quot;You should not call an overloaded function. &quot;</span>
-<span class="linenos">2564</span>        <span class="s2">&quot;A series of @overload-decorated functions &quot;</span>
-<span class="linenos">2565</span>        <span class="s2">&quot;outside a stub module should always be followed &quot;</span>
-<span class="linenos">2566</span>        <span class="s2">&quot;by an implementation that is not @overload-ed.&quot;</span><span class="p">)</span>
-<span class="linenos">2567</span>
-<span class="linenos">2568</span>
-<span class="linenos">2569</span><span class="c1"># {module: {qualname: {firstlineno: func}}}</span>
-<span class="linenos">2570</span><span class="n">_overload_registry</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="n">functools</span><span class="o">.</span><span class="n">partial</span><span class="p">(</span><span class="n">defaultdict</span><span class="p">,</span> <span class="nb">dict</span><span class="p">))</span>
-<span class="linenos">2571</span>
-<span class="linenos">2572</span>
-<span class="linenos">2573</span><span class="k">def</span> <span class="nf">overload</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
-<span class="linenos">2574</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator for overloaded functions/methods.</span>
-<span class="linenos">2575</span>
-<span class="linenos">2576</span><span class="sd">    In a stub file, place two or more stub definitions for the same</span>
-<span class="linenos">2577</span><span class="sd">    function in a row, each decorated with @overload.</span>
-<span class="linenos">2578</span>
-<span class="linenos">2579</span><span class="sd">    For example::</span>
-<span class="linenos">2580</span>
-<span class="linenos">2581</span><span class="sd">        @overload</span>
-<span class="linenos">2582</span><span class="sd">        def utf8(value: None) -&gt; None: ...</span>
-<span class="linenos">2583</span><span class="sd">        @overload</span>
-<span class="linenos">2584</span><span class="sd">        def utf8(value: bytes) -&gt; bytes: ...</span>
-<span class="linenos">2585</span><span class="sd">        @overload</span>
-<span class="linenos">2586</span><span class="sd">        def utf8(value: str) -&gt; bytes: ...</span>
-<span class="linenos">2587</span>
-<span class="linenos">2588</span><span class="sd">    In a non-stub file (i.e. a regular .py file), do the same but</span>
-<span class="linenos">2589</span><span class="sd">    follow it with an implementation.  The implementation should *not*</span>
-<span class="linenos">2590</span><span class="sd">    be decorated with @overload::</span>
-<span class="linenos">2591</span>
-<span class="linenos">2592</span><span class="sd">        @overload</span>
-<span class="linenos">2593</span><span class="sd">        def utf8(value: None) -&gt; None: ...</span>
-<span class="linenos">2594</span><span class="sd">        @overload</span>
-<span class="linenos">2595</span><span class="sd">        def utf8(value: bytes) -&gt; bytes: ...</span>
-<span class="linenos">2596</span><span class="sd">        @overload</span>
-<span class="linenos">2597</span><span class="sd">        def utf8(value: str) -&gt; bytes: ...</span>
-<span class="linenos">2598</span><span class="sd">        def utf8(value):</span>
-<span class="linenos">2599</span><span class="sd">            ...  # implementation goes here</span>
-<span class="linenos">2600</span>
-<span class="linenos">2601</span><span class="sd">    The overloads for a function can be retrieved at runtime using the</span>
-<span class="linenos">2602</span><span class="sd">    get_overloads() function.</span>
-<span class="linenos">2603</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2604</span>    <span class="c1"># classmethod and staticmethod</span>
-<span class="linenos">2605</span>    <span class="n">f</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="s2">&quot;__func__&quot;</span><span class="p">,</span> <span class="n">func</span><span class="p">)</span>
-<span class="linenos">2606</span>    <span class="k">try</span><span class="p">:</span>
-<span class="linenos">2607</span>        <span class="n">_overload_registry</span><span class="p">[</span><span class="n">f</span><span class="o">.</span><span class="vm">__module__</span><span class="p">][</span><span class="n">f</span><span class="o">.</span><span class="vm">__qualname__</span><span class="p">][</span><span class="n">f</span><span class="o">.</span><span class="vm">__code__</span><span class="o">.</span><span class="n">co_firstlineno</span><span class="p">]</span> <span class="o">=</span> <span class="n">func</span>
-<span class="linenos">2608</span>    <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
-<span class="linenos">2609</span>        <span class="c1"># Not a normal function; ignore.</span>
-<span class="linenos">2610</span>        <span class="k">pass</span>
-<span class="linenos">2611</span>    <span class="k">return</span> <span class="n">_overload_dummy</span>
-<span class="linenos">2612</span>
-<span class="linenos">2613</span>
-<span class="linenos">2614</span><span class="k">def</span> <span class="nf">get_overloads</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
-<span class="linenos">2615</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Return all defined overloads for *func* as a sequence.&quot;&quot;&quot;</span>
-<span class="linenos">2616</span>    <span class="c1"># classmethod and staticmethod</span>
-<span class="linenos">2617</span>    <span class="n">f</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="s2">&quot;__func__&quot;</span><span class="p">,</span> <span class="n">func</span><span class="p">)</span>
-<span class="linenos">2618</span>    <span class="k">if</span> <span class="n">f</span><span class="o">.</span><span class="vm">__module__</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">_overload_registry</span><span class="p">:</span>
-<span class="linenos">2619</span>        <span class="k">return</span> <span class="p">[]</span>
-<span class="linenos">2620</span>    <span class="n">mod_dict</span> <span class="o">=</span> <span class="n">_overload_registry</span><span class="p">[</span><span class="n">f</span><span class="o">.</span><span class="vm">__module__</span><span class="p">]</span>
-<span class="linenos">2621</span>    <span class="k">if</span> <span class="n">f</span><span class="o">.</span><span class="vm">__qualname__</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">mod_dict</span><span class="p">:</span>
-<span class="linenos">2622</span>        <span class="k">return</span> <span class="p">[]</span>
-<span class="linenos">2623</span>    <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="n">mod_dict</span><span class="p">[</span><span class="n">f</span><span class="o">.</span><span class="vm">__qualname__</span><span class="p">]</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
+<span class="linenos">2560</span>
+<span class="linenos">2561</span><span class="k">def</span> <span class="nf">overload</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
+<span class="linenos">2562</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator for overloaded functions/methods.</span>
+<span class="linenos">2563</span>
+<span class="linenos">2564</span><span class="sd">    In a stub file, place two or more stub definitions for the same</span>
+<span class="linenos">2565</span><span class="sd">    function in a row, each decorated with @overload.  For example::</span>
+<span class="linenos">2566</span>
+<span class="linenos">2567</span><span class="sd">        @overload</span>
+<span class="linenos">2568</span><span class="sd">        def utf8(value: None) -&gt; None: ...</span>
+<span class="linenos">2569</span><span class="sd">        @overload</span>
+<span class="linenos">2570</span><span class="sd">        def utf8(value: bytes) -&gt; bytes: ...</span>
+<span class="linenos">2571</span><span class="sd">        @overload</span>
+<span class="linenos">2572</span><span class="sd">        def utf8(value: str) -&gt; bytes: ...</span>
+<span class="linenos">2573</span>
+<span class="linenos">2574</span><span class="sd">    In a non-stub file (i.e. a regular .py file), do the same but</span>
+<span class="linenos">2575</span><span class="sd">    follow it with an implementation.  The implementation should *not*</span>
+<span class="linenos">2576</span><span class="sd">    be decorated with @overload.  For example::</span>
+<span class="linenos">2577</span>
+<span class="linenos">2578</span><span class="sd">        @overload</span>
+<span class="linenos">2579</span><span class="sd">        def utf8(value: None) -&gt; None: ...</span>
+<span class="linenos">2580</span><span class="sd">        @overload</span>
+<span class="linenos">2581</span><span class="sd">        def utf8(value: bytes) -&gt; bytes: ...</span>
+<span class="linenos">2582</span><span class="sd">        @overload</span>
+<span class="linenos">2583</span><span class="sd">        def utf8(value: str) -&gt; bytes: ...</span>
+<span class="linenos">2584</span><span class="sd">        def utf8(value):</span>
+<span class="linenos">2585</span><span class="sd">            ...  # implementation goes here</span>
+<span class="linenos">2586</span>
+<span class="linenos">2587</span><span class="sd">    The overloads for a function can be retrieved at runtime using the</span>
+<span class="linenos">2588</span><span class="sd">    get_overloads() function.</span>
+<span class="linenos">2589</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2590</span>    <span class="c1"># classmethod and staticmethod</span>
+<span class="linenos">2591</span>    <span class="n">f</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="s2">&quot;__func__&quot;</span><span class="p">,</span> <span class="n">func</span><span class="p">)</span>
+<span class="linenos">2592</span>    <span class="k">try</span><span class="p">:</span>
+<span class="linenos">2593</span>        <span class="n">_overload_registry</span><span class="p">[</span><span class="n">f</span><span class="o">.</span><span class="vm">__module__</span><span class="p">][</span><span class="n">f</span><span class="o">.</span><span class="vm">__qualname__</span><span class="p">][</span><span class="n">f</span><span class="o">.</span><span class="vm">__code__</span><span class="o">.</span><span class="n">co_firstlineno</span><span class="p">]</span> <span class="o">=</span> <span class="n">func</span>
+<span class="linenos">2594</span>    <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+<span class="linenos">2595</span>        <span class="c1"># Not a normal function; ignore.</span>
+<span class="linenos">2596</span>        <span class="k">pass</span>
+<span class="linenos">2597</span>    <span class="k">return</span> <span class="n">_overload_dummy</span>
+<span class="linenos">2598</span>
+<span class="linenos">2599</span>
+<span class="linenos">2600</span><span class="k">def</span> <span class="nf">get_overloads</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
+<span class="linenos">2601</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Return all defined overloads for *func* as a sequence.&quot;&quot;&quot;</span>
+<span class="linenos">2602</span>    <span class="c1"># classmethod and staticmethod</span>
+<span class="linenos">2603</span>    <span class="n">f</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="s2">&quot;__func__&quot;</span><span class="p">,</span> <span class="n">func</span><span class="p">)</span>
+<span class="linenos">2604</span>    <span class="k">if</span> <span class="n">f</span><span class="o">.</span><span class="vm">__module__</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">_overload_registry</span><span class="p">:</span>
+<span class="linenos">2605</span>        <span class="k">return</span> <span class="p">[]</span>
+<span class="linenos">2606</span>    <span class="n">mod_dict</span> <span class="o">=</span> <span class="n">_overload_registry</span><span class="p">[</span><span class="n">f</span><span class="o">.</span><span class="vm">__module__</span><span class="p">]</span>
+<span class="linenos">2607</span>    <span class="k">if</span> <span class="n">f</span><span class="o">.</span><span class="vm">__qualname__</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">mod_dict</span><span class="p">:</span>
+<span class="linenos">2608</span>        <span class="k">return</span> <span class="p">[]</span>
+<span class="linenos">2609</span>    <span class="k">return</span> <span class="nb">list</span><span class="p">(</span><span class="n">mod_dict</span><span class="p">[</span><span class="n">f</span><span class="o">.</span><span class="vm">__qualname__</span><span class="p">]</span><span class="o">.</span><span class="n">values</span><span class="p">())</span>
+<span class="linenos">2610</span>
+<span class="linenos">2611</span>
+<span class="linenos">2612</span><span class="k">def</span> <span class="nf">clear_overloads</span><span class="p">():</span>
+<span class="linenos">2613</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Clear all overloads in the registry.&quot;&quot;&quot;</span>
+<span class="linenos">2614</span>    <span class="n">_overload_registry</span><span class="o">.</span><span class="n">clear</span><span class="p">()</span>
+<span class="linenos">2615</span>
+<span class="linenos">2616</span>
+<span class="linenos">2617</span><span class="k">def</span> <span class="nf">final</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
+<span class="linenos">2618</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator to indicate final methods and final classes.</span>
+<span class="linenos">2619</span>
+<span class="linenos">2620</span><span class="sd">    Use this decorator to indicate to type checkers that the decorated</span>
+<span class="linenos">2621</span><span class="sd">    method cannot be overridden, and decorated class cannot be subclassed.</span>
+<span class="linenos">2622</span>
+<span class="linenos">2623</span><span class="sd">    For example::</span>
 <span class="linenos">2624</span>
-<span class="linenos">2625</span>
-<span class="linenos">2626</span><span class="k">def</span> <span class="nf">clear_overloads</span><span class="p">():</span>
-<span class="linenos">2627</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Clear all overloads in the registry.&quot;&quot;&quot;</span>
-<span class="linenos">2628</span>    <span class="n">_overload_registry</span><span class="o">.</span><span class="n">clear</span><span class="p">()</span>
-<span class="linenos">2629</span>
-<span class="linenos">2630</span>
-<span class="linenos">2631</span><span class="k">def</span> <span class="nf">final</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
-<span class="linenos">2632</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator to indicate final methods and final classes.</span>
-<span class="linenos">2633</span>
-<span class="linenos">2634</span><span class="sd">    Use this decorator to indicate to type checkers that the decorated</span>
-<span class="linenos">2635</span><span class="sd">    method cannot be overridden, and decorated class cannot be subclassed.</span>
-<span class="linenos">2636</span>
-<span class="linenos">2637</span><span class="sd">    For example::</span>
+<span class="linenos">2625</span><span class="sd">        class Base:</span>
+<span class="linenos">2626</span><span class="sd">            @final</span>
+<span class="linenos">2627</span><span class="sd">            def done(self) -&gt; None:</span>
+<span class="linenos">2628</span><span class="sd">                ...</span>
+<span class="linenos">2629</span><span class="sd">        class Sub(Base):</span>
+<span class="linenos">2630</span><span class="sd">            def done(self) -&gt; None:  # Error reported by type checker</span>
+<span class="linenos">2631</span><span class="sd">                ...</span>
+<span class="linenos">2632</span>
+<span class="linenos">2633</span><span class="sd">        @final</span>
+<span class="linenos">2634</span><span class="sd">        class Leaf:</span>
+<span class="linenos">2635</span><span class="sd">            ...</span>
+<span class="linenos">2636</span><span class="sd">        class Other(Leaf):  # Error reported by type checker</span>
+<span class="linenos">2637</span><span class="sd">            ...</span>
 <span class="linenos">2638</span>
-<span class="linenos">2639</span><span class="sd">        class Base:</span>
-<span class="linenos">2640</span><span class="sd">            @final</span>
-<span class="linenos">2641</span><span class="sd">            def done(self) -&gt; None:</span>
-<span class="linenos">2642</span><span class="sd">                ...</span>
-<span class="linenos">2643</span><span class="sd">        class Sub(Base):</span>
-<span class="linenos">2644</span><span class="sd">            def done(self) -&gt; None:  # Error reported by type checker</span>
-<span class="linenos">2645</span><span class="sd">                ...</span>
-<span class="linenos">2646</span>
-<span class="linenos">2647</span><span class="sd">        @final</span>
-<span class="linenos">2648</span><span class="sd">        class Leaf:</span>
-<span class="linenos">2649</span><span class="sd">            ...</span>
-<span class="linenos">2650</span><span class="sd">        class Other(Leaf):  # Error reported by type checker</span>
-<span class="linenos">2651</span><span class="sd">            ...</span>
+<span class="linenos">2639</span><span class="sd">    There is no runtime checking of these properties. The decorator</span>
+<span class="linenos">2640</span><span class="sd">    attempts to set the ``__final__`` attribute to ``True`` on the decorated</span>
+<span class="linenos">2641</span><span class="sd">    object to allow runtime introspection.</span>
+<span class="linenos">2642</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2643</span>    <span class="k">try</span><span class="p">:</span>
+<span class="linenos">2644</span>        <span class="n">f</span><span class="o">.</span><span class="n">__final__</span> <span class="o">=</span> <span class="kc">True</span>
+<span class="linenos">2645</span>    <span class="k">except</span> <span class="p">(</span><span class="ne">AttributeError</span><span class="p">,</span> <span class="ne">TypeError</span><span class="p">):</span>
+<span class="linenos">2646</span>        <span class="c1"># Skip the attribute silently if it is not writable.</span>
+<span class="linenos">2647</span>        <span class="c1"># AttributeError happens if the object has __slots__ or a</span>
+<span class="linenos">2648</span>        <span class="c1"># read-only property, TypeError if it&#39;s a builtin class.</span>
+<span class="linenos">2649</span>        <span class="k">pass</span>
+<span class="linenos">2650</span>    <span class="k">return</span> <span class="n">f</span>
+<span class="linenos">2651</span>
 <span class="linenos">2652</span>
-<span class="linenos">2653</span><span class="sd">    There is no runtime checking of these properties. The decorator</span>
-<span class="linenos">2654</span><span class="sd">    attempts to set the ``__final__`` attribute to ``True`` on the decorated</span>
-<span class="linenos">2655</span><span class="sd">    object to allow runtime introspection.</span>
-<span class="linenos">2656</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2657</span>    <span class="k">try</span><span class="p">:</span>
-<span class="linenos">2658</span>        <span class="n">f</span><span class="o">.</span><span class="n">__final__</span> <span class="o">=</span> <span class="kc">True</span>
-<span class="linenos">2659</span>    <span class="k">except</span> <span class="p">(</span><span class="ne">AttributeError</span><span class="p">,</span> <span class="ne">TypeError</span><span class="p">):</span>
-<span class="linenos">2660</span>        <span class="c1"># Skip the attribute silently if it is not writable.</span>
-<span class="linenos">2661</span>        <span class="c1"># AttributeError happens if the object has __slots__ or a</span>
-<span class="linenos">2662</span>        <span class="c1"># read-only property, TypeError if it&#39;s a builtin class.</span>
-<span class="linenos">2663</span>        <span class="k">pass</span>
-<span class="linenos">2664</span>    <span class="k">return</span> <span class="n">f</span>
-<span class="linenos">2665</span>
-<span class="linenos">2666</span>
-<span class="linenos">2667</span><span class="c1"># Some unconstrained type variables.  These are used by the container types.</span>
-<span class="linenos">2668</span><span class="c1"># (These are not for export.)</span>
-<span class="linenos">2669</span><span class="n">T</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;T&#39;</span><span class="p">)</span>  <span class="c1"># Any type.</span>
-<span class="linenos">2670</span><span class="n">KT</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;KT&#39;</span><span class="p">)</span>  <span class="c1"># Key type.</span>
-<span class="linenos">2671</span><span class="n">VT</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;VT&#39;</span><span class="p">)</span>  <span class="c1"># Value type.</span>
-<span class="linenos">2672</span><span class="n">T_co</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;T_co&#39;</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># Any type covariant containers.</span>
-<span class="linenos">2673</span><span class="n">V_co</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;V_co&#39;</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># Any type covariant containers.</span>
-<span class="linenos">2674</span><span class="n">VT_co</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;VT_co&#39;</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># Value type covariant containers.</span>
-<span class="linenos">2675</span><span class="n">T_contra</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;T_contra&#39;</span><span class="p">,</span> <span class="n">contravariant</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># Ditto contravariant.</span>
-<span class="linenos">2676</span><span class="c1"># Internal type variable used for Type[].</span>
-<span class="linenos">2677</span><span class="n">CT_co</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;CT_co&#39;</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">bound</span><span class="o">=</span><span class="nb">type</span><span class="p">)</span>
-<span class="linenos">2678</span>
-<span class="linenos">2679</span><span class="c1"># A useful type variable with constraints.  This represents string types.</span>
-<span class="linenos">2680</span><span class="c1"># (This one *is* for export!)</span>
-<span class="linenos">2681</span><span class="n">AnyStr</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;AnyStr&#39;</span><span class="p">,</span> <span class="nb">bytes</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span>
-<span class="linenos">2682</span>
-<span class="linenos">2683</span>
-<span class="linenos">2684</span><span class="c1"># Various ABCs mimicking those in collections.abc.</span>
-<span class="linenos">2685</span><span class="n">_alias</span> <span class="o">=</span> <span class="n">_SpecialGenericAlias</span>
-<span class="linenos">2686</span>
-<span class="linenos">2687</span><span class="n">Hashable</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Hashable</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>  <span class="c1"># Not generic.</span>
-<span class="linenos">2688</span><span class="n">Awaitable</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Awaitable</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2689</span><span class="n">Coroutine</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Coroutine</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
-<span class="linenos">2690</span><span class="n">AsyncIterable</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">AsyncIterable</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2691</span><span class="n">AsyncIterator</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">AsyncIterator</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2692</span><span class="n">Iterable</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Iterable</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2693</span><span class="n">Iterator</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Iterator</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2694</span><span class="n">Reversible</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Reversible</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2695</span><span class="n">Sized</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Sized</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>  <span class="c1"># Not generic.</span>
-<span class="linenos">2696</span><span class="n">Container</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Container</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2697</span><span class="n">Collection</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Collection</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2698</span><span class="n">Callable</span> <span class="o">=</span> <span class="n">_CallableType</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Callable</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="linenos">2699</span><span class="n">Callable</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> \
-<span class="linenos">2700</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Deprecated alias to collections.abc.Callable.</span>
-<span class="linenos">2701</span>
-<span class="linenos">2702</span><span class="sd">    Callable[[int], str] signifies a function that takes a single</span>
-<span class="linenos">2703</span><span class="sd">    parameter of type int and returns a str.</span>
-<span class="linenos">2704</span>
-<span class="linenos">2705</span><span class="sd">    The subscription syntax must always be used with exactly two</span>
-<span class="linenos">2706</span><span class="sd">    values: the argument list and the return type.</span>
-<span class="linenos">2707</span><span class="sd">    The argument list must be a list of types, a ParamSpec,</span>
-<span class="linenos">2708</span><span class="sd">    Concatenate or ellipsis. The return type must be a single type.</span>
+<span class="linenos">2653</span><span class="c1"># Some unconstrained type variables.  These are used by the container types.</span>
+<span class="linenos">2654</span><span class="c1"># (These are not for export.)</span>
+<span class="linenos">2655</span><span class="n">T</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;T&#39;</span><span class="p">)</span>  <span class="c1"># Any type.</span>
+<span class="linenos">2656</span><span class="n">KT</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;KT&#39;</span><span class="p">)</span>  <span class="c1"># Key type.</span>
+<span class="linenos">2657</span><span class="n">VT</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;VT&#39;</span><span class="p">)</span>  <span class="c1"># Value type.</span>
+<span class="linenos">2658</span><span class="n">T_co</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;T_co&#39;</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># Any type covariant containers.</span>
+<span class="linenos">2659</span><span class="n">V_co</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;V_co&#39;</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># Any type covariant containers.</span>
+<span class="linenos">2660</span><span class="n">VT_co</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;VT_co&#39;</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># Value type covariant containers.</span>
+<span class="linenos">2661</span><span class="n">T_contra</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;T_contra&#39;</span><span class="p">,</span> <span class="n">contravariant</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>  <span class="c1"># Ditto contravariant.</span>
+<span class="linenos">2662</span><span class="c1"># Internal type variable used for Type[].</span>
+<span class="linenos">2663</span><span class="n">CT_co</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;CT_co&#39;</span><span class="p">,</span> <span class="n">covariant</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">bound</span><span class="o">=</span><span class="nb">type</span><span class="p">)</span>
+<span class="linenos">2664</span>
+<span class="linenos">2665</span><span class="c1"># A useful type variable with constraints.  This represents string types.</span>
+<span class="linenos">2666</span><span class="c1"># (This one *is* for export!)</span>
+<span class="linenos">2667</span><span class="n">AnyStr</span> <span class="o">=</span> <span class="n">TypeVar</span><span class="p">(</span><span class="s1">&#39;AnyStr&#39;</span><span class="p">,</span> <span class="nb">bytes</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span>
+<span class="linenos">2668</span>
+<span class="linenos">2669</span>
+<span class="linenos">2670</span><span class="c1"># Various ABCs mimicking those in collections.abc.</span>
+<span class="linenos">2671</span><span class="n">_alias</span> <span class="o">=</span> <span class="n">_SpecialGenericAlias</span>
+<span class="linenos">2672</span>
+<span class="linenos">2673</span><span class="n">Hashable</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Hashable</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>  <span class="c1"># Not generic.</span>
+<span class="linenos">2674</span><span class="n">Awaitable</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Awaitable</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2675</span><span class="n">Coroutine</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Coroutine</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
+<span class="linenos">2676</span><span class="n">AsyncIterable</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">AsyncIterable</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2677</span><span class="n">AsyncIterator</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">AsyncIterator</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2678</span><span class="n">Iterable</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Iterable</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2679</span><span class="n">Iterator</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Iterator</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2680</span><span class="n">Reversible</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Reversible</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2681</span><span class="n">Sized</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Sized</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>  <span class="c1"># Not generic.</span>
+<span class="linenos">2682</span><span class="n">Container</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Container</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2683</span><span class="n">Collection</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Collection</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2684</span><span class="n">Callable</span> <span class="o">=</span> <span class="n">_CallableType</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Callable</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+<span class="linenos">2685</span><span class="n">Callable</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> \
+<span class="linenos">2686</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Deprecated alias to collections.abc.Callable.</span>
+<span class="linenos">2687</span>
+<span class="linenos">2688</span><span class="sd">    Callable[[int], str] signifies a function of (int) -&gt; str.</span>
+<span class="linenos">2689</span><span class="sd">    The subscription syntax must always be used with exactly two</span>
+<span class="linenos">2690</span><span class="sd">    values: the argument list and the return type.</span>
+<span class="linenos">2691</span><span class="sd">    The argument list must be a list of types, a ParamSpec or ellipsis.</span>
+<span class="linenos">2692</span><span class="sd">    The return type must be a single type.</span>
+<span class="linenos">2693</span>
+<span class="linenos">2694</span><span class="sd">    There is no syntax to indicate optional or keyword arguments;</span>
+<span class="linenos">2695</span><span class="sd">    such function types are rarely used as callback types.</span>
+<span class="linenos">2696</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2697</span><span class="n">AbstractSet</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Set</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;AbstractSet&#39;</span><span class="p">)</span>
+<span class="linenos">2698</span><span class="n">MutableSet</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">MutableSet</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2699</span><span class="c1"># NOTE: Mapping is only covariant in the value type.</span>
+<span class="linenos">2700</span><span class="n">Mapping</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Mapping</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+<span class="linenos">2701</span><span class="n">MutableMapping</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">MutableMapping</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+<span class="linenos">2702</span><span class="n">Sequence</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2703</span><span class="n">MutableSequence</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">MutableSequence</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2704</span><span class="n">ByteString</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">ByteString</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>  <span class="c1"># Not generic</span>
+<span class="linenos">2705</span><span class="c1"># Tuple accepts variable number of parameters.</span>
+<span class="linenos">2706</span><span class="n">Tuple</span> <span class="o">=</span> <span class="n">_TupleType</span><span class="p">(</span><span class="nb">tuple</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Tuple&#39;</span><span class="p">)</span>
+<span class="linenos">2707</span><span class="n">Tuple</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> \
+<span class="linenos">2708</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Deprecated alias to builtins.tuple.</span>
 <span class="linenos">2709</span>
-<span class="linenos">2710</span><span class="sd">    There is no syntax to indicate optional or keyword arguments;</span>
-<span class="linenos">2711</span><span class="sd">    such function types are rarely used as callback types.</span>
-<span class="linenos">2712</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2713</span><span class="n">AbstractSet</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Set</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;AbstractSet&#39;</span><span class="p">)</span>
-<span class="linenos">2714</span><span class="n">MutableSet</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">MutableSet</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2715</span><span class="c1"># NOTE: Mapping is only covariant in the value type.</span>
-<span class="linenos">2716</span><span class="n">Mapping</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Mapping</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="linenos">2717</span><span class="n">MutableMapping</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">MutableMapping</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="linenos">2718</span><span class="n">Sequence</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2719</span><span class="n">MutableSequence</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">MutableSequence</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2720</span><span class="n">ByteString</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">ByteString</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>  <span class="c1"># Not generic</span>
-<span class="linenos">2721</span><span class="c1"># Tuple accepts variable number of parameters.</span>
-<span class="linenos">2722</span><span class="n">Tuple</span> <span class="o">=</span> <span class="n">_TupleType</span><span class="p">(</span><span class="nb">tuple</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Tuple&#39;</span><span class="p">)</span>
-<span class="linenos">2723</span><span class="n">Tuple</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> \
-<span class="linenos">2724</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Deprecated alias to builtins.tuple.</span>
-<span class="linenos">2725</span>
-<span class="linenos">2726</span><span class="sd">    Tuple[X, Y] is the cross-product type of X and Y.</span>
-<span class="linenos">2727</span>
-<span class="linenos">2728</span><span class="sd">    Example: Tuple[T1, T2] is a tuple of two elements corresponding</span>
-<span class="linenos">2729</span><span class="sd">    to type variables T1 and T2.  Tuple[int, float, str] is a tuple</span>
-<span class="linenos">2730</span><span class="sd">    of an int, a float and a string.</span>
-<span class="linenos">2731</span>
-<span class="linenos">2732</span><span class="sd">    To specify a variable-length tuple of homogeneous type, use Tuple[T, ...].</span>
-<span class="linenos">2733</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2734</span><span class="n">List</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;List&#39;</span><span class="p">)</span>
-<span class="linenos">2735</span><span class="n">Deque</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">deque</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Deque&#39;</span><span class="p">)</span>
-<span class="linenos">2736</span><span class="n">Set</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">set</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Set&#39;</span><span class="p">)</span>
-<span class="linenos">2737</span><span class="n">FrozenSet</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">frozenset</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;FrozenSet&#39;</span><span class="p">)</span>
-<span class="linenos">2738</span><span class="n">MappingView</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">MappingView</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2739</span><span class="n">KeysView</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">KeysView</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2740</span><span class="n">ItemsView</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">ItemsView</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="linenos">2741</span><span class="n">ValuesView</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">ValuesView</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2742</span><span class="n">ContextManager</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">contextlib</span><span class="o">.</span><span class="n">AbstractContextManager</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;ContextManager&#39;</span><span class="p">)</span>
-<span class="linenos">2743</span><span class="n">AsyncContextManager</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">contextlib</span><span class="o">.</span><span class="n">AbstractAsyncContextManager</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;AsyncContextManager&#39;</span><span class="p">)</span>
-<span class="linenos">2744</span><span class="n">Dict</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">dict</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Dict&#39;</span><span class="p">)</span>
-<span class="linenos">2745</span><span class="n">DefaultDict</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;DefaultDict&#39;</span><span class="p">)</span>
-<span class="linenos">2746</span><span class="n">OrderedDict</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">OrderedDict</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="linenos">2747</span><span class="n">Counter</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">Counter</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">2748</span><span class="n">ChainMap</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">ChainMap</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="linenos">2749</span><span class="n">Generator</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Generator</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
-<span class="linenos">2750</span><span class="n">AsyncGenerator</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">AsyncGenerator</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
-<span class="linenos">2751</span><span class="n">Type</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">type</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Type&#39;</span><span class="p">)</span>
-<span class="linenos">2752</span><span class="n">Type</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> \
-<span class="linenos">2753</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Deprecated alias to builtins.type.</span>
-<span class="linenos">2754</span>
-<span class="linenos">2755</span><span class="sd">    builtins.type or typing.Type can be used to annotate class objects.</span>
-<span class="linenos">2756</span><span class="sd">    For example, suppose we have the following classes::</span>
+<span class="linenos">2710</span><span class="sd">    Tuple[X, Y] is the cross-product type of X and Y.</span>
+<span class="linenos">2711</span>
+<span class="linenos">2712</span><span class="sd">    Example: Tuple[T1, T2] is a tuple of two elements corresponding</span>
+<span class="linenos">2713</span><span class="sd">    to type variables T1 and T2.  Tuple[int, float, str] is a tuple</span>
+<span class="linenos">2714</span><span class="sd">    of an int, a float and a string.</span>
+<span class="linenos">2715</span>
+<span class="linenos">2716</span><span class="sd">    To specify a variable-length tuple of homogeneous type, use Tuple[T, ...].</span>
+<span class="linenos">2717</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2718</span><span class="n">List</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;List&#39;</span><span class="p">)</span>
+<span class="linenos">2719</span><span class="n">Deque</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">deque</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Deque&#39;</span><span class="p">)</span>
+<span class="linenos">2720</span><span class="n">Set</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">set</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Set&#39;</span><span class="p">)</span>
+<span class="linenos">2721</span><span class="n">FrozenSet</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">frozenset</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;FrozenSet&#39;</span><span class="p">)</span>
+<span class="linenos">2722</span><span class="n">MappingView</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">MappingView</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2723</span><span class="n">KeysView</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">KeysView</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2724</span><span class="n">ItemsView</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">ItemsView</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+<span class="linenos">2725</span><span class="n">ValuesView</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">ValuesView</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2726</span><span class="n">ContextManager</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">contextlib</span><span class="o">.</span><span class="n">AbstractContextManager</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;ContextManager&#39;</span><span class="p">)</span>
+<span class="linenos">2727</span><span class="n">AsyncContextManager</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">contextlib</span><span class="o">.</span><span class="n">AbstractAsyncContextManager</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;AsyncContextManager&#39;</span><span class="p">)</span>
+<span class="linenos">2728</span><span class="n">Dict</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">dict</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Dict&#39;</span><span class="p">)</span>
+<span class="linenos">2729</span><span class="n">DefaultDict</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">defaultdict</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;DefaultDict&#39;</span><span class="p">)</span>
+<span class="linenos">2730</span><span class="n">OrderedDict</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">OrderedDict</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+<span class="linenos">2731</span><span class="n">Counter</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">Counter</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">2732</span><span class="n">ChainMap</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">ChainMap</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+<span class="linenos">2733</span><span class="n">Generator</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">Generator</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
+<span class="linenos">2734</span><span class="n">AsyncGenerator</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">collections</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">AsyncGenerator</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+<span class="linenos">2735</span><span class="n">Type</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="nb">type</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">inst</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="s1">&#39;Type&#39;</span><span class="p">)</span>
+<span class="linenos">2736</span><span class="n">Type</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> \
+<span class="linenos">2737</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Deprecated alias to builtins.type.</span>
+<span class="linenos">2738</span>
+<span class="linenos">2739</span><span class="sd">    builtins.type or typing.Type can be used to annotate class objects.</span>
+<span class="linenos">2740</span><span class="sd">    For example, suppose we have the following classes::</span>
+<span class="linenos">2741</span>
+<span class="linenos">2742</span><span class="sd">        class User: ...  # Abstract base for User classes</span>
+<span class="linenos">2743</span><span class="sd">        class BasicUser(User): ...</span>
+<span class="linenos">2744</span><span class="sd">        class ProUser(User): ...</span>
+<span class="linenos">2745</span><span class="sd">        class TeamUser(User): ...</span>
+<span class="linenos">2746</span>
+<span class="linenos">2747</span><span class="sd">    And a function that takes a class argument that&#39;s a subclass of</span>
+<span class="linenos">2748</span><span class="sd">    User and returns an instance of the corresponding class::</span>
+<span class="linenos">2749</span>
+<span class="linenos">2750</span><span class="sd">        U = TypeVar(&#39;U&#39;, bound=User)</span>
+<span class="linenos">2751</span><span class="sd">        def new_user(user_class: Type[U]) -&gt; U:</span>
+<span class="linenos">2752</span><span class="sd">            user = user_class()</span>
+<span class="linenos">2753</span><span class="sd">            # (Here we could write the user object to a database)</span>
+<span class="linenos">2754</span><span class="sd">            return user</span>
+<span class="linenos">2755</span>
+<span class="linenos">2756</span><span class="sd">        joe = new_user(BasicUser)</span>
 <span class="linenos">2757</span>
-<span class="linenos">2758</span><span class="sd">        class User: ...  # Abstract base for User classes</span>
-<span class="linenos">2759</span><span class="sd">        class BasicUser(User): ...</span>
-<span class="linenos">2760</span><span class="sd">        class ProUser(User): ...</span>
-<span class="linenos">2761</span><span class="sd">        class TeamUser(User): ...</span>
-<span class="linenos">2762</span>
-<span class="linenos">2763</span><span class="sd">    And a function that takes a class argument that&#39;s a subclass of</span>
-<span class="linenos">2764</span><span class="sd">    User and returns an instance of the corresponding class::</span>
+<span class="linenos">2758</span><span class="sd">    At this point the type checker knows that joe has type BasicUser.</span>
+<span class="linenos">2759</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2760</span>
+<span class="linenos">2761</span>
+<span class="linenos">2762</span><span class="nd">@runtime_checkable</span>
+<span class="linenos">2763</span><span class="k">class</span> <span class="nc">SupportsInt</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
+<span class="linenos">2764</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __int__.&quot;&quot;&quot;</span>
 <span class="linenos">2765</span>
-<span class="linenos">2766</span><span class="sd">        U = TypeVar(&#39;U&#39;, bound=User)</span>
-<span class="linenos">2767</span><span class="sd">        def new_user(user_class: Type[U]) -&gt; U:</span>
-<span class="linenos">2768</span><span class="sd">            user = user_class()</span>
-<span class="linenos">2769</span><span class="sd">            # (Here we could write the user object to a database)</span>
-<span class="linenos">2770</span><span class="sd">            return user</span>
+<span class="linenos">2766</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2767</span>
+<span class="linenos">2768</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">2769</span>    <span class="k">def</span> <span class="fm">__int__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<span class="linenos">2770</span>        <span class="k">pass</span>
 <span class="linenos">2771</span>
-<span class="linenos">2772</span><span class="sd">        joe = new_user(BasicUser)</span>
-<span class="linenos">2773</span>
-<span class="linenos">2774</span><span class="sd">    At this point the type checker knows that joe has type BasicUser.</span>
-<span class="linenos">2775</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2772</span>
+<span class="linenos">2773</span><span class="nd">@runtime_checkable</span>
+<span class="linenos">2774</span><span class="k">class</span> <span class="nc">SupportsFloat</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
+<span class="linenos">2775</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __float__.&quot;&quot;&quot;</span>
 <span class="linenos">2776</span>
-<span class="linenos">2777</span>
-<span class="linenos">2778</span><span class="nd">@runtime_checkable</span>
-<span class="linenos">2779</span><span class="k">class</span> <span class="nc">SupportsInt</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
-<span class="linenos">2780</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __int__.&quot;&quot;&quot;</span>
-<span class="linenos">2781</span>
-<span class="linenos">2782</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2777</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2778</span>
+<span class="linenos">2779</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">2780</span>    <span class="k">def</span> <span class="fm">__float__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
+<span class="linenos">2781</span>        <span class="k">pass</span>
+<span class="linenos">2782</span>
 <span class="linenos">2783</span>
-<span class="linenos">2784</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">2785</span>    <span class="k">def</span> <span class="fm">__int__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<span class="linenos">2786</span>        <span class="k">pass</span>
+<span class="linenos">2784</span><span class="nd">@runtime_checkable</span>
+<span class="linenos">2785</span><span class="k">class</span> <span class="nc">SupportsComplex</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
+<span class="linenos">2786</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __complex__.&quot;&quot;&quot;</span>
 <span class="linenos">2787</span>
-<span class="linenos">2788</span>
-<span class="linenos">2789</span><span class="nd">@runtime_checkable</span>
-<span class="linenos">2790</span><span class="k">class</span> <span class="nc">SupportsFloat</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
-<span class="linenos">2791</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __float__.&quot;&quot;&quot;</span>
-<span class="linenos">2792</span>
-<span class="linenos">2793</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2788</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2789</span>
+<span class="linenos">2790</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">2791</span>    <span class="k">def</span> <span class="fm">__complex__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">complex</span><span class="p">:</span>
+<span class="linenos">2792</span>        <span class="k">pass</span>
+<span class="linenos">2793</span>
 <span class="linenos">2794</span>
-<span class="linenos">2795</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">2796</span>    <span class="k">def</span> <span class="fm">__float__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
-<span class="linenos">2797</span>        <span class="k">pass</span>
+<span class="linenos">2795</span><span class="nd">@runtime_checkable</span>
+<span class="linenos">2796</span><span class="k">class</span> <span class="nc">SupportsBytes</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
+<span class="linenos">2797</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __bytes__.&quot;&quot;&quot;</span>
 <span class="linenos">2798</span>
-<span class="linenos">2799</span>
-<span class="linenos">2800</span><span class="nd">@runtime_checkable</span>
-<span class="linenos">2801</span><span class="k">class</span> <span class="nc">SupportsComplex</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
-<span class="linenos">2802</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __complex__.&quot;&quot;&quot;</span>
-<span class="linenos">2803</span>
-<span class="linenos">2804</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2799</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2800</span>
+<span class="linenos">2801</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">2802</span>    <span class="k">def</span> <span class="fm">__bytes__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bytes</span><span class="p">:</span>
+<span class="linenos">2803</span>        <span class="k">pass</span>
+<span class="linenos">2804</span>
 <span class="linenos">2805</span>
-<span class="linenos">2806</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">2807</span>    <span class="k">def</span> <span class="fm">__complex__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">complex</span><span class="p">:</span>
-<span class="linenos">2808</span>        <span class="k">pass</span>
+<span class="linenos">2806</span><span class="nd">@runtime_checkable</span>
+<span class="linenos">2807</span><span class="k">class</span> <span class="nc">SupportsIndex</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
+<span class="linenos">2808</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __index__.&quot;&quot;&quot;</span>
 <span class="linenos">2809</span>
-<span class="linenos">2810</span>
-<span class="linenos">2811</span><span class="nd">@runtime_checkable</span>
-<span class="linenos">2812</span><span class="k">class</span> <span class="nc">SupportsBytes</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
-<span class="linenos">2813</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __bytes__.&quot;&quot;&quot;</span>
-<span class="linenos">2814</span>
-<span class="linenos">2815</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2810</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2811</span>
+<span class="linenos">2812</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">2813</span>    <span class="k">def</span> <span class="fm">__index__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<span class="linenos">2814</span>        <span class="k">pass</span>
+<span class="linenos">2815</span>
 <span class="linenos">2816</span>
-<span class="linenos">2817</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">2818</span>    <span class="k">def</span> <span class="fm">__bytes__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bytes</span><span class="p">:</span>
-<span class="linenos">2819</span>        <span class="k">pass</span>
+<span class="linenos">2817</span><span class="nd">@runtime_checkable</span>
+<span class="linenos">2818</span><span class="k">class</span> <span class="nc">SupportsAbs</span><span class="p">(</span><span class="n">Protocol</span><span class="p">[</span><span class="n">T_co</span><span class="p">]):</span>
+<span class="linenos">2819</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __abs__ that is covariant in its return type.&quot;&quot;&quot;</span>
 <span class="linenos">2820</span>
-<span class="linenos">2821</span>
-<span class="linenos">2822</span><span class="nd">@runtime_checkable</span>
-<span class="linenos">2823</span><span class="k">class</span> <span class="nc">SupportsIndex</span><span class="p">(</span><span class="n">Protocol</span><span class="p">):</span>
-<span class="linenos">2824</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __index__.&quot;&quot;&quot;</span>
-<span class="linenos">2825</span>
-<span class="linenos">2826</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2821</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2822</span>
+<span class="linenos">2823</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">2824</span>    <span class="k">def</span> <span class="fm">__abs__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">T_co</span><span class="p">:</span>
+<span class="linenos">2825</span>        <span class="k">pass</span>
+<span class="linenos">2826</span>
 <span class="linenos">2827</span>
-<span class="linenos">2828</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">2829</span>    <span class="k">def</span> <span class="fm">__index__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<span class="linenos">2830</span>        <span class="k">pass</span>
+<span class="linenos">2828</span><span class="nd">@runtime_checkable</span>
+<span class="linenos">2829</span><span class="k">class</span> <span class="nc">SupportsRound</span><span class="p">(</span><span class="n">Protocol</span><span class="p">[</span><span class="n">T_co</span><span class="p">]):</span>
+<span class="linenos">2830</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __round__ that is covariant in its return type.&quot;&quot;&quot;</span>
 <span class="linenos">2831</span>
-<span class="linenos">2832</span>
-<span class="linenos">2833</span><span class="nd">@runtime_checkable</span>
-<span class="linenos">2834</span><span class="k">class</span> <span class="nc">SupportsAbs</span><span class="p">(</span><span class="n">Protocol</span><span class="p">[</span><span class="n">T_co</span><span class="p">]):</span>
-<span class="linenos">2835</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __abs__ that is covariant in its return type.&quot;&quot;&quot;</span>
-<span class="linenos">2836</span>
-<span class="linenos">2837</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2832</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2833</span>
+<span class="linenos">2834</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">2835</span>    <span class="k">def</span> <span class="fm">__round__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ndigits</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">T_co</span><span class="p">:</span>
+<span class="linenos">2836</span>        <span class="k">pass</span>
+<span class="linenos">2837</span>
 <span class="linenos">2838</span>
-<span class="linenos">2839</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">2840</span>    <span class="k">def</span> <span class="fm">__abs__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">T_co</span><span class="p">:</span>
-<span class="linenos">2841</span>        <span class="k">pass</span>
-<span class="linenos">2842</span>
-<span class="linenos">2843</span>
-<span class="linenos">2844</span><span class="nd">@runtime_checkable</span>
-<span class="linenos">2845</span><span class="k">class</span> <span class="nc">SupportsRound</span><span class="p">(</span><span class="n">Protocol</span><span class="p">[</span><span class="n">T_co</span><span class="p">]):</span>
-<span class="linenos">2846</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;An ABC with one abstract method __round__ that is covariant in its return type.&quot;&quot;&quot;</span>
+<span class="linenos">2839</span><span class="k">def</span> <span class="nf">_make_nmtuple</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">types</span><span class="p">,</span> <span class="n">module</span><span class="p">,</span> <span class="n">defaults</span> <span class="o">=</span> <span class="p">()):</span>
+<span class="linenos">2840</span>    <span class="n">fields</span> <span class="o">=</span> <span class="p">[</span><span class="n">n</span> <span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">types</span><span class="p">]</span>
+<span class="linenos">2841</span>    <span class="n">types</span> <span class="o">=</span> <span class="p">{</span><span class="n">n</span><span class="p">:</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;field </span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s2"> annotation must be a type&quot;</span><span class="p">)</span>
+<span class="linenos">2842</span>             <span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">types</span><span class="p">}</span>
+<span class="linenos">2843</span>    <span class="n">nm_tpl</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">namedtuple</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">fields</span><span class="p">,</span>
+<span class="linenos">2844</span>                                    <span class="n">defaults</span><span class="o">=</span><span class="n">defaults</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="n">module</span><span class="p">)</span>
+<span class="linenos">2845</span>    <span class="n">nm_tpl</span><span class="o">.</span><span class="vm">__annotations__</span> <span class="o">=</span> <span class="n">nm_tpl</span><span class="o">.</span><span class="fm">__new__</span><span class="o">.</span><span class="vm">__annotations__</span> <span class="o">=</span> <span class="n">types</span>
+<span class="linenos">2846</span>    <span class="k">return</span> <span class="n">nm_tpl</span>
 <span class="linenos">2847</span>
-<span class="linenos">2848</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
-<span class="linenos">2849</span>
-<span class="linenos">2850</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">2851</span>    <span class="k">def</span> <span class="fm">__round__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ndigits</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">T_co</span><span class="p">:</span>
-<span class="linenos">2852</span>        <span class="k">pass</span>
+<span class="linenos">2848</span>
+<span class="linenos">2849</span><span class="c1"># attributes prohibited to set in NamedTuple class syntax</span>
+<span class="linenos">2850</span><span class="n">_prohibited</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;__new__&#39;</span><span class="p">,</span> <span class="s1">&#39;__init__&#39;</span><span class="p">,</span> <span class="s1">&#39;__slots__&#39;</span><span class="p">,</span> <span class="s1">&#39;__getnewargs__&#39;</span><span class="p">,</span>
+<span class="linenos">2851</span>                         <span class="s1">&#39;_fields&#39;</span><span class="p">,</span> <span class="s1">&#39;_field_defaults&#39;</span><span class="p">,</span>
+<span class="linenos">2852</span>                         <span class="s1">&#39;_make&#39;</span><span class="p">,</span> <span class="s1">&#39;_replace&#39;</span><span class="p">,</span> <span class="s1">&#39;_asdict&#39;</span><span class="p">,</span> <span class="s1">&#39;_source&#39;</span><span class="p">})</span>
 <span class="linenos">2853</span>
-<span class="linenos">2854</span>
-<span class="linenos">2855</span><span class="k">def</span> <span class="nf">_make_nmtuple</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">types</span><span class="p">,</span> <span class="n">module</span><span class="p">,</span> <span class="n">defaults</span> <span class="o">=</span> <span class="p">()):</span>
-<span class="linenos">2856</span>    <span class="n">fields</span> <span class="o">=</span> <span class="p">[</span><span class="n">n</span> <span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">types</span><span class="p">]</span>
-<span class="linenos">2857</span>    <span class="n">types</span> <span class="o">=</span> <span class="p">{</span><span class="n">n</span><span class="p">:</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="sa">f</span><span class="s2">&quot;field </span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s2"> annotation must be a type&quot;</span><span class="p">)</span>
-<span class="linenos">2858</span>             <span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">types</span><span class="p">}</span>
-<span class="linenos">2859</span>    <span class="n">nm_tpl</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">namedtuple</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">fields</span><span class="p">,</span>
-<span class="linenos">2860</span>                                    <span class="n">defaults</span><span class="o">=</span><span class="n">defaults</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="n">module</span><span class="p">)</span>
-<span class="linenos">2861</span>    <span class="n">nm_tpl</span><span class="o">.</span><span class="vm">__annotations__</span> <span class="o">=</span> <span class="n">nm_tpl</span><span class="o">.</span><span class="fm">__new__</span><span class="o">.</span><span class="vm">__annotations__</span> <span class="o">=</span> <span class="n">types</span>
-<span class="linenos">2862</span>    <span class="k">return</span> <span class="n">nm_tpl</span>
-<span class="linenos">2863</span>
-<span class="linenos">2864</span>
-<span class="linenos">2865</span><span class="c1"># attributes prohibited to set in NamedTuple class syntax</span>
-<span class="linenos">2866</span><span class="n">_prohibited</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;__new__&#39;</span><span class="p">,</span> <span class="s1">&#39;__init__&#39;</span><span class="p">,</span> <span class="s1">&#39;__slots__&#39;</span><span class="p">,</span> <span class="s1">&#39;__getnewargs__&#39;</span><span class="p">,</span>
-<span class="linenos">2867</span>                         <span class="s1">&#39;_fields&#39;</span><span class="p">,</span> <span class="s1">&#39;_field_defaults&#39;</span><span class="p">,</span>
-<span class="linenos">2868</span>                         <span class="s1">&#39;_make&#39;</span><span class="p">,</span> <span class="s1">&#39;_replace&#39;</span><span class="p">,</span> <span class="s1">&#39;_asdict&#39;</span><span class="p">,</span> <span class="s1">&#39;_source&#39;</span><span class="p">})</span>
-<span class="linenos">2869</span>
-<span class="linenos">2870</span><span class="n">_special</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;__module__&#39;</span><span class="p">,</span> <span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">})</span>
-<span class="linenos">2871</span>
-<span class="linenos">2872</span>
-<span class="linenos">2873</span><span class="k">class</span> <span class="nc">NamedTupleMeta</span><span class="p">(</span><span class="nb">type</span><span class="p">):</span>
-<span class="linenos">2874</span>    <span class="k">def</span> <span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">typename</span><span class="p">,</span> <span class="n">bases</span><span class="p">,</span> <span class="n">ns</span><span class="p">):</span>
-<span class="linenos">2875</span>        <span class="k">assert</span> <span class="n">_NamedTuple</span> <span class="ow">in</span> <span class="n">bases</span>
-<span class="linenos">2876</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
-<span class="linenos">2877</span>            <span class="k">if</span> <span class="n">base</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">_NamedTuple</span> <span class="ow">and</span> <span class="n">base</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">Generic</span><span class="p">:</span>
-<span class="linenos">2878</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
-<span class="linenos">2879</span>                    <span class="s1">&#39;can only inherit from a NamedTuple type and Generic&#39;</span><span class="p">)</span>
-<span class="linenos">2880</span>        <span class="n">bases</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="nb">tuple</span> <span class="k">if</span> <span class="n">base</span> <span class="ow">is</span> <span class="n">_NamedTuple</span> <span class="k">else</span> <span class="n">base</span> <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">)</span>
-<span class="linenos">2881</span>        <span class="n">types</span> <span class="o">=</span> <span class="n">ns</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
-<span class="linenos">2882</span>        <span class="n">default_names</span> <span class="o">=</span> <span class="p">[]</span>
-<span class="linenos">2883</span>        <span class="k">for</span> <span class="n">field_name</span> <span class="ow">in</span> <span class="n">types</span><span class="p">:</span>
-<span class="linenos">2884</span>            <span class="k">if</span> <span class="n">field_name</span> <span class="ow">in</span> <span class="n">ns</span><span class="p">:</span>
-<span class="linenos">2885</span>                <span class="n">default_names</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">field_name</span><span class="p">)</span>
-<span class="linenos">2886</span>            <span class="k">elif</span> <span class="n">default_names</span><span class="p">:</span>
-<span class="linenos">2887</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Non-default namedtuple field </span><span class="si">{</span><span class="n">field_name</span><span class="si">}</span><span class="s2"> &quot;</span>
-<span class="linenos">2888</span>                                <span class="sa">f</span><span class="s2">&quot;cannot follow default field&quot;</span>
-<span class="linenos">2889</span>                                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;s&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="n">default_names</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;&#39;</span><span class="si">}</span><span class="s2"> &quot;</span>
-<span class="linenos">2890</span>                                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">default_names</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-<span class="linenos">2891</span>        <span class="n">nm_tpl</span> <span class="o">=</span> <span class="n">_make_nmtuple</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">items</span><span class="p">(),</span>
-<span class="linenos">2892</span>                               <span class="n">defaults</span><span class="o">=</span><span class="p">[</span><span class="n">ns</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">default_names</span><span class="p">],</span>
-<span class="linenos">2893</span>                               <span class="n">module</span><span class="o">=</span><span class="n">ns</span><span class="p">[</span><span class="s1">&#39;__module__&#39;</span><span class="p">])</span>
-<span class="linenos">2894</span>        <span class="n">nm_tpl</span><span class="o">.</span><span class="vm">__bases__</span> <span class="o">=</span> <span class="n">bases</span>
-<span class="linenos">2895</span>        <span class="k">if</span> <span class="n">Generic</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
-<span class="linenos">2896</span>            <span class="n">class_getitem</span> <span class="o">=</span> <span class="n">Generic</span><span class="o">.</span><span class="n">__class_getitem__</span><span class="o">.</span><span class="vm">__func__</span>
-<span class="linenos">2897</span>            <span class="n">nm_tpl</span><span class="o">.</span><span class="n">__class_getitem__</span> <span class="o">=</span> <span class="nb">classmethod</span><span class="p">(</span><span class="n">class_getitem</span><span class="p">)</span>
-<span class="linenos">2898</span>        <span class="c1"># update from user namespace without overriding special namedtuple attributes</span>
-<span class="linenos">2899</span>        <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">ns</span><span class="p">:</span>
-<span class="linenos">2900</span>            <span class="k">if</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">_prohibited</span><span class="p">:</span>
-<span class="linenos">2901</span>                <span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="s2">&quot;Cannot overwrite NamedTuple attribute &quot;</span> <span class="o">+</span> <span class="n">key</span><span class="p">)</span>
-<span class="linenos">2902</span>            <span class="k">elif</span> <span class="n">key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">_special</span> <span class="ow">and</span> <span class="n">key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">nm_tpl</span><span class="o">.</span><span class="n">_fields</span><span class="p">:</span>
-<span class="linenos">2903</span>                <span class="nb">setattr</span><span class="p">(</span><span class="n">nm_tpl</span><span class="p">,</span> <span class="n">key</span><span class="p">,</span> <span class="n">ns</span><span class="p">[</span><span class="n">key</span><span class="p">])</span>
-<span class="linenos">2904</span>        <span class="k">if</span> <span class="n">Generic</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
-<span class="linenos">2905</span>            <span class="n">nm_tpl</span><span class="o">.</span><span class="n">__init_subclass__</span><span class="p">()</span>
-<span class="linenos">2906</span>        <span class="k">return</span> <span class="n">nm_tpl</span>
-<span class="linenos">2907</span>
-<span class="linenos">2908</span>
-<span class="linenos">2909</span><span class="k">def</span> <span class="nf">NamedTuple</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="n">fields</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">/</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos">2910</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Typed version of namedtuple.</span>
-<span class="linenos">2911</span>
-<span class="linenos">2912</span><span class="sd">    Usage::</span>
-<span class="linenos">2913</span>
-<span class="linenos">2914</span><span class="sd">        class Employee(NamedTuple):</span>
-<span class="linenos">2915</span><span class="sd">            name: str</span>
-<span class="linenos">2916</span><span class="sd">            id: int</span>
-<span class="linenos">2917</span>
-<span class="linenos">2918</span><span class="sd">    This is equivalent to::</span>
+<span class="linenos">2854</span><span class="n">_special</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">({</span><span class="s1">&#39;__module__&#39;</span><span class="p">,</span> <span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="s1">&#39;__annotations__&#39;</span><span class="p">})</span>
+<span class="linenos">2855</span>
+<span class="linenos">2856</span>
+<span class="linenos">2857</span><span class="k">class</span> <span class="nc">NamedTupleMeta</span><span class="p">(</span><span class="nb">type</span><span class="p">):</span>
+<span class="linenos">2858</span>    <span class="k">def</span> <span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">typename</span><span class="p">,</span> <span class="n">bases</span><span class="p">,</span> <span class="n">ns</span><span class="p">):</span>
+<span class="linenos">2859</span>        <span class="k">assert</span> <span class="n">_NamedTuple</span> <span class="ow">in</span> <span class="n">bases</span>
+<span class="linenos">2860</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
+<span class="linenos">2861</span>            <span class="k">if</span> <span class="n">base</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">_NamedTuple</span> <span class="ow">and</span> <span class="n">base</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">Generic</span><span class="p">:</span>
+<span class="linenos">2862</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
+<span class="linenos">2863</span>                    <span class="s1">&#39;can only inherit from a NamedTuple type and Generic&#39;</span><span class="p">)</span>
+<span class="linenos">2864</span>        <span class="n">bases</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="nb">tuple</span> <span class="k">if</span> <span class="n">base</span> <span class="ow">is</span> <span class="n">_NamedTuple</span> <span class="k">else</span> <span class="n">base</span> <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">)</span>
+<span class="linenos">2865</span>        <span class="n">types</span> <span class="o">=</span> <span class="n">ns</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
+<span class="linenos">2866</span>        <span class="n">default_names</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="linenos">2867</span>        <span class="k">for</span> <span class="n">field_name</span> <span class="ow">in</span> <span class="n">types</span><span class="p">:</span>
+<span class="linenos">2868</span>            <span class="k">if</span> <span class="n">field_name</span> <span class="ow">in</span> <span class="n">ns</span><span class="p">:</span>
+<span class="linenos">2869</span>                <span class="n">default_names</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">field_name</span><span class="p">)</span>
+<span class="linenos">2870</span>            <span class="k">elif</span> <span class="n">default_names</span><span class="p">:</span>
+<span class="linenos">2871</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Non-default namedtuple field </span><span class="si">{</span><span class="n">field_name</span><span class="si">}</span><span class="s2"> &quot;</span>
+<span class="linenos">2872</span>                                <span class="sa">f</span><span class="s2">&quot;cannot follow default field&quot;</span>
+<span class="linenos">2873</span>                                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;s&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="n">default_names</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;&#39;</span><span class="si">}</span><span class="s2"> &quot;</span>
+<span class="linenos">2874</span>                                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="s1">&#39;, &#39;</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">default_names</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="linenos">2875</span>        <span class="n">nm_tpl</span> <span class="o">=</span> <span class="n">_make_nmtuple</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="n">types</span><span class="o">.</span><span class="n">items</span><span class="p">(),</span>
+<span class="linenos">2876</span>                               <span class="n">defaults</span><span class="o">=</span><span class="p">[</span><span class="n">ns</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">default_names</span><span class="p">],</span>
+<span class="linenos">2877</span>                               <span class="n">module</span><span class="o">=</span><span class="n">ns</span><span class="p">[</span><span class="s1">&#39;__module__&#39;</span><span class="p">])</span>
+<span class="linenos">2878</span>        <span class="n">nm_tpl</span><span class="o">.</span><span class="vm">__bases__</span> <span class="o">=</span> <span class="n">bases</span>
+<span class="linenos">2879</span>        <span class="k">if</span> <span class="n">Generic</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
+<span class="linenos">2880</span>            <span class="n">class_getitem</span> <span class="o">=</span> <span class="n">Generic</span><span class="o">.</span><span class="n">__class_getitem__</span><span class="o">.</span><span class="vm">__func__</span>
+<span class="linenos">2881</span>            <span class="n">nm_tpl</span><span class="o">.</span><span class="n">__class_getitem__</span> <span class="o">=</span> <span class="nb">classmethod</span><span class="p">(</span><span class="n">class_getitem</span><span class="p">)</span>
+<span class="linenos">2882</span>        <span class="c1"># update from user namespace without overriding special namedtuple attributes</span>
+<span class="linenos">2883</span>        <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">ns</span><span class="p">:</span>
+<span class="linenos">2884</span>            <span class="k">if</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">_prohibited</span><span class="p">:</span>
+<span class="linenos">2885</span>                <span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="s2">&quot;Cannot overwrite NamedTuple attribute &quot;</span> <span class="o">+</span> <span class="n">key</span><span class="p">)</span>
+<span class="linenos">2886</span>            <span class="k">elif</span> <span class="n">key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">_special</span> <span class="ow">and</span> <span class="n">key</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">nm_tpl</span><span class="o">.</span><span class="n">_fields</span><span class="p">:</span>
+<span class="linenos">2887</span>                <span class="nb">setattr</span><span class="p">(</span><span class="n">nm_tpl</span><span class="p">,</span> <span class="n">key</span><span class="p">,</span> <span class="n">ns</span><span class="p">[</span><span class="n">key</span><span class="p">])</span>
+<span class="linenos">2888</span>        <span class="k">if</span> <span class="n">Generic</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
+<span class="linenos">2889</span>            <span class="n">nm_tpl</span><span class="o">.</span><span class="n">__init_subclass__</span><span class="p">()</span>
+<span class="linenos">2890</span>        <span class="k">return</span> <span class="n">nm_tpl</span>
+<span class="linenos">2891</span>
+<span class="linenos">2892</span>
+<span class="linenos">2893</span><span class="k">def</span> <span class="nf">NamedTuple</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="n">fields</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">/</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos">2894</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Typed version of namedtuple.</span>
+<span class="linenos">2895</span>
+<span class="linenos">2896</span><span class="sd">    Usage::</span>
+<span class="linenos">2897</span>
+<span class="linenos">2898</span><span class="sd">        class Employee(NamedTuple):</span>
+<span class="linenos">2899</span><span class="sd">            name: str</span>
+<span class="linenos">2900</span><span class="sd">            id: int</span>
+<span class="linenos">2901</span>
+<span class="linenos">2902</span><span class="sd">    This is equivalent to::</span>
+<span class="linenos">2903</span>
+<span class="linenos">2904</span><span class="sd">        Employee = collections.namedtuple(&#39;Employee&#39;, [&#39;name&#39;, &#39;id&#39;])</span>
+<span class="linenos">2905</span>
+<span class="linenos">2906</span><span class="sd">    The resulting class has an extra __annotations__ attribute, giving a</span>
+<span class="linenos">2907</span><span class="sd">    dict that maps field names to types.  (The field names are also in</span>
+<span class="linenos">2908</span><span class="sd">    the _fields attribute, which is part of the namedtuple API.)</span>
+<span class="linenos">2909</span><span class="sd">    An alternative equivalent functional syntax is also accepted::</span>
+<span class="linenos">2910</span>
+<span class="linenos">2911</span><span class="sd">        Employee = NamedTuple(&#39;Employee&#39;, [(&#39;name&#39;, str), (&#39;id&#39;, int)])</span>
+<span class="linenos">2912</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">2913</span>    <span class="k">if</span> <span class="n">fields</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">2914</span>        <span class="n">fields</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">items</span><span class="p">()</span>
+<span class="linenos">2915</span>    <span class="k">elif</span> <span class="n">kwargs</span><span class="p">:</span>
+<span class="linenos">2916</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Either list of fields or keywords&quot;</span>
+<span class="linenos">2917</span>                        <span class="s2">&quot; can be provided to NamedTuple, not both&quot;</span><span class="p">)</span>
+<span class="linenos">2918</span>    <span class="k">return</span> <span class="n">_make_nmtuple</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="n">fields</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="n">_caller</span><span class="p">())</span>
 <span class="linenos">2919</span>
-<span class="linenos">2920</span><span class="sd">        Employee = collections.namedtuple(&#39;Employee&#39;, [&#39;name&#39;, &#39;id&#39;])</span>
+<span class="linenos">2920</span><span class="n">_NamedTuple</span> <span class="o">=</span> <span class="nb">type</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="n">NamedTupleMeta</span><span class="p">,</span> <span class="s1">&#39;NamedTuple&#39;</span><span class="p">,</span> <span class="p">(),</span> <span class="p">{})</span>
 <span class="linenos">2921</span>
-<span class="linenos">2922</span><span class="sd">    The resulting class has an extra __annotations__ attribute, giving a</span>
-<span class="linenos">2923</span><span class="sd">    dict that maps field names to types.  (The field names are also in</span>
-<span class="linenos">2924</span><span class="sd">    the _fields attribute, which is part of the namedtuple API.)</span>
-<span class="linenos">2925</span><span class="sd">    An alternative equivalent functional syntax is also accepted::</span>
-<span class="linenos">2926</span>
-<span class="linenos">2927</span><span class="sd">        Employee = NamedTuple(&#39;Employee&#39;, [(&#39;name&#39;, str), (&#39;id&#39;, int)])</span>
-<span class="linenos">2928</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">2929</span>    <span class="k">if</span> <span class="n">fields</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">2930</span>        <span class="n">fields</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">items</span><span class="p">()</span>
-<span class="linenos">2931</span>    <span class="k">elif</span> <span class="n">kwargs</span><span class="p">:</span>
-<span class="linenos">2932</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Either list of fields or keywords&quot;</span>
-<span class="linenos">2933</span>                        <span class="s2">&quot; can be provided to NamedTuple, not both&quot;</span><span class="p">)</span>
-<span class="linenos">2934</span>    <span class="k">return</span> <span class="n">_make_nmtuple</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="n">fields</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="n">_caller</span><span class="p">())</span>
-<span class="linenos">2935</span>
-<span class="linenos">2936</span><span class="n">_NamedTuple</span> <span class="o">=</span> <span class="nb">type</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="n">NamedTupleMeta</span><span class="p">,</span> <span class="s1">&#39;NamedTuple&#39;</span><span class="p">,</span> <span class="p">(),</span> <span class="p">{})</span>
-<span class="linenos">2937</span>
-<span class="linenos">2938</span><span class="k">def</span> <span class="nf">_namedtuple_mro_entries</span><span class="p">(</span><span class="n">bases</span><span class="p">):</span>
-<span class="linenos">2939</span>    <span class="k">assert</span> <span class="n">NamedTuple</span> <span class="ow">in</span> <span class="n">bases</span>
-<span class="linenos">2940</span>    <span class="k">return</span> <span class="p">(</span><span class="n">_NamedTuple</span><span class="p">,)</span>
-<span class="linenos">2941</span>
-<span class="linenos">2942</span><span class="n">NamedTuple</span><span class="o">.</span><span class="n">__mro_entries__</span> <span class="o">=</span> <span class="n">_namedtuple_mro_entries</span>
-<span class="linenos">2943</span>
-<span class="linenos">2944</span>
-<span class="linenos">2945</span><span class="k">class</span> <span class="nc">_TypedDictMeta</span><span class="p">(</span><span class="nb">type</span><span class="p">):</span>
-<span class="linenos">2946</span>    <span class="k">def</span> <span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">bases</span><span class="p">,</span> <span class="n">ns</span><span class="p">,</span> <span class="n">total</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-<span class="linenos">2947</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Create a new typed dict class object.</span>
-<span class="linenos">2948</span>
-<span class="linenos">2949</span><span class="sd">        This method is called when TypedDict is subclassed,</span>
-<span class="linenos">2950</span><span class="sd">        or when TypedDict is instantiated. This way</span>
-<span class="linenos">2951</span><span class="sd">        TypedDict supports all three syntax forms described in its docstring.</span>
-<span class="linenos">2952</span><span class="sd">        Subclasses and instances of TypedDict return actual dictionaries.</span>
-<span class="linenos">2953</span><span class="sd">        &quot;&quot;&quot;</span>
-<span class="linenos">2954</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
-<span class="linenos">2955</span>            <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">base</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">_TypedDictMeta</span> <span class="ow">and</span> <span class="n">base</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">Generic</span><span class="p">:</span>
-<span class="linenos">2956</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;cannot inherit from both a TypedDict type &#39;</span>
-<span class="linenos">2957</span>                                <span class="s1">&#39;and a non-TypedDict base class&#39;</span><span class="p">)</span>
-<span class="linenos">2958</span>
-<span class="linenos">2959</span>        <span class="k">if</span> <span class="nb">any</span><span class="p">(</span><span class="nb">issubclass</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">):</span>
-<span class="linenos">2960</span>            <span class="n">generic_base</span> <span class="o">=</span> <span class="p">(</span><span class="n">Generic</span><span class="p">,)</span>
-<span class="linenos">2961</span>        <span class="k">else</span><span class="p">:</span>
-<span class="linenos">2962</span>            <span class="n">generic_base</span> <span class="o">=</span> <span class="p">()</span>
-<span class="linenos">2963</span>
-<span class="linenos">2964</span>        <span class="n">tp_dict</span> <span class="o">=</span> <span class="nb">type</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="n">_TypedDictMeta</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="p">(</span><span class="o">*</span><span class="n">generic_base</span><span class="p">,</span> <span class="nb">dict</span><span class="p">),</span> <span class="n">ns</span><span class="p">)</span>
-<span class="linenos">2965</span>
-<span class="linenos">2966</span>        <span class="n">annotations</span> <span class="o">=</span> <span class="p">{}</span>
-<span class="linenos">2967</span>        <span class="n">own_annotations</span> <span class="o">=</span> <span class="n">ns</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
-<span class="linenos">2968</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;TypedDict(&#39;Name&#39;, {f0: t0, f1: t1, ...}); each t must be a type&quot;</span>
-<span class="linenos">2969</span>        <span class="n">own_annotations</span> <span class="o">=</span> <span class="p">{</span>
-<span class="linenos">2970</span>            <span class="n">n</span><span class="p">:</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">msg</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="n">tp_dict</span><span class="o">.</span><span class="vm">__module__</span><span class="p">)</span>
-<span class="linenos">2971</span>            <span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">tp</span> <span class="ow">in</span> <span class="n">own_annotations</span><span class="o">.</span><span class="n">items</span><span class="p">()</span>
-<span class="linenos">2972</span>        <span class="p">}</span>
-<span class="linenos">2973</span>        <span class="n">required_keys</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
-<span class="linenos">2974</span>        <span class="n">optional_keys</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
-<span class="linenos">2975</span>
-<span class="linenos">2976</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
-<span class="linenos">2977</span>            <span class="n">annotations</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{}))</span>
-<span class="linenos">2978</span>            <span class="n">required_keys</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__required_keys__&#39;</span><span class="p">,</span> <span class="p">()))</span>
-<span class="linenos">2979</span>            <span class="n">optional_keys</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__optional_keys__&#39;</span><span class="p">,</span> <span class="p">()))</span>
-<span class="linenos">2980</span>
-<span class="linenos">2981</span>        <span class="n">annotations</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">own_annotations</span><span class="p">)</span>
-<span class="linenos">2982</span>        <span class="k">for</span> <span class="n">annotation_key</span><span class="p">,</span> <span class="n">annotation_type</span> <span class="ow">in</span> <span class="n">own_annotations</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-<span class="linenos">2983</span>            <span class="n">annotation_origin</span> <span class="o">=</span> <span class="n">get_origin</span><span class="p">(</span><span class="n">annotation_type</span><span class="p">)</span>
-<span class="linenos">2984</span>            <span class="k">if</span> <span class="n">annotation_origin</span> <span class="ow">is</span> <span class="n">Annotated</span><span class="p">:</span>
-<span class="linenos">2985</span>                <span class="n">annotation_args</span> <span class="o">=</span> <span class="n">get_args</span><span class="p">(</span><span class="n">annotation_type</span><span class="p">)</span>
-<span class="linenos">2986</span>                <span class="k">if</span> <span class="n">annotation_args</span><span class="p">:</span>
-<span class="linenos">2987</span>                    <span class="n">annotation_type</span> <span class="o">=</span> <span class="n">annotation_args</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-<span class="linenos">2988</span>                    <span class="n">annotation_origin</span> <span class="o">=</span> <span class="n">get_origin</span><span class="p">(</span><span class="n">annotation_type</span><span class="p">)</span>
+<span class="linenos">2922</span><span class="k">def</span> <span class="nf">_namedtuple_mro_entries</span><span class="p">(</span><span class="n">bases</span><span class="p">):</span>
+<span class="linenos">2923</span>    <span class="k">assert</span> <span class="n">NamedTuple</span> <span class="ow">in</span> <span class="n">bases</span>
+<span class="linenos">2924</span>    <span class="k">return</span> <span class="p">(</span><span class="n">_NamedTuple</span><span class="p">,)</span>
+<span class="linenos">2925</span>
+<span class="linenos">2926</span><span class="n">NamedTuple</span><span class="o">.</span><span class="n">__mro_entries__</span> <span class="o">=</span> <span class="n">_namedtuple_mro_entries</span>
+<span class="linenos">2927</span>
+<span class="linenos">2928</span>
+<span class="linenos">2929</span><span class="k">class</span> <span class="nc">_TypedDictMeta</span><span class="p">(</span><span class="nb">type</span><span class="p">):</span>
+<span class="linenos">2930</span>    <span class="k">def</span> <span class="fm">__new__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">bases</span><span class="p">,</span> <span class="n">ns</span><span class="p">,</span> <span class="n">total</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="linenos">2931</span><span class="w">        </span><span class="sd">&quot;&quot;&quot;Create a new typed dict class object.</span>
+<span class="linenos">2932</span>
+<span class="linenos">2933</span><span class="sd">        This method is called when TypedDict is subclassed,</span>
+<span class="linenos">2934</span><span class="sd">        or when TypedDict is instantiated. This way</span>
+<span class="linenos">2935</span><span class="sd">        TypedDict supports all three syntax forms described in its docstring.</span>
+<span class="linenos">2936</span><span class="sd">        Subclasses and instances of TypedDict return actual dictionaries.</span>
+<span class="linenos">2937</span><span class="sd">        &quot;&quot;&quot;</span>
+<span class="linenos">2938</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
+<span class="linenos">2939</span>            <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">base</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">_TypedDictMeta</span> <span class="ow">and</span> <span class="n">base</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">Generic</span><span class="p">:</span>
+<span class="linenos">2940</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;cannot inherit from both a TypedDict type &#39;</span>
+<span class="linenos">2941</span>                                <span class="s1">&#39;and a non-TypedDict base class&#39;</span><span class="p">)</span>
+<span class="linenos">2942</span>
+<span class="linenos">2943</span>        <span class="k">if</span> <span class="nb">any</span><span class="p">(</span><span class="nb">issubclass</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">Generic</span><span class="p">)</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">):</span>
+<span class="linenos">2944</span>            <span class="n">generic_base</span> <span class="o">=</span> <span class="p">(</span><span class="n">Generic</span><span class="p">,)</span>
+<span class="linenos">2945</span>        <span class="k">else</span><span class="p">:</span>
+<span class="linenos">2946</span>            <span class="n">generic_base</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">2947</span>
+<span class="linenos">2948</span>        <span class="n">tp_dict</span> <span class="o">=</span> <span class="nb">type</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="n">_TypedDictMeta</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="p">(</span><span class="o">*</span><span class="n">generic_base</span><span class="p">,</span> <span class="nb">dict</span><span class="p">),</span> <span class="n">ns</span><span class="p">)</span>
+<span class="linenos">2949</span>
+<span class="linenos">2950</span>        <span class="n">annotations</span> <span class="o">=</span> <span class="p">{}</span>
+<span class="linenos">2951</span>        <span class="n">own_annotations</span> <span class="o">=</span> <span class="n">ns</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{})</span>
+<span class="linenos">2952</span>        <span class="n">msg</span> <span class="o">=</span> <span class="s2">&quot;TypedDict(&#39;Name&#39;, {f0: t0, f1: t1, ...}); each t must be a type&quot;</span>
+<span class="linenos">2953</span>        <span class="n">own_annotations</span> <span class="o">=</span> <span class="p">{</span>
+<span class="linenos">2954</span>            <span class="n">n</span><span class="p">:</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">tp</span><span class="p">,</span> <span class="n">msg</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="n">tp_dict</span><span class="o">.</span><span class="vm">__module__</span><span class="p">)</span>
+<span class="linenos">2955</span>            <span class="k">for</span> <span class="n">n</span><span class="p">,</span> <span class="n">tp</span> <span class="ow">in</span> <span class="n">own_annotations</span><span class="o">.</span><span class="n">items</span><span class="p">()</span>
+<span class="linenos">2956</span>        <span class="p">}</span>
+<span class="linenos">2957</span>        <span class="n">required_keys</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
+<span class="linenos">2958</span>        <span class="n">optional_keys</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
+<span class="linenos">2959</span>
+<span class="linenos">2960</span>        <span class="k">for</span> <span class="n">base</span> <span class="ow">in</span> <span class="n">bases</span><span class="p">:</span>
+<span class="linenos">2961</span>            <span class="n">annotations</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">,</span> <span class="p">{}))</span>
+<span class="linenos">2962</span>            <span class="n">required_keys</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__required_keys__&#39;</span><span class="p">,</span> <span class="p">()))</span>
+<span class="linenos">2963</span>            <span class="n">optional_keys</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;__optional_keys__&#39;</span><span class="p">,</span> <span class="p">()))</span>
+<span class="linenos">2964</span>
+<span class="linenos">2965</span>        <span class="n">annotations</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">own_annotations</span><span class="p">)</span>
+<span class="linenos">2966</span>        <span class="k">for</span> <span class="n">annotation_key</span><span class="p">,</span> <span class="n">annotation_type</span> <span class="ow">in</span> <span class="n">own_annotations</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<span class="linenos">2967</span>            <span class="n">annotation_origin</span> <span class="o">=</span> <span class="n">get_origin</span><span class="p">(</span><span class="n">annotation_type</span><span class="p">)</span>
+<span class="linenos">2968</span>            <span class="k">if</span> <span class="n">annotation_origin</span> <span class="ow">is</span> <span class="n">Annotated</span><span class="p">:</span>
+<span class="linenos">2969</span>                <span class="n">annotation_args</span> <span class="o">=</span> <span class="n">get_args</span><span class="p">(</span><span class="n">annotation_type</span><span class="p">)</span>
+<span class="linenos">2970</span>                <span class="k">if</span> <span class="n">annotation_args</span><span class="p">:</span>
+<span class="linenos">2971</span>                    <span class="n">annotation_type</span> <span class="o">=</span> <span class="n">annotation_args</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<span class="linenos">2972</span>                    <span class="n">annotation_origin</span> <span class="o">=</span> <span class="n">get_origin</span><span class="p">(</span><span class="n">annotation_type</span><span class="p">)</span>
+<span class="linenos">2973</span>
+<span class="linenos">2974</span>            <span class="k">if</span> <span class="n">annotation_origin</span> <span class="ow">is</span> <span class="n">Required</span><span class="p">:</span>
+<span class="linenos">2975</span>                <span class="n">required_keys</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">annotation_key</span><span class="p">)</span>
+<span class="linenos">2976</span>            <span class="k">elif</span> <span class="n">annotation_origin</span> <span class="ow">is</span> <span class="n">NotRequired</span><span class="p">:</span>
+<span class="linenos">2977</span>                <span class="n">optional_keys</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">annotation_key</span><span class="p">)</span>
+<span class="linenos">2978</span>            <span class="k">elif</span> <span class="n">total</span><span class="p">:</span>
+<span class="linenos">2979</span>                <span class="n">required_keys</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">annotation_key</span><span class="p">)</span>
+<span class="linenos">2980</span>            <span class="k">else</span><span class="p">:</span>
+<span class="linenos">2981</span>                <span class="n">optional_keys</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">annotation_key</span><span class="p">)</span>
+<span class="linenos">2982</span>
+<span class="linenos">2983</span>        <span class="n">tp_dict</span><span class="o">.</span><span class="vm">__annotations__</span> <span class="o">=</span> <span class="n">annotations</span>
+<span class="linenos">2984</span>        <span class="n">tp_dict</span><span class="o">.</span><span class="n">__required_keys__</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">(</span><span class="n">required_keys</span><span class="p">)</span>
+<span class="linenos">2985</span>        <span class="n">tp_dict</span><span class="o">.</span><span class="n">__optional_keys__</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">(</span><span class="n">optional_keys</span><span class="p">)</span>
+<span class="linenos">2986</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">tp_dict</span><span class="p">,</span> <span class="s1">&#39;__total__&#39;</span><span class="p">):</span>
+<span class="linenos">2987</span>            <span class="n">tp_dict</span><span class="o">.</span><span class="n">__total__</span> <span class="o">=</span> <span class="n">total</span>
+<span class="linenos">2988</span>        <span class="k">return</span> <span class="n">tp_dict</span>
 <span class="linenos">2989</span>
-<span class="linenos">2990</span>            <span class="k">if</span> <span class="n">annotation_origin</span> <span class="ow">is</span> <span class="n">Required</span><span class="p">:</span>
-<span class="linenos">2991</span>                <span class="n">required_keys</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">annotation_key</span><span class="p">)</span>
-<span class="linenos">2992</span>            <span class="k">elif</span> <span class="n">annotation_origin</span> <span class="ow">is</span> <span class="n">NotRequired</span><span class="p">:</span>
-<span class="linenos">2993</span>                <span class="n">optional_keys</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">annotation_key</span><span class="p">)</span>
-<span class="linenos">2994</span>            <span class="k">elif</span> <span class="n">total</span><span class="p">:</span>
-<span class="linenos">2995</span>                <span class="n">required_keys</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">annotation_key</span><span class="p">)</span>
-<span class="linenos">2996</span>            <span class="k">else</span><span class="p">:</span>
-<span class="linenos">2997</span>                <span class="n">optional_keys</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">annotation_key</span><span class="p">)</span>
+<span class="linenos">2990</span>    <span class="fm">__call__</span> <span class="o">=</span> <span class="nb">dict</span>  <span class="c1"># static method</span>
+<span class="linenos">2991</span>
+<span class="linenos">2992</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos">2993</span>        <span class="c1"># Typed dicts are only for static structural subtyping.</span>
+<span class="linenos">2994</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;TypedDict does not support instance and class checks&#39;</span><span class="p">)</span>
+<span class="linenos">2995</span>
+<span class="linenos">2996</span>    <span class="fm">__instancecheck__</span> <span class="o">=</span> <span class="fm">__subclasscheck__</span>
+<span class="linenos">2997</span>
 <span class="linenos">2998</span>
-<span class="linenos">2999</span>        <span class="n">tp_dict</span><span class="o">.</span><span class="vm">__annotations__</span> <span class="o">=</span> <span class="n">annotations</span>
-<span class="linenos">3000</span>        <span class="n">tp_dict</span><span class="o">.</span><span class="n">__required_keys__</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">(</span><span class="n">required_keys</span><span class="p">)</span>
-<span class="linenos">3001</span>        <span class="n">tp_dict</span><span class="o">.</span><span class="n">__optional_keys__</span> <span class="o">=</span> <span class="nb">frozenset</span><span class="p">(</span><span class="n">optional_keys</span><span class="p">)</span>
-<span class="linenos">3002</span>        <span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">tp_dict</span><span class="p">,</span> <span class="s1">&#39;__total__&#39;</span><span class="p">):</span>
-<span class="linenos">3003</span>            <span class="n">tp_dict</span><span class="o">.</span><span class="n">__total__</span> <span class="o">=</span> <span class="n">total</span>
-<span class="linenos">3004</span>        <span class="k">return</span> <span class="n">tp_dict</span>
-<span class="linenos">3005</span>
-<span class="linenos">3006</span>    <span class="fm">__call__</span> <span class="o">=</span> <span class="nb">dict</span>  <span class="c1"># static method</span>
-<span class="linenos">3007</span>
-<span class="linenos">3008</span>    <span class="k">def</span> <span class="fm">__subclasscheck__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos">3009</span>        <span class="c1"># Typed dicts are only for static structural subtyping.</span>
-<span class="linenos">3010</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">&#39;TypedDict does not support instance and class checks&#39;</span><span class="p">)</span>
-<span class="linenos">3011</span>
-<span class="linenos">3012</span>    <span class="fm">__instancecheck__</span> <span class="o">=</span> <span class="fm">__subclasscheck__</span>
+<span class="linenos">2999</span><span class="k">def</span> <span class="nf">TypedDict</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="n">fields</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">/</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">total</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="linenos">3000</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;A simple typed namespace. At runtime it is equivalent to a plain dict.</span>
+<span class="linenos">3001</span>
+<span class="linenos">3002</span><span class="sd">    TypedDict creates a dictionary type such that a type checker will expect all</span>
+<span class="linenos">3003</span><span class="sd">    instances to have a certain set of keys, where each key is</span>
+<span class="linenos">3004</span><span class="sd">    associated with a value of a consistent type. This expectation</span>
+<span class="linenos">3005</span><span class="sd">    is not checked at runtime.</span>
+<span class="linenos">3006</span>
+<span class="linenos">3007</span><span class="sd">    Usage::</span>
+<span class="linenos">3008</span>
+<span class="linenos">3009</span><span class="sd">        class Point2D(TypedDict):</span>
+<span class="linenos">3010</span><span class="sd">            x: int</span>
+<span class="linenos">3011</span><span class="sd">            y: int</span>
+<span class="linenos">3012</span><span class="sd">            label: str</span>
 <span class="linenos">3013</span>
-<span class="linenos">3014</span>
-<span class="linenos">3015</span><span class="k">def</span> <span class="nf">TypedDict</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="n">fields</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">/</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">total</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="linenos">3016</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;A simple typed namespace. At runtime it is equivalent to a plain dict.</span>
-<span class="linenos">3017</span>
-<span class="linenos">3018</span><span class="sd">    TypedDict creates a dictionary type such that a type checker will expect all</span>
-<span class="linenos">3019</span><span class="sd">    instances to have a certain set of keys, where each key is</span>
-<span class="linenos">3020</span><span class="sd">    associated with a value of a consistent type. This expectation</span>
-<span class="linenos">3021</span><span class="sd">    is not checked at runtime.</span>
+<span class="linenos">3014</span><span class="sd">        a: Point2D = {&#39;x&#39;: 1, &#39;y&#39;: 2, &#39;label&#39;: &#39;good&#39;}  # OK</span>
+<span class="linenos">3015</span><span class="sd">        b: Point2D = {&#39;z&#39;: 3, &#39;label&#39;: &#39;bad&#39;}           # Fails type check</span>
+<span class="linenos">3016</span>
+<span class="linenos">3017</span><span class="sd">        assert Point2D(x=1, y=2, label=&#39;first&#39;) == dict(x=1, y=2, label=&#39;first&#39;)</span>
+<span class="linenos">3018</span>
+<span class="linenos">3019</span><span class="sd">    The type info can be accessed via the Point2D.__annotations__ dict, and</span>
+<span class="linenos">3020</span><span class="sd">    the Point2D.__required_keys__ and Point2D.__optional_keys__ frozensets.</span>
+<span class="linenos">3021</span><span class="sd">    TypedDict supports an additional equivalent form::</span>
 <span class="linenos">3022</span>
-<span class="linenos">3023</span><span class="sd">    Usage::</span>
+<span class="linenos">3023</span><span class="sd">        Point2D = TypedDict(&#39;Point2D&#39;, {&#39;x&#39;: int, &#39;y&#39;: int, &#39;label&#39;: str})</span>
 <span class="linenos">3024</span>
-<span class="linenos">3025</span><span class="sd">        class Point2D(TypedDict):</span>
-<span class="linenos">3026</span><span class="sd">            x: int</span>
-<span class="linenos">3027</span><span class="sd">            y: int</span>
-<span class="linenos">3028</span><span class="sd">            label: str</span>
-<span class="linenos">3029</span>
-<span class="linenos">3030</span><span class="sd">        a: Point2D = {&#39;x&#39;: 1, &#39;y&#39;: 2, &#39;label&#39;: &#39;good&#39;}  # OK</span>
-<span class="linenos">3031</span><span class="sd">        b: Point2D = {&#39;z&#39;: 3, &#39;label&#39;: &#39;bad&#39;}           # Fails type check</span>
-<span class="linenos">3032</span>
-<span class="linenos">3033</span><span class="sd">        assert Point2D(x=1, y=2, label=&#39;first&#39;) == dict(x=1, y=2, label=&#39;first&#39;)</span>
-<span class="linenos">3034</span>
-<span class="linenos">3035</span><span class="sd">    The type info can be accessed via the Point2D.__annotations__ dict, and</span>
-<span class="linenos">3036</span><span class="sd">    the Point2D.__required_keys__ and Point2D.__optional_keys__ frozensets.</span>
-<span class="linenos">3037</span><span class="sd">    TypedDict supports an additional equivalent form::</span>
-<span class="linenos">3038</span>
-<span class="linenos">3039</span><span class="sd">        Point2D = TypedDict(&#39;Point2D&#39;, {&#39;x&#39;: int, &#39;y&#39;: int, &#39;label&#39;: str})</span>
-<span class="linenos">3040</span>
-<span class="linenos">3041</span><span class="sd">    By default, all keys must be present in a TypedDict. It is possible</span>
-<span class="linenos">3042</span><span class="sd">    to override this by specifying totality::</span>
+<span class="linenos">3025</span><span class="sd">    By default, all keys must be present in a TypedDict. It is possible</span>
+<span class="linenos">3026</span><span class="sd">    to override this by specifying totality::</span>
+<span class="linenos">3027</span>
+<span class="linenos">3028</span><span class="sd">        class Point2D(TypedDict, total=False):</span>
+<span class="linenos">3029</span><span class="sd">            x: int</span>
+<span class="linenos">3030</span><span class="sd">            y: int</span>
+<span class="linenos">3031</span>
+<span class="linenos">3032</span><span class="sd">    This means that a Point2D TypedDict can have any of the keys omitted. A type</span>
+<span class="linenos">3033</span><span class="sd">    checker is only expected to support a literal False or True as the value of</span>
+<span class="linenos">3034</span><span class="sd">    the total argument. True is the default, and makes all items defined in the</span>
+<span class="linenos">3035</span><span class="sd">    class body be required.</span>
+<span class="linenos">3036</span>
+<span class="linenos">3037</span><span class="sd">    The Required and NotRequired special forms can also be used to mark</span>
+<span class="linenos">3038</span><span class="sd">    individual keys as being required or not required::</span>
+<span class="linenos">3039</span>
+<span class="linenos">3040</span><span class="sd">        class Point2D(TypedDict):</span>
+<span class="linenos">3041</span><span class="sd">            x: int               # the &quot;x&quot; key must always be present (Required is the default)</span>
+<span class="linenos">3042</span><span class="sd">            y: NotRequired[int]  # the &quot;y&quot; key can be omitted</span>
 <span class="linenos">3043</span>
-<span class="linenos">3044</span><span class="sd">        class Point2D(TypedDict, total=False):</span>
-<span class="linenos">3045</span><span class="sd">            x: int</span>
-<span class="linenos">3046</span><span class="sd">            y: int</span>
-<span class="linenos">3047</span>
-<span class="linenos">3048</span><span class="sd">    This means that a Point2D TypedDict can have any of the keys omitted. A type</span>
-<span class="linenos">3049</span><span class="sd">    checker is only expected to support a literal False or True as the value of</span>
-<span class="linenos">3050</span><span class="sd">    the total argument. True is the default, and makes all items defined in the</span>
-<span class="linenos">3051</span><span class="sd">    class body be required.</span>
-<span class="linenos">3052</span>
-<span class="linenos">3053</span><span class="sd">    The Required and NotRequired special forms can also be used to mark</span>
-<span class="linenos">3054</span><span class="sd">    individual keys as being required or not required::</span>
-<span class="linenos">3055</span>
-<span class="linenos">3056</span><span class="sd">        class Point2D(TypedDict):</span>
-<span class="linenos">3057</span><span class="sd">            x: int               # the &quot;x&quot; key must always be present (Required is the default)</span>
-<span class="linenos">3058</span><span class="sd">            y: NotRequired[int]  # the &quot;y&quot; key can be omitted</span>
+<span class="linenos">3044</span><span class="sd">    See PEP 655 for more details on Required and NotRequired.</span>
+<span class="linenos">3045</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">3046</span>    <span class="k">if</span> <span class="n">fields</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">3047</span>        <span class="n">fields</span> <span class="o">=</span> <span class="n">kwargs</span>
+<span class="linenos">3048</span>    <span class="k">elif</span> <span class="n">kwargs</span><span class="p">:</span>
+<span class="linenos">3049</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;TypedDict takes either a dict or keyword arguments,&quot;</span>
+<span class="linenos">3050</span>                        <span class="s2">&quot; but not both&quot;</span><span class="p">)</span>
+<span class="linenos">3051</span>    <span class="k">if</span> <span class="n">kwargs</span><span class="p">:</span>
+<span class="linenos">3052</span>        <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
+<span class="linenos">3053</span>            <span class="s2">&quot;The kwargs-based syntax for TypedDict definitions is deprecated &quot;</span>
+<span class="linenos">3054</span>            <span class="s2">&quot;in Python 3.11, will be removed in Python 3.13, and may not be &quot;</span>
+<span class="linenos">3055</span>            <span class="s2">&quot;understood by third-party type checkers.&quot;</span><span class="p">,</span>
+<span class="linenos">3056</span>            <span class="ne">DeprecationWarning</span><span class="p">,</span>
+<span class="linenos">3057</span>            <span class="n">stacklevel</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
+<span class="linenos">3058</span>        <span class="p">)</span>
 <span class="linenos">3059</span>
-<span class="linenos">3060</span><span class="sd">    See PEP 655 for more details on Required and NotRequired.</span>
-<span class="linenos">3061</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">3062</span>    <span class="k">if</span> <span class="n">fields</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">3063</span>        <span class="n">fields</span> <span class="o">=</span> <span class="n">kwargs</span>
-<span class="linenos">3064</span>    <span class="k">elif</span> <span class="n">kwargs</span><span class="p">:</span>
-<span class="linenos">3065</span>        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;TypedDict takes either a dict or keyword arguments,&quot;</span>
-<span class="linenos">3066</span>                        <span class="s2">&quot; but not both&quot;</span><span class="p">)</span>
-<span class="linenos">3067</span>    <span class="k">if</span> <span class="n">kwargs</span><span class="p">:</span>
-<span class="linenos">3068</span>        <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
-<span class="linenos">3069</span>            <span class="s2">&quot;The kwargs-based syntax for TypedDict definitions is deprecated &quot;</span>
-<span class="linenos">3070</span>            <span class="s2">&quot;in Python 3.11, will be removed in Python 3.13, and may not be &quot;</span>
-<span class="linenos">3071</span>            <span class="s2">&quot;understood by third-party type checkers.&quot;</span><span class="p">,</span>
-<span class="linenos">3072</span>            <span class="ne">DeprecationWarning</span><span class="p">,</span>
-<span class="linenos">3073</span>            <span class="n">stacklevel</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
-<span class="linenos">3074</span>        <span class="p">)</span>
+<span class="linenos">3060</span>    <span class="n">ns</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">:</span> <span class="nb">dict</span><span class="p">(</span><span class="n">fields</span><span class="p">)}</span>
+<span class="linenos">3061</span>    <span class="n">module</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
+<span class="linenos">3062</span>    <span class="k">if</span> <span class="n">module</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">3063</span>        <span class="c1"># Setting correct module is necessary to make typed dict classes pickleable.</span>
+<span class="linenos">3064</span>        <span class="n">ns</span><span class="p">[</span><span class="s1">&#39;__module__&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">module</span>
+<span class="linenos">3065</span>
+<span class="linenos">3066</span>    <span class="k">return</span> <span class="n">_TypedDictMeta</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="p">(),</span> <span class="n">ns</span><span class="p">,</span> <span class="n">total</span><span class="o">=</span><span class="n">total</span><span class="p">)</span>
+<span class="linenos">3067</span>
+<span class="linenos">3068</span><span class="n">_TypedDict</span> <span class="o">=</span> <span class="nb">type</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="n">_TypedDictMeta</span><span class="p">,</span> <span class="s1">&#39;TypedDict&#39;</span><span class="p">,</span> <span class="p">(),</span> <span class="p">{})</span>
+<span class="linenos">3069</span><span class="n">TypedDict</span><span class="o">.</span><span class="n">__mro_entries__</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">bases</span><span class="p">:</span> <span class="p">(</span><span class="n">_TypedDict</span><span class="p">,)</span>
+<span class="linenos">3070</span>
+<span class="linenos">3071</span>
+<span class="linenos">3072</span><span class="nd">@_SpecialForm</span>
+<span class="linenos">3073</span><span class="k">def</span> <span class="nf">Required</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos">3074</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing construct to mark a TypedDict key as required.</span>
 <span class="linenos">3075</span>
-<span class="linenos">3076</span>    <span class="n">ns</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;__annotations__&#39;</span><span class="p">:</span> <span class="nb">dict</span><span class="p">(</span><span class="n">fields</span><span class="p">)}</span>
-<span class="linenos">3077</span>    <span class="n">module</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
-<span class="linenos">3078</span>    <span class="k">if</span> <span class="n">module</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">3079</span>        <span class="c1"># Setting correct module is necessary to make typed dict classes pickleable.</span>
-<span class="linenos">3080</span>        <span class="n">ns</span><span class="p">[</span><span class="s1">&#39;__module__&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">module</span>
+<span class="linenos">3076</span><span class="sd">    This is mainly useful for total=False TypedDicts. For example::</span>
+<span class="linenos">3077</span>
+<span class="linenos">3078</span><span class="sd">        class Movie(TypedDict, total=False):</span>
+<span class="linenos">3079</span><span class="sd">            title: Required[str]</span>
+<span class="linenos">3080</span><span class="sd">            year: int</span>
 <span class="linenos">3081</span>
-<span class="linenos">3082</span>    <span class="k">return</span> <span class="n">_TypedDictMeta</span><span class="p">(</span><span class="n">typename</span><span class="p">,</span> <span class="p">(),</span> <span class="n">ns</span><span class="p">,</span> <span class="n">total</span><span class="o">=</span><span class="n">total</span><span class="p">)</span>
-<span class="linenos">3083</span>
-<span class="linenos">3084</span><span class="n">_TypedDict</span> <span class="o">=</span> <span class="nb">type</span><span class="o">.</span><span class="fm">__new__</span><span class="p">(</span><span class="n">_TypedDictMeta</span><span class="p">,</span> <span class="s1">&#39;TypedDict&#39;</span><span class="p">,</span> <span class="p">(),</span> <span class="p">{})</span>
-<span class="linenos">3085</span><span class="n">TypedDict</span><span class="o">.</span><span class="n">__mro_entries__</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">bases</span><span class="p">:</span> <span class="p">(</span><span class="n">_TypedDict</span><span class="p">,)</span>
+<span class="linenos">3082</span><span class="sd">        m = Movie(</span>
+<span class="linenos">3083</span><span class="sd">            title=&#39;The Matrix&#39;,  # typechecker error if key is omitted</span>
+<span class="linenos">3084</span><span class="sd">            year=1999,</span>
+<span class="linenos">3085</span><span class="sd">        )</span>
 <span class="linenos">3086</span>
-<span class="linenos">3087</span>
-<span class="linenos">3088</span><span class="nd">@_SpecialForm</span>
-<span class="linenos">3089</span><span class="k">def</span> <span class="nf">Required</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos">3090</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing construct to mark a TypedDict key as required.</span>
-<span class="linenos">3091</span>
-<span class="linenos">3092</span><span class="sd">    This is mainly useful for total=False TypedDicts.</span>
+<span class="linenos">3087</span><span class="sd">    There is no runtime checking that a required key is actually provided</span>
+<span class="linenos">3088</span><span class="sd">    when instantiating a related TypedDict.</span>
+<span class="linenos">3089</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">3090</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="si">}</span><span class="s1"> accepts only a single type.&#39;</span><span class="p">)</span>
+<span class="linenos">3091</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
+<span class="linenos">3092</span>
 <span class="linenos">3093</span>
-<span class="linenos">3094</span><span class="sd">    For example::</span>
-<span class="linenos">3095</span>
-<span class="linenos">3096</span><span class="sd">        class Movie(TypedDict, total=False):</span>
-<span class="linenos">3097</span><span class="sd">            title: Required[str]</span>
-<span class="linenos">3098</span><span class="sd">            year: int</span>
+<span class="linenos">3094</span><span class="nd">@_SpecialForm</span>
+<span class="linenos">3095</span><span class="k">def</span> <span class="nf">NotRequired</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
+<span class="linenos">3096</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing construct to mark a TypedDict key as potentially missing.</span>
+<span class="linenos">3097</span>
+<span class="linenos">3098</span><span class="sd">    For example::</span>
 <span class="linenos">3099</span>
-<span class="linenos">3100</span><span class="sd">        m = Movie(</span>
-<span class="linenos">3101</span><span class="sd">            title=&#39;The Matrix&#39;,  # typechecker error if key is omitted</span>
-<span class="linenos">3102</span><span class="sd">            year=1999,</span>
-<span class="linenos">3103</span><span class="sd">        )</span>
-<span class="linenos">3104</span>
-<span class="linenos">3105</span><span class="sd">    There is no runtime checking that a required key is actually provided</span>
-<span class="linenos">3106</span><span class="sd">    when instantiating a related TypedDict.</span>
-<span class="linenos">3107</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">3108</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="si">}</span><span class="s1"> accepts only a single type.&#39;</span><span class="p">)</span>
-<span class="linenos">3109</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
-<span class="linenos">3110</span>
+<span class="linenos">3100</span><span class="sd">        class Movie(TypedDict):</span>
+<span class="linenos">3101</span><span class="sd">            title: str</span>
+<span class="linenos">3102</span><span class="sd">            year: NotRequired[int]</span>
+<span class="linenos">3103</span>
+<span class="linenos">3104</span><span class="sd">        m = Movie(</span>
+<span class="linenos">3105</span><span class="sd">            title=&#39;The Matrix&#39;,  # typechecker error if key is omitted</span>
+<span class="linenos">3106</span><span class="sd">            year=1999,</span>
+<span class="linenos">3107</span><span class="sd">        )</span>
+<span class="linenos">3108</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">3109</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="si">}</span><span class="s1"> accepts only a single type.&#39;</span><span class="p">)</span>
+<span class="linenos">3110</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
 <span class="linenos">3111</span>
-<span class="linenos">3112</span><span class="nd">@_SpecialForm</span>
-<span class="linenos">3113</span><span class="k">def</span> <span class="nf">NotRequired</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parameters</span><span class="p">):</span>
-<span class="linenos">3114</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Special typing construct to mark a TypedDict key as potentially missing.</span>
+<span class="linenos">3112</span>
+<span class="linenos">3113</span><span class="k">class</span> <span class="nc">NewType</span><span class="p">:</span>
+<span class="linenos">3114</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;NewType creates simple unique types with almost zero runtime overhead.</span>
 <span class="linenos">3115</span>
-<span class="linenos">3116</span><span class="sd">    For example::</span>
-<span class="linenos">3117</span>
-<span class="linenos">3118</span><span class="sd">        class Movie(TypedDict):</span>
-<span class="linenos">3119</span><span class="sd">            title: str</span>
-<span class="linenos">3120</span><span class="sd">            year: NotRequired[int]</span>
+<span class="linenos">3116</span><span class="sd">    NewType(name, tp) is considered a subtype of tp</span>
+<span class="linenos">3117</span><span class="sd">    by static type checkers. At runtime, NewType(name, tp) returns</span>
+<span class="linenos">3118</span><span class="sd">    a dummy callable that simply returns its argument. Usage::</span>
+<span class="linenos">3119</span>
+<span class="linenos">3120</span><span class="sd">        UserId = NewType(&#39;UserId&#39;, int)</span>
 <span class="linenos">3121</span>
-<span class="linenos">3122</span><span class="sd">        m = Movie(</span>
-<span class="linenos">3123</span><span class="sd">            title=&#39;The Matrix&#39;,  # typechecker error if key is omitted</span>
-<span class="linenos">3124</span><span class="sd">            year=1999,</span>
-<span class="linenos">3125</span><span class="sd">        )</span>
-<span class="linenos">3126</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">3127</span>    <span class="n">item</span> <span class="o">=</span> <span class="n">_type_check</span><span class="p">(</span><span class="n">parameters</span><span class="p">,</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">_name</span><span class="si">}</span><span class="s1"> accepts only a single type.&#39;</span><span class="p">)</span>
-<span class="linenos">3128</span>    <span class="k">return</span> <span class="n">_GenericAlias</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="p">(</span><span class="n">item</span><span class="p">,))</span>
+<span class="linenos">3122</span><span class="sd">        def name_by_id(user_id: UserId) -&gt; str:</span>
+<span class="linenos">3123</span><span class="sd">            ...</span>
+<span class="linenos">3124</span>
+<span class="linenos">3125</span><span class="sd">        UserId(&#39;user&#39;)          # Fails type check</span>
+<span class="linenos">3126</span>
+<span class="linenos">3127</span><span class="sd">        name_by_id(42)          # Fails type check</span>
+<span class="linenos">3128</span><span class="sd">        name_by_id(UserId(42))  # OK</span>
 <span class="linenos">3129</span>
-<span class="linenos">3130</span>
-<span class="linenos">3131</span><span class="k">class</span> <span class="nc">NewType</span><span class="p">:</span>
-<span class="linenos">3132</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;NewType creates simple unique types with almost zero runtime overhead.</span>
-<span class="linenos">3133</span>
-<span class="linenos">3134</span><span class="sd">    NewType(name, tp) is considered a subtype of tp</span>
-<span class="linenos">3135</span><span class="sd">    by static type checkers. At runtime, NewType(name, tp) returns</span>
-<span class="linenos">3136</span><span class="sd">    a dummy callable that simply returns its argument.</span>
-<span class="linenos">3137</span>
-<span class="linenos">3138</span><span class="sd">    Usage::</span>
-<span class="linenos">3139</span>
-<span class="linenos">3140</span><span class="sd">        UserId = NewType(&#39;UserId&#39;, int)</span>
-<span class="linenos">3141</span>
-<span class="linenos">3142</span><span class="sd">        def name_by_id(user_id: UserId) -&gt; str:</span>
-<span class="linenos">3143</span><span class="sd">            ...</span>
+<span class="linenos">3130</span><span class="sd">        num = UserId(5) + 1     # type: int</span>
+<span class="linenos">3131</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">3132</span>
+<span class="linenos">3133</span>    <span class="fm">__call__</span> <span class="o">=</span> <span class="n">_idfunc</span>
+<span class="linenos">3134</span>
+<span class="linenos">3135</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">tp</span><span class="p">):</span>
+<span class="linenos">3136</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__qualname__</span> <span class="o">=</span> <span class="n">name</span>
+<span class="linenos">3137</span>        <span class="k">if</span> <span class="s1">&#39;.&#39;</span> <span class="ow">in</span> <span class="n">name</span><span class="p">:</span>
+<span class="linenos">3138</span>            <span class="n">name</span> <span class="o">=</span> <span class="n">name</span><span class="o">.</span><span class="n">rpartition</span><span class="p">(</span><span class="s1">&#39;.&#39;</span><span class="p">)[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="linenos">3139</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="n">name</span>
+<span class="linenos">3140</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__supertype__</span> <span class="o">=</span> <span class="n">tp</span>
+<span class="linenos">3141</span>        <span class="n">def_mod</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
+<span class="linenos">3142</span>        <span class="k">if</span> <span class="n">def_mod</span> <span class="o">!=</span> <span class="s1">&#39;typing&#39;</span><span class="p">:</span>
+<span class="linenos">3143</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">def_mod</span>
 <span class="linenos">3144</span>
-<span class="linenos">3145</span><span class="sd">        UserId(&#39;user&#39;)          # Fails type check</span>
-<span class="linenos">3146</span>
-<span class="linenos">3147</span><span class="sd">        name_by_id(42)          # Fails type check</span>
-<span class="linenos">3148</span><span class="sd">        name_by_id(UserId(42))  # OK</span>
+<span class="linenos">3145</span>    <span class="k">def</span> <span class="nf">__mro_entries__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bases</span><span class="p">):</span>
+<span class="linenos">3146</span>        <span class="c1"># We defined __mro_entries__ to get a better error message</span>
+<span class="linenos">3147</span>        <span class="c1"># if a user attempts to subclass a NewType instance. bpo-46170</span>
+<span class="linenos">3148</span>        <span class="n">superclass_name</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span>
 <span class="linenos">3149</span>
-<span class="linenos">3150</span><span class="sd">        num = UserId(5) + 1     # type: int</span>
-<span class="linenos">3151</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">3152</span>
-<span class="linenos">3153</span>    <span class="fm">__call__</span> <span class="o">=</span> <span class="n">_idfunc</span>
-<span class="linenos">3154</span>
-<span class="linenos">3155</span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">tp</span><span class="p">):</span>
-<span class="linenos">3156</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__qualname__</span> <span class="o">=</span> <span class="n">name</span>
-<span class="linenos">3157</span>        <span class="k">if</span> <span class="s1">&#39;.&#39;</span> <span class="ow">in</span> <span class="n">name</span><span class="p">:</span>
-<span class="linenos">3158</span>            <span class="n">name</span> <span class="o">=</span> <span class="n">name</span><span class="o">.</span><span class="n">rpartition</span><span class="p">(</span><span class="s1">&#39;.&#39;</span><span class="p">)[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-<span class="linenos">3159</span>        <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="n">name</span>
-<span class="linenos">3160</span>        <span class="bp">self</span><span class="o">.</span><span class="n">__supertype__</span> <span class="o">=</span> <span class="n">tp</span>
-<span class="linenos">3161</span>        <span class="n">def_mod</span> <span class="o">=</span> <span class="n">_caller</span><span class="p">()</span>
-<span class="linenos">3162</span>        <span class="k">if</span> <span class="n">def_mod</span> <span class="o">!=</span> <span class="s1">&#39;typing&#39;</span><span class="p">:</span>
-<span class="linenos">3163</span>            <span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">def_mod</span>
-<span class="linenos">3164</span>
-<span class="linenos">3165</span>    <span class="k">def</span> <span class="nf">__mro_entries__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bases</span><span class="p">):</span>
-<span class="linenos">3166</span>        <span class="c1"># We defined __mro_entries__ to get a better error message</span>
-<span class="linenos">3167</span>        <span class="c1"># if a user attempts to subclass a NewType instance. bpo-46170</span>
-<span class="linenos">3168</span>        <span class="n">superclass_name</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__name__</span>
-<span class="linenos">3169</span>
-<span class="linenos">3170</span>        <span class="k">class</span> <span class="nc">Dummy</span><span class="p">:</span>
-<span class="linenos">3171</span>            <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
-<span class="linenos">3172</span>                <span class="n">subclass_name</span> <span class="o">=</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span>
-<span class="linenos">3173</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
-<span class="linenos">3174</span>                    <span class="sa">f</span><span class="s2">&quot;Cannot subclass an instance of NewType. Perhaps you were looking for: &quot;</span>
-<span class="linenos">3175</span>                    <span class="sa">f</span><span class="s2">&quot;`</span><span class="si">{</span><span class="n">subclass_name</span><span class="si">}</span><span class="s2"> = NewType(</span><span class="si">{</span><span class="n">subclass_name</span><span class="si">!r}</span><span class="s2">, </span><span class="si">{</span><span class="n">superclass_name</span><span class="si">}</span><span class="s2">)`&quot;</span>
-<span class="linenos">3176</span>                <span class="p">)</span>
-<span class="linenos">3177</span>
-<span class="linenos">3178</span>        <span class="k">return</span> <span class="p">(</span><span class="n">Dummy</span><span class="p">,)</span>
+<span class="linenos">3150</span>        <span class="k">class</span> <span class="nc">Dummy</span><span class="p">:</span>
+<span class="linenos">3151</span>            <span class="k">def</span> <span class="nf">__init_subclass__</span><span class="p">(</span><span class="bp">cls</span><span class="p">):</span>
+<span class="linenos">3152</span>                <span class="n">subclass_name</span> <span class="o">=</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span>
+<span class="linenos">3153</span>                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
+<span class="linenos">3154</span>                    <span class="sa">f</span><span class="s2">&quot;Cannot subclass an instance of NewType. Perhaps you were looking for: &quot;</span>
+<span class="linenos">3155</span>                    <span class="sa">f</span><span class="s2">&quot;`</span><span class="si">{</span><span class="n">subclass_name</span><span class="si">}</span><span class="s2"> = NewType(</span><span class="si">{</span><span class="n">subclass_name</span><span class="si">!r}</span><span class="s2">, </span><span class="si">{</span><span class="n">superclass_name</span><span class="si">}</span><span class="s2">)`&quot;</span>
+<span class="linenos">3156</span>                <span class="p">)</span>
+<span class="linenos">3157</span>
+<span class="linenos">3158</span>        <span class="k">return</span> <span class="p">(</span><span class="n">Dummy</span><span class="p">,)</span>
+<span class="linenos">3159</span>
+<span class="linenos">3160</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">3161</span>        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">&#39;</span>
+<span class="linenos">3162</span>
+<span class="linenos">3163</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="linenos">3164</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__qualname__</span>
+<span class="linenos">3165</span>
+<span class="linenos">3166</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos">3167</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">]</span>
+<span class="linenos">3168</span>
+<span class="linenos">3169</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
+<span class="linenos">3170</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
+<span class="linenos">3171</span>
+<span class="linenos">3172</span>
+<span class="linenos">3173</span><span class="c1"># Python-version-specific alias (Python 2: unicode; Python 3: str)</span>
+<span class="linenos">3174</span><span class="n">Text</span> <span class="o">=</span> <span class="nb">str</span>
+<span class="linenos">3175</span>
+<span class="linenos">3176</span>
+<span class="linenos">3177</span><span class="c1"># Constant that&#39;s True when type checking, but False here.</span>
+<span class="linenos">3178</span><span class="n">TYPE_CHECKING</span> <span class="o">=</span> <span class="kc">False</span>
 <span class="linenos">3179</span>
-<span class="linenos">3180</span>    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">3181</span>        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="vm">__module__</span><span class="si">}</span><span class="s1">.</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="vm">__qualname__</span><span class="si">}</span><span class="s1">&#39;</span>
-<span class="linenos">3182</span>
-<span class="linenos">3183</span>    <span class="k">def</span> <span class="nf">__reduce__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-<span class="linenos">3184</span>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__qualname__</span>
+<span class="linenos">3180</span>
+<span class="linenos">3181</span><span class="k">class</span> <span class="nc">IO</span><span class="p">(</span><span class="n">Generic</span><span class="p">[</span><span class="n">AnyStr</span><span class="p">]):</span>
+<span class="linenos">3182</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Generic base class for TextIO and BinaryIO.</span>
+<span class="linenos">3183</span>
+<span class="linenos">3184</span><span class="sd">    This is an abstract, generic version of the return of open().</span>
 <span class="linenos">3185</span>
-<span class="linenos">3186</span>    <span class="k">def</span> <span class="fm">__or__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos">3187</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">]</span>
-<span class="linenos">3188</span>
-<span class="linenos">3189</span>    <span class="k">def</span> <span class="fm">__ror__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span>
-<span class="linenos">3190</span>        <span class="k">return</span> <span class="n">Union</span><span class="p">[</span><span class="n">other</span><span class="p">,</span> <span class="bp">self</span><span class="p">]</span>
-<span class="linenos">3191</span>
-<span class="linenos">3192</span>
-<span class="linenos">3193</span><span class="c1"># Python-version-specific alias (Python 2: unicode; Python 3: str)</span>
-<span class="linenos">3194</span><span class="n">Text</span> <span class="o">=</span> <span class="nb">str</span>
+<span class="linenos">3186</span><span class="sd">    NOTE: This does not distinguish between the different possible</span>
+<span class="linenos">3187</span><span class="sd">    classes (text vs. binary, read vs. write vs. read/write,</span>
+<span class="linenos">3188</span><span class="sd">    append-only, unbuffered).  The TextIO and BinaryIO subclasses</span>
+<span class="linenos">3189</span><span class="sd">    below capture the distinctions between text vs. binary, which is</span>
+<span class="linenos">3190</span><span class="sd">    pervasive in the interface; however we currently do not offer a</span>
+<span class="linenos">3191</span><span class="sd">    way to track the other distinctions in the type system.</span>
+<span class="linenos">3192</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">3193</span>
+<span class="linenos">3194</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
 <span class="linenos">3195</span>
-<span class="linenos">3196</span>
-<span class="linenos">3197</span><span class="c1"># Constant that&#39;s True when type checking, but False here.</span>
-<span class="linenos">3198</span><span class="n">TYPE_CHECKING</span> <span class="o">=</span> <span class="kc">False</span>
-<span class="linenos">3199</span>
+<span class="linenos">3196</span>    <span class="nd">@property</span>
+<span class="linenos">3197</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3198</span>    <span class="k">def</span> <span class="nf">mode</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
+<span class="linenos">3199</span>        <span class="k">pass</span>
 <span class="linenos">3200</span>
-<span class="linenos">3201</span><span class="k">class</span> <span class="nc">IO</span><span class="p">(</span><span class="n">Generic</span><span class="p">[</span><span class="n">AnyStr</span><span class="p">]):</span>
-<span class="linenos">3202</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Generic base class for TextIO and BinaryIO.</span>
-<span class="linenos">3203</span>
-<span class="linenos">3204</span><span class="sd">    This is an abstract, generic version of the return of open().</span>
+<span class="linenos">3201</span>    <span class="nd">@property</span>
+<span class="linenos">3202</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3203</span>    <span class="k">def</span> <span class="nf">name</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
+<span class="linenos">3204</span>        <span class="k">pass</span>
 <span class="linenos">3205</span>
-<span class="linenos">3206</span><span class="sd">    NOTE: This does not distinguish between the different possible</span>
-<span class="linenos">3207</span><span class="sd">    classes (text vs. binary, read vs. write vs. read/write,</span>
-<span class="linenos">3208</span><span class="sd">    append-only, unbuffered).  The TextIO and BinaryIO subclasses</span>
-<span class="linenos">3209</span><span class="sd">    below capture the distinctions between text vs. binary, which is</span>
-<span class="linenos">3210</span><span class="sd">    pervasive in the interface; however we currently do not offer a</span>
-<span class="linenos">3211</span><span class="sd">    way to track the other distinctions in the type system.</span>
-<span class="linenos">3212</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">3213</span>
-<span class="linenos">3214</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
-<span class="linenos">3215</span>
-<span class="linenos">3216</span>    <span class="nd">@property</span>
-<span class="linenos">3217</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3218</span>    <span class="k">def</span> <span class="nf">mode</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
-<span class="linenos">3219</span>        <span class="k">pass</span>
-<span class="linenos">3220</span>
-<span class="linenos">3221</span>    <span class="nd">@property</span>
-<span class="linenos">3222</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3223</span>    <span class="k">def</span> <span class="nf">name</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
-<span class="linenos">3224</span>        <span class="k">pass</span>
-<span class="linenos">3225</span>
-<span class="linenos">3226</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3227</span>    <span class="k">def</span> <span class="nf">close</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">3228</span>        <span class="k">pass</span>
-<span class="linenos">3229</span>
-<span class="linenos">3230</span>    <span class="nd">@property</span>
+<span class="linenos">3206</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3207</span>    <span class="k">def</span> <span class="nf">close</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">3208</span>        <span class="k">pass</span>
+<span class="linenos">3209</span>
+<span class="linenos">3210</span>    <span class="nd">@property</span>
+<span class="linenos">3211</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3212</span>    <span class="k">def</span> <span class="nf">closed</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<span class="linenos">3213</span>        <span class="k">pass</span>
+<span class="linenos">3214</span>
+<span class="linenos">3215</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3216</span>    <span class="k">def</span> <span class="nf">fileno</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<span class="linenos">3217</span>        <span class="k">pass</span>
+<span class="linenos">3218</span>
+<span class="linenos">3219</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3220</span>    <span class="k">def</span> <span class="nf">flush</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">3221</span>        <span class="k">pass</span>
+<span class="linenos">3222</span>
+<span class="linenos">3223</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3224</span>    <span class="k">def</span> <span class="nf">isatty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<span class="linenos">3225</span>        <span class="k">pass</span>
+<span class="linenos">3226</span>
+<span class="linenos">3227</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3228</span>    <span class="k">def</span> <span class="nf">read</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">AnyStr</span><span class="p">:</span>
+<span class="linenos">3229</span>        <span class="k">pass</span>
+<span class="linenos">3230</span>
 <span class="linenos">3231</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3232</span>    <span class="k">def</span> <span class="nf">closed</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<span class="linenos">3232</span>    <span class="k">def</span> <span class="nf">readable</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
 <span class="linenos">3233</span>        <span class="k">pass</span>
 <span class="linenos">3234</span>
 <span class="linenos">3235</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3236</span>    <span class="k">def</span> <span class="nf">fileno</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<span class="linenos">3236</span>    <span class="k">def</span> <span class="nf">readline</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">limit</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">AnyStr</span><span class="p">:</span>
 <span class="linenos">3237</span>        <span class="k">pass</span>
 <span class="linenos">3238</span>
 <span class="linenos">3239</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3240</span>    <span class="k">def</span> <span class="nf">flush</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
+<span class="linenos">3240</span>    <span class="k">def</span> <span class="nf">readlines</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">hint</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">AnyStr</span><span class="p">]:</span>
 <span class="linenos">3241</span>        <span class="k">pass</span>
 <span class="linenos">3242</span>
 <span class="linenos">3243</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3244</span>    <span class="k">def</span> <span class="nf">isatty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<span class="linenos">3244</span>    <span class="k">def</span> <span class="nf">seek</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">offset</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">whence</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <span class="linenos">3245</span>        <span class="k">pass</span>
 <span class="linenos">3246</span>
 <span class="linenos">3247</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3248</span>    <span class="k">def</span> <span class="nf">read</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">AnyStr</span><span class="p">:</span>
+<span class="linenos">3248</span>    <span class="k">def</span> <span class="nf">seekable</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
 <span class="linenos">3249</span>        <span class="k">pass</span>
 <span class="linenos">3250</span>
 <span class="linenos">3251</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3252</span>    <span class="k">def</span> <span class="nf">readable</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<span class="linenos">3252</span>    <span class="k">def</span> <span class="nf">tell</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <span class="linenos">3253</span>        <span class="k">pass</span>
 <span class="linenos">3254</span>
 <span class="linenos">3255</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3256</span>    <span class="k">def</span> <span class="nf">readline</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">limit</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">AnyStr</span><span class="p">:</span>
+<span class="linenos">3256</span>    <span class="k">def</span> <span class="nf">truncate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <span class="linenos">3257</span>        <span class="k">pass</span>
 <span class="linenos">3258</span>
 <span class="linenos">3259</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3260</span>    <span class="k">def</span> <span class="nf">readlines</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">hint</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">AnyStr</span><span class="p">]:</span>
+<span class="linenos">3260</span>    <span class="k">def</span> <span class="nf">writable</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
 <span class="linenos">3261</span>        <span class="k">pass</span>
 <span class="linenos">3262</span>
 <span class="linenos">3263</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3264</span>    <span class="k">def</span> <span class="nf">seek</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">offset</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">whence</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<span class="linenos">3264</span>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">:</span> <span class="n">AnyStr</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
 <span class="linenos">3265</span>        <span class="k">pass</span>
 <span class="linenos">3266</span>
 <span class="linenos">3267</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3268</span>    <span class="k">def</span> <span class="nf">seekable</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<span class="linenos">3268</span>    <span class="k">def</span> <span class="nf">writelines</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">lines</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">AnyStr</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <span class="linenos">3269</span>        <span class="k">pass</span>
 <span class="linenos">3270</span>
 <span class="linenos">3271</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3272</span>    <span class="k">def</span> <span class="nf">tell</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<span class="linenos">3272</span>    <span class="k">def</span> <span class="fm">__enter__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s1">&#39;IO[AnyStr]&#39;</span><span class="p">:</span>
 <span class="linenos">3273</span>        <span class="k">pass</span>
 <span class="linenos">3274</span>
 <span class="linenos">3275</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3276</span>    <span class="k">def</span> <span class="nf">truncate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<span class="linenos">3276</span>    <span class="k">def</span> <span class="fm">__exit__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">type</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">traceback</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
 <span class="linenos">3277</span>        <span class="k">pass</span>
 <span class="linenos">3278</span>
-<span class="linenos">3279</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3280</span>    <span class="k">def</span> <span class="nf">writable</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<span class="linenos">3281</span>        <span class="k">pass</span>
+<span class="linenos">3279</span>
+<span class="linenos">3280</span><span class="k">class</span> <span class="nc">BinaryIO</span><span class="p">(</span><span class="n">IO</span><span class="p">[</span><span class="nb">bytes</span><span class="p">]):</span>
+<span class="linenos">3281</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Typed version of the return of open() in binary mode.&quot;&quot;&quot;</span>
 <span class="linenos">3282</span>
-<span class="linenos">3283</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3284</span>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">:</span> <span class="n">AnyStr</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
-<span class="linenos">3285</span>        <span class="k">pass</span>
-<span class="linenos">3286</span>
-<span class="linenos">3287</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3288</span>    <span class="k">def</span> <span class="nf">writelines</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">lines</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">AnyStr</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">3289</span>        <span class="k">pass</span>
-<span class="linenos">3290</span>
-<span class="linenos">3291</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3292</span>    <span class="k">def</span> <span class="fm">__enter__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s1">&#39;IO[AnyStr]&#39;</span><span class="p">:</span>
-<span class="linenos">3293</span>        <span class="k">pass</span>
-<span class="linenos">3294</span>
-<span class="linenos">3295</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3296</span>    <span class="k">def</span> <span class="fm">__exit__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">type</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">traceback</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kc">None</span><span class="p">:</span>
-<span class="linenos">3297</span>        <span class="k">pass</span>
+<span class="linenos">3283</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">3284</span>
+<span class="linenos">3285</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3286</span>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">bytes</span><span class="p">,</span> <span class="nb">bytearray</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<span class="linenos">3287</span>        <span class="k">pass</span>
+<span class="linenos">3288</span>
+<span class="linenos">3289</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3290</span>    <span class="k">def</span> <span class="fm">__enter__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s1">&#39;BinaryIO&#39;</span><span class="p">:</span>
+<span class="linenos">3291</span>        <span class="k">pass</span>
+<span class="linenos">3292</span>
+<span class="linenos">3293</span>
+<span class="linenos">3294</span><span class="k">class</span> <span class="nc">TextIO</span><span class="p">(</span><span class="n">IO</span><span class="p">[</span><span class="nb">str</span><span class="p">]):</span>
+<span class="linenos">3295</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Typed version of the return of open() in text mode.&quot;&quot;&quot;</span>
+<span class="linenos">3296</span>
+<span class="linenos">3297</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
 <span class="linenos">3298</span>
-<span class="linenos">3299</span>
-<span class="linenos">3300</span><span class="k">class</span> <span class="nc">BinaryIO</span><span class="p">(</span><span class="n">IO</span><span class="p">[</span><span class="nb">bytes</span><span class="p">]):</span>
-<span class="linenos">3301</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Typed version of the return of open() in binary mode.&quot;&quot;&quot;</span>
-<span class="linenos">3302</span>
-<span class="linenos">3303</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
-<span class="linenos">3304</span>
+<span class="linenos">3299</span>    <span class="nd">@property</span>
+<span class="linenos">3300</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3301</span>    <span class="k">def</span> <span class="nf">buffer</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">BinaryIO</span><span class="p">:</span>
+<span class="linenos">3302</span>        <span class="k">pass</span>
+<span class="linenos">3303</span>
+<span class="linenos">3304</span>    <span class="nd">@property</span>
 <span class="linenos">3305</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3306</span>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">bytes</span><span class="p">,</span> <span class="nb">bytearray</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<span class="linenos">3306</span>    <span class="k">def</span> <span class="nf">encoding</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
 <span class="linenos">3307</span>        <span class="k">pass</span>
 <span class="linenos">3308</span>
-<span class="linenos">3309</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3310</span>    <span class="k">def</span> <span class="fm">__enter__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s1">&#39;BinaryIO&#39;</span><span class="p">:</span>
-<span class="linenos">3311</span>        <span class="k">pass</span>
-<span class="linenos">3312</span>
+<span class="linenos">3309</span>    <span class="nd">@property</span>
+<span class="linenos">3310</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3311</span>    <span class="k">def</span> <span class="nf">errors</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Optional</span><span class="p">[</span><span class="nb">str</span><span class="p">]:</span>
+<span class="linenos">3312</span>        <span class="k">pass</span>
 <span class="linenos">3313</span>
-<span class="linenos">3314</span><span class="k">class</span> <span class="nc">TextIO</span><span class="p">(</span><span class="n">IO</span><span class="p">[</span><span class="nb">str</span><span class="p">]):</span>
-<span class="linenos">3315</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Typed version of the return of open() in text mode.&quot;&quot;&quot;</span>
-<span class="linenos">3316</span>
-<span class="linenos">3317</span>    <span class="vm">__slots__</span> <span class="o">=</span> <span class="p">()</span>
+<span class="linenos">3314</span>    <span class="nd">@property</span>
+<span class="linenos">3315</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3316</span>    <span class="k">def</span> <span class="nf">line_buffering</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<span class="linenos">3317</span>        <span class="k">pass</span>
 <span class="linenos">3318</span>
 <span class="linenos">3319</span>    <span class="nd">@property</span>
 <span class="linenos">3320</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3321</span>    <span class="k">def</span> <span class="nf">buffer</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">BinaryIO</span><span class="p">:</span>
+<span class="linenos">3321</span>    <span class="k">def</span> <span class="nf">newlines</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Any</span><span class="p">:</span>
 <span class="linenos">3322</span>        <span class="k">pass</span>
 <span class="linenos">3323</span>
-<span class="linenos">3324</span>    <span class="nd">@property</span>
-<span class="linenos">3325</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3326</span>    <span class="k">def</span> <span class="nf">encoding</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
-<span class="linenos">3327</span>        <span class="k">pass</span>
+<span class="linenos">3324</span>    <span class="nd">@abstractmethod</span>
+<span class="linenos">3325</span>    <span class="k">def</span> <span class="fm">__enter__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s1">&#39;TextIO&#39;</span><span class="p">:</span>
+<span class="linenos">3326</span>        <span class="k">pass</span>
+<span class="linenos">3327</span>
 <span class="linenos">3328</span>
-<span class="linenos">3329</span>    <span class="nd">@property</span>
-<span class="linenos">3330</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3331</span>    <span class="k">def</span> <span class="nf">errors</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Optional</span><span class="p">[</span><span class="nb">str</span><span class="p">]:</span>
-<span class="linenos">3332</span>        <span class="k">pass</span>
-<span class="linenos">3333</span>
-<span class="linenos">3334</span>    <span class="nd">@property</span>
-<span class="linenos">3335</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3336</span>    <span class="k">def</span> <span class="nf">line_buffering</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
-<span class="linenos">3337</span>        <span class="k">pass</span>
-<span class="linenos">3338</span>
-<span class="linenos">3339</span>    <span class="nd">@property</span>
-<span class="linenos">3340</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3341</span>    <span class="k">def</span> <span class="nf">newlines</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Any</span><span class="p">:</span>
-<span class="linenos">3342</span>        <span class="k">pass</span>
-<span class="linenos">3343</span>
-<span class="linenos">3344</span>    <span class="nd">@abstractmethod</span>
-<span class="linenos">3345</span>    <span class="k">def</span> <span class="fm">__enter__</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="s1">&#39;TextIO&#39;</span><span class="p">:</span>
-<span class="linenos">3346</span>        <span class="k">pass</span>
-<span class="linenos">3347</span>
-<span class="linenos">3348</span>
-<span class="linenos">3349</span><span class="k">class</span> <span class="nc">_DeprecatedType</span><span class="p">(</span><span class="nb">type</span><span class="p">):</span>
-<span class="linenos">3350</span>    <span class="k">def</span> <span class="fm">__getattribute__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span>
-<span class="linenos">3351</span>        <span class="k">if</span> <span class="n">name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">(</span><span class="s2">&quot;__dict__&quot;</span><span class="p">,</span> <span class="s2">&quot;__module__&quot;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">name</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
-<span class="linenos">3352</span>            <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
-<span class="linenos">3353</span>                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2"> is deprecated, import directly &quot;</span>
-<span class="linenos">3354</span>                <span class="sa">f</span><span class="s2">&quot;from typing instead. </span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2"> will be removed &quot;</span>
-<span class="linenos">3355</span>                <span class="s2">&quot;in Python 3.12.&quot;</span><span class="p">,</span>
-<span class="linenos">3356</span>                <span class="ne">DeprecationWarning</span><span class="p">,</span>
-<span class="linenos">3357</span>                <span class="n">stacklevel</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
-<span class="linenos">3358</span>            <span class="p">)</span>
-<span class="linenos">3359</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
-<span class="linenos">3360</span>
-<span class="linenos">3361</span>
-<span class="linenos">3362</span><span class="k">class</span> <span class="nc">io</span><span class="p">(</span><span class="n">metaclass</span><span class="o">=</span><span class="n">_DeprecatedType</span><span class="p">):</span>
-<span class="linenos">3363</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Wrapper namespace for IO generic classes.&quot;&quot;&quot;</span>
+<span class="linenos">3329</span><span class="k">class</span> <span class="nc">_DeprecatedType</span><span class="p">(</span><span class="nb">type</span><span class="p">):</span>
+<span class="linenos">3330</span>    <span class="k">def</span> <span class="fm">__getattribute__</span><span class="p">(</span><span class="bp">cls</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span>
+<span class="linenos">3331</span>        <span class="k">if</span> <span class="n">name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">(</span><span class="s2">&quot;__dict__&quot;</span><span class="p">,</span> <span class="s2">&quot;__module__&quot;</span><span class="p">)</span> <span class="ow">and</span> <span class="n">name</span> <span class="ow">in</span> <span class="bp">cls</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">:</span>
+<span class="linenos">3332</span>            <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
+<span class="linenos">3333</span>                <span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2"> is deprecated, import directly &quot;</span>
+<span class="linenos">3334</span>                <span class="sa">f</span><span class="s2">&quot;from typing instead. </span><span class="si">{</span><span class="bp">cls</span><span class="o">.</span><span class="vm">__name__</span><span class="si">}</span><span class="s2"> will be removed &quot;</span>
+<span class="linenos">3335</span>                <span class="s2">&quot;in Python 3.12.&quot;</span><span class="p">,</span>
+<span class="linenos">3336</span>                <span class="ne">DeprecationWarning</span><span class="p">,</span>
+<span class="linenos">3337</span>                <span class="n">stacklevel</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
+<span class="linenos">3338</span>            <span class="p">)</span>
+<span class="linenos">3339</span>        <span class="k">return</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
+<span class="linenos">3340</span>
+<span class="linenos">3341</span>
+<span class="linenos">3342</span><span class="k">class</span> <span class="nc">io</span><span class="p">(</span><span class="n">metaclass</span><span class="o">=</span><span class="n">_DeprecatedType</span><span class="p">):</span>
+<span class="linenos">3343</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Wrapper namespace for IO generic classes.&quot;&quot;&quot;</span>
+<span class="linenos">3344</span>
+<span class="linenos">3345</span>    <span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;IO&#39;</span><span class="p">,</span> <span class="s1">&#39;TextIO&#39;</span><span class="p">,</span> <span class="s1">&#39;BinaryIO&#39;</span><span class="p">]</span>
+<span class="linenos">3346</span>    <span class="n">IO</span> <span class="o">=</span> <span class="n">IO</span>
+<span class="linenos">3347</span>    <span class="n">TextIO</span> <span class="o">=</span> <span class="n">TextIO</span>
+<span class="linenos">3348</span>    <span class="n">BinaryIO</span> <span class="o">=</span> <span class="n">BinaryIO</span>
+<span class="linenos">3349</span>
+<span class="linenos">3350</span>
+<span class="linenos">3351</span><span class="n">io</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="vm">__name__</span> <span class="o">+</span> <span class="s1">&#39;.io&#39;</span>
+<span class="linenos">3352</span><span class="n">sys</span><span class="o">.</span><span class="n">modules</span><span class="p">[</span><span class="n">io</span><span class="o">.</span><span class="vm">__name__</span><span class="p">]</span> <span class="o">=</span> <span class="n">io</span>
+<span class="linenos">3353</span>
+<span class="linenos">3354</span><span class="n">Pattern</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">stdlib_re</span><span class="o">.</span><span class="n">Pattern</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">3355</span><span class="n">Match</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">stdlib_re</span><span class="o">.</span><span class="n">Match</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="linenos">3356</span>
+<span class="linenos">3357</span><span class="k">class</span> <span class="nc">re</span><span class="p">(</span><span class="n">metaclass</span><span class="o">=</span><span class="n">_DeprecatedType</span><span class="p">):</span>
+<span class="linenos">3358</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Wrapper namespace for re type aliases.&quot;&quot;&quot;</span>
+<span class="linenos">3359</span>
+<span class="linenos">3360</span>    <span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;Pattern&#39;</span><span class="p">,</span> <span class="s1">&#39;Match&#39;</span><span class="p">]</span>
+<span class="linenos">3361</span>    <span class="n">Pattern</span> <span class="o">=</span> <span class="n">Pattern</span>
+<span class="linenos">3362</span>    <span class="n">Match</span> <span class="o">=</span> <span class="n">Match</span>
+<span class="linenos">3363</span>
 <span class="linenos">3364</span>
-<span class="linenos">3365</span>    <span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;IO&#39;</span><span class="p">,</span> <span class="s1">&#39;TextIO&#39;</span><span class="p">,</span> <span class="s1">&#39;BinaryIO&#39;</span><span class="p">]</span>
-<span class="linenos">3366</span>    <span class="n">IO</span> <span class="o">=</span> <span class="n">IO</span>
-<span class="linenos">3367</span>    <span class="n">TextIO</span> <span class="o">=</span> <span class="n">TextIO</span>
-<span class="linenos">3368</span>    <span class="n">BinaryIO</span> <span class="o">=</span> <span class="n">BinaryIO</span>
-<span class="linenos">3369</span>
-<span class="linenos">3370</span>
-<span class="linenos">3371</span><span class="n">io</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="vm">__name__</span> <span class="o">+</span> <span class="s1">&#39;.io&#39;</span>
-<span class="linenos">3372</span><span class="n">sys</span><span class="o">.</span><span class="n">modules</span><span class="p">[</span><span class="n">io</span><span class="o">.</span><span class="vm">__name__</span><span class="p">]</span> <span class="o">=</span> <span class="n">io</span>
-<span class="linenos">3373</span>
-<span class="linenos">3374</span><span class="n">Pattern</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">stdlib_re</span><span class="o">.</span><span class="n">Pattern</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">3375</span><span class="n">Match</span> <span class="o">=</span> <span class="n">_alias</span><span class="p">(</span><span class="n">stdlib_re</span><span class="o">.</span><span class="n">Match</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="linenos">3376</span>
-<span class="linenos">3377</span><span class="k">class</span> <span class="nc">re</span><span class="p">(</span><span class="n">metaclass</span><span class="o">=</span><span class="n">_DeprecatedType</span><span class="p">):</span>
-<span class="linenos">3378</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Wrapper namespace for re type aliases.&quot;&quot;&quot;</span>
-<span class="linenos">3379</span>
-<span class="linenos">3380</span>    <span class="n">__all__</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;Pattern&#39;</span><span class="p">,</span> <span class="s1">&#39;Match&#39;</span><span class="p">]</span>
-<span class="linenos">3381</span>    <span class="n">Pattern</span> <span class="o">=</span> <span class="n">Pattern</span>
-<span class="linenos">3382</span>    <span class="n">Match</span> <span class="o">=</span> <span class="n">Match</span>
-<span class="linenos">3383</span>
-<span class="linenos">3384</span>
-<span class="linenos">3385</span><span class="n">re</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="vm">__name__</span> <span class="o">+</span> <span class="s1">&#39;.re&#39;</span>
-<span class="linenos">3386</span><span class="n">sys</span><span class="o">.</span><span class="n">modules</span><span class="p">[</span><span class="n">re</span><span class="o">.</span><span class="vm">__name__</span><span class="p">]</span> <span class="o">=</span> <span class="n">re</span>
+<span class="linenos">3365</span><span class="n">re</span><span class="o">.</span><span class="vm">__name__</span> <span class="o">=</span> <span class="vm">__name__</span> <span class="o">+</span> <span class="s1">&#39;.re&#39;</span>
+<span class="linenos">3366</span><span class="n">sys</span><span class="o">.</span><span class="n">modules</span><span class="p">[</span><span class="n">re</span><span class="o">.</span><span class="vm">__name__</span><span class="p">]</span> <span class="o">=</span> <span class="n">re</span>
+<span class="linenos">3367</span>
+<span class="linenos">3368</span>
+<span class="linenos">3369</span><span class="k">def</span> <span class="nf">reveal_type</span><span class="p">(</span><span class="n">obj</span><span class="p">:</span> <span class="n">T</span><span class="p">,</span> <span class="o">/</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">T</span><span class="p">:</span>
+<span class="linenos">3370</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Reveal the inferred type of a variable.</span>
+<span class="linenos">3371</span>
+<span class="linenos">3372</span><span class="sd">    When a static type checker encounters a call to ``reveal_type()``,</span>
+<span class="linenos">3373</span><span class="sd">    it will emit the inferred type of the argument::</span>
+<span class="linenos">3374</span>
+<span class="linenos">3375</span><span class="sd">        x: int = 1</span>
+<span class="linenos">3376</span><span class="sd">        reveal_type(x)</span>
+<span class="linenos">3377</span>
+<span class="linenos">3378</span><span class="sd">    Running a static type checker (e.g., mypy) on this example</span>
+<span class="linenos">3379</span><span class="sd">    will produce output similar to &#39;Revealed type is &quot;builtins.int&quot;&#39;.</span>
+<span class="linenos">3380</span>
+<span class="linenos">3381</span><span class="sd">    At runtime, the function prints the runtime type of the</span>
+<span class="linenos">3382</span><span class="sd">    argument and returns it unchanged.</span>
+<span class="linenos">3383</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">3384</span>    <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Runtime type is </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span><span class="o">.</span><span class="vm">__name__</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">stderr</span><span class="p">)</span>
+<span class="linenos">3385</span>    <span class="k">return</span> <span class="n">obj</span>
+<span class="linenos">3386</span>
 <span class="linenos">3387</span>
-<span class="linenos">3388</span>
-<span class="linenos">3389</span><span class="k">def</span> <span class="nf">reveal_type</span><span class="p">(</span><span class="n">obj</span><span class="p">:</span> <span class="n">T</span><span class="p">,</span> <span class="o">/</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">T</span><span class="p">:</span>
-<span class="linenos">3390</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Reveal the inferred type of a variable.</span>
-<span class="linenos">3391</span>
-<span class="linenos">3392</span><span class="sd">    When a static type checker encounters a call to ``reveal_type()``,</span>
-<span class="linenos">3393</span><span class="sd">    it will emit the inferred type of the argument::</span>
-<span class="linenos">3394</span>
-<span class="linenos">3395</span><span class="sd">        x: int = 1</span>
-<span class="linenos">3396</span><span class="sd">        reveal_type(x)</span>
+<span class="linenos">3388</span><span class="k">def</span> <span class="nf">dataclass_transform</span><span class="p">(</span>
+<span class="linenos">3389</span>    <span class="o">*</span><span class="p">,</span>
+<span class="linenos">3390</span>    <span class="n">eq_default</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
+<span class="linenos">3391</span>    <span class="n">order_default</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
+<span class="linenos">3392</span>    <span class="n">kw_only_default</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
+<span class="linenos">3393</span>    <span class="n">field_specifiers</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">type</span><span class="p">[</span><span class="n">Any</span><span class="p">]</span> <span class="o">|</span> <span class="n">Callable</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">Any</span><span class="p">],</span> <span class="o">...</span><span class="p">]</span> <span class="o">=</span> <span class="p">(),</span>
+<span class="linenos">3394</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">Any</span><span class="p">,</span>
+<span class="linenos">3395</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Callable</span><span class="p">[[</span><span class="n">T</span><span class="p">],</span> <span class="n">T</span><span class="p">]:</span>
+<span class="linenos">3396</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator to mark an object as providing dataclass-like behaviour.</span>
 <span class="linenos">3397</span>
-<span class="linenos">3398</span><span class="sd">    Running a static type checker (e.g., mypy) on this example</span>
-<span class="linenos">3399</span><span class="sd">    will produce output similar to &#39;Revealed type is &quot;builtins.int&quot;&#39;.</span>
-<span class="linenos">3400</span>
-<span class="linenos">3401</span><span class="sd">    At runtime, the function prints the runtime type of the</span>
-<span class="linenos">3402</span><span class="sd">    argument and returns it unchanged.</span>
-<span class="linenos">3403</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">3404</span>    <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Runtime type is </span><span class="si">{</span><span class="nb">type</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span><span class="o">.</span><span class="vm">__name__</span><span class="si">!r}</span><span class="s2">&quot;</span><span class="p">,</span> <span class="n">file</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">stderr</span><span class="p">)</span>
-<span class="linenos">3405</span>    <span class="k">return</span> <span class="n">obj</span>
-<span class="linenos">3406</span>
-<span class="linenos">3407</span>
-<span class="linenos">3408</span><span class="k">def</span> <span class="nf">dataclass_transform</span><span class="p">(</span>
-<span class="linenos">3409</span>    <span class="o">*</span><span class="p">,</span>
-<span class="linenos">3410</span>    <span class="n">eq_default</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span>
-<span class="linenos">3411</span>    <span class="n">order_default</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
-<span class="linenos">3412</span>    <span class="n">kw_only_default</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
-<span class="linenos">3413</span>    <span class="n">field_specifiers</span><span class="p">:</span> <span class="nb">tuple</span><span class="p">[</span><span class="nb">type</span><span class="p">[</span><span class="n">Any</span><span class="p">]</span> <span class="o">|</span> <span class="n">Callable</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">Any</span><span class="p">],</span> <span class="o">...</span><span class="p">]</span> <span class="o">=</span> <span class="p">(),</span>
-<span class="linenos">3414</span>    <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">Any</span><span class="p">,</span>
-<span class="linenos">3415</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Callable</span><span class="p">[[</span><span class="n">T</span><span class="p">],</span> <span class="n">T</span><span class="p">]:</span>
-<span class="linenos">3416</span><span class="w">    </span><span class="sd">&quot;&quot;&quot;Decorator to mark an object as providing dataclass-like behaviour.</span>
-<span class="linenos">3417</span>
-<span class="linenos">3418</span><span class="sd">    The decorator can be applied to a function, class, or metaclass.</span>
-<span class="linenos">3419</span>
-<span class="linenos">3420</span><span class="sd">    Example usage with a decorator function::</span>
-<span class="linenos">3421</span>
-<span class="linenos">3422</span><span class="sd">        T = TypeVar(&quot;T&quot;)</span>
-<span class="linenos">3423</span>
-<span class="linenos">3424</span><span class="sd">        @dataclass_transform()</span>
-<span class="linenos">3425</span><span class="sd">        def create_model(cls: type[T]) -&gt; type[T]:</span>
-<span class="linenos">3426</span><span class="sd">            ...</span>
-<span class="linenos">3427</span><span class="sd">            return cls</span>
-<span class="linenos">3428</span>
-<span class="linenos">3429</span><span class="sd">        @create_model</span>
-<span class="linenos">3430</span><span class="sd">        class CustomerModel:</span>
+<span class="linenos">3398</span><span class="sd">    The decorator can be applied to a function, class, or metaclass.</span>
+<span class="linenos">3399</span>
+<span class="linenos">3400</span><span class="sd">    Example usage with a decorator function::</span>
+<span class="linenos">3401</span>
+<span class="linenos">3402</span><span class="sd">        T = TypeVar(&quot;T&quot;)</span>
+<span class="linenos">3403</span>
+<span class="linenos">3404</span><span class="sd">        @dataclass_transform()</span>
+<span class="linenos">3405</span><span class="sd">        def create_model(cls: type[T]) -&gt; type[T]:</span>
+<span class="linenos">3406</span><span class="sd">            ...</span>
+<span class="linenos">3407</span><span class="sd">            return cls</span>
+<span class="linenos">3408</span>
+<span class="linenos">3409</span><span class="sd">        @create_model</span>
+<span class="linenos">3410</span><span class="sd">        class CustomerModel:</span>
+<span class="linenos">3411</span><span class="sd">            id: int</span>
+<span class="linenos">3412</span><span class="sd">            name: str</span>
+<span class="linenos">3413</span>
+<span class="linenos">3414</span><span class="sd">    On a base class::</span>
+<span class="linenos">3415</span>
+<span class="linenos">3416</span><span class="sd">        @dataclass_transform()</span>
+<span class="linenos">3417</span><span class="sd">        class ModelBase: ...</span>
+<span class="linenos">3418</span>
+<span class="linenos">3419</span><span class="sd">        class CustomerModel(ModelBase):</span>
+<span class="linenos">3420</span><span class="sd">            id: int</span>
+<span class="linenos">3421</span><span class="sd">            name: str</span>
+<span class="linenos">3422</span>
+<span class="linenos">3423</span><span class="sd">    On a metaclass::</span>
+<span class="linenos">3424</span>
+<span class="linenos">3425</span><span class="sd">        @dataclass_transform()</span>
+<span class="linenos">3426</span><span class="sd">        class ModelMeta(type): ...</span>
+<span class="linenos">3427</span>
+<span class="linenos">3428</span><span class="sd">        class ModelBase(metaclass=ModelMeta): ...</span>
+<span class="linenos">3429</span>
+<span class="linenos">3430</span><span class="sd">        class CustomerModel(ModelBase):</span>
 <span class="linenos">3431</span><span class="sd">            id: int</span>
 <span class="linenos">3432</span><span class="sd">            name: str</span>
 <span class="linenos">3433</span>
-<span class="linenos">3434</span><span class="sd">    On a base class::</span>
-<span class="linenos">3435</span>
-<span class="linenos">3436</span><span class="sd">        @dataclass_transform()</span>
-<span class="linenos">3437</span><span class="sd">        class ModelBase: ...</span>
-<span class="linenos">3438</span>
-<span class="linenos">3439</span><span class="sd">        class CustomerModel(ModelBase):</span>
-<span class="linenos">3440</span><span class="sd">            id: int</span>
-<span class="linenos">3441</span><span class="sd">            name: str</span>
-<span class="linenos">3442</span>
-<span class="linenos">3443</span><span class="sd">    On a metaclass::</span>
-<span class="linenos">3444</span>
-<span class="linenos">3445</span><span class="sd">        @dataclass_transform()</span>
-<span class="linenos">3446</span><span class="sd">        class ModelMeta(type): ...</span>
-<span class="linenos">3447</span>
-<span class="linenos">3448</span><span class="sd">        class ModelBase(metaclass=ModelMeta): ...</span>
-<span class="linenos">3449</span>
-<span class="linenos">3450</span><span class="sd">        class CustomerModel(ModelBase):</span>
-<span class="linenos">3451</span><span class="sd">            id: int</span>
-<span class="linenos">3452</span><span class="sd">            name: str</span>
-<span class="linenos">3453</span>
-<span class="linenos">3454</span><span class="sd">    The ``CustomerModel`` classes defined above will</span>
-<span class="linenos">3455</span><span class="sd">    be treated by type checkers similarly to classes created with</span>
-<span class="linenos">3456</span><span class="sd">    ``@dataclasses.dataclass``.</span>
-<span class="linenos">3457</span><span class="sd">    For example, type checkers will assume these classes have</span>
-<span class="linenos">3458</span><span class="sd">    ``__init__`` methods that accept ``id`` and ``name``.</span>
-<span class="linenos">3459</span>
-<span class="linenos">3460</span><span class="sd">    The arguments to this decorator can be used to customize this behavior:</span>
-<span class="linenos">3461</span><span class="sd">    - ``eq_default`` indicates whether the ``eq`` parameter is assumed to be</span>
-<span class="linenos">3462</span><span class="sd">        ``True`` or ``False`` if it is omitted by the caller.</span>
-<span class="linenos">3463</span><span class="sd">    - ``order_default`` indicates whether the ``order`` parameter is</span>
-<span class="linenos">3464</span><span class="sd">        assumed to be True or False if it is omitted by the caller.</span>
-<span class="linenos">3465</span><span class="sd">    - ``kw_only_default`` indicates whether the ``kw_only`` parameter is</span>
-<span class="linenos">3466</span><span class="sd">        assumed to be True or False if it is omitted by the caller.</span>
-<span class="linenos">3467</span><span class="sd">    - ``field_specifiers`` specifies a static list of supported classes</span>
-<span class="linenos">3468</span><span class="sd">        or functions that describe fields, similar to ``dataclasses.field()``.</span>
-<span class="linenos">3469</span><span class="sd">    - Arbitrary other keyword arguments are accepted in order to allow for</span>
-<span class="linenos">3470</span><span class="sd">        possible future extensions.</span>
-<span class="linenos">3471</span>
-<span class="linenos">3472</span><span class="sd">    At runtime, this decorator records its arguments in the</span>
-<span class="linenos">3473</span><span class="sd">    ``__dataclass_transform__`` attribute on the decorated object.</span>
-<span class="linenos">3474</span><span class="sd">    It has no other runtime effect.</span>
-<span class="linenos">3475</span>
-<span class="linenos">3476</span><span class="sd">    See PEP 681 for more details.</span>
-<span class="linenos">3477</span><span class="sd">    &quot;&quot;&quot;</span>
-<span class="linenos">3478</span>    <span class="k">def</span> <span class="nf">decorator</span><span class="p">(</span><span class="n">cls_or_fn</span><span class="p">):</span>
-<span class="linenos">3479</span>        <span class="n">cls_or_fn</span><span class="o">.</span><span class="n">__dataclass_transform__</span> <span class="o">=</span> <span class="p">{</span>
-<span class="linenos">3480</span>            <span class="s2">&quot;eq_default&quot;</span><span class="p">:</span> <span class="n">eq_default</span><span class="p">,</span>
-<span class="linenos">3481</span>            <span class="s2">&quot;order_default&quot;</span><span class="p">:</span> <span class="n">order_default</span><span class="p">,</span>
-<span class="linenos">3482</span>            <span class="s2">&quot;kw_only_default&quot;</span><span class="p">:</span> <span class="n">kw_only_default</span><span class="p">,</span>
-<span class="linenos">3483</span>            <span class="s2">&quot;field_specifiers&quot;</span><span class="p">:</span> <span class="n">field_specifiers</span><span class="p">,</span>
-<span class="linenos">3484</span>            <span class="s2">&quot;kwargs&quot;</span><span class="p">:</span> <span class="n">kwargs</span><span class="p">,</span>
-<span class="linenos">3485</span>        <span class="p">}</span>
-<span class="linenos">3486</span>        <span class="k">return</span> <span class="n">cls_or_fn</span>
-<span class="linenos">3487</span>    <span class="k">return</span> <span class="n">decorator</span>
+<span class="linenos">3434</span><span class="sd">    The ``CustomerModel`` classes defined above will</span>
+<span class="linenos">3435</span><span class="sd">    be treated by type checkers similarly to classes created with</span>
+<span class="linenos">3436</span><span class="sd">    ``@dataclasses.dataclass``.</span>
+<span class="linenos">3437</span><span class="sd">    For example, type checkers will assume these classes have</span>
+<span class="linenos">3438</span><span class="sd">    ``__init__`` methods that accept ``id`` and ``name``.</span>
+<span class="linenos">3439</span>
+<span class="linenos">3440</span><span class="sd">    The arguments to this decorator can be used to customize this behavior:</span>
+<span class="linenos">3441</span><span class="sd">    - ``eq_default`` indicates whether the ``eq`` parameter is assumed to be</span>
+<span class="linenos">3442</span><span class="sd">        ``True`` or ``False`` if it is omitted by the caller.</span>
+<span class="linenos">3443</span><span class="sd">    - ``order_default`` indicates whether the ``order`` parameter is</span>
+<span class="linenos">3444</span><span class="sd">        assumed to be True or False if it is omitted by the caller.</span>
+<span class="linenos">3445</span><span class="sd">    - ``kw_only_default`` indicates whether the ``kw_only`` parameter is</span>
+<span class="linenos">3446</span><span class="sd">        assumed to be True or False if it is omitted by the caller.</span>
+<span class="linenos">3447</span><span class="sd">    - ``field_specifiers`` specifies a static list of supported classes</span>
+<span class="linenos">3448</span><span class="sd">        or functions that describe fields, similar to ``dataclasses.field()``.</span>
+<span class="linenos">3449</span><span class="sd">    - Arbitrary other keyword arguments are accepted in order to allow for</span>
+<span class="linenos">3450</span><span class="sd">        possible future extensions.</span>
+<span class="linenos">3451</span>
+<span class="linenos">3452</span><span class="sd">    At runtime, this decorator records its arguments in the</span>
+<span class="linenos">3453</span><span class="sd">    ``__dataclass_transform__`` attribute on the decorated object.</span>
+<span class="linenos">3454</span><span class="sd">    It has no other runtime effect.</span>
+<span class="linenos">3455</span>
+<span class="linenos">3456</span><span class="sd">    See PEP 681 for more details.</span>
+<span class="linenos">3457</span><span class="sd">    &quot;&quot;&quot;</span>
+<span class="linenos">3458</span>    <span class="k">def</span> <span class="nf">decorator</span><span class="p">(</span><span class="n">cls_or_fn</span><span class="p">):</span>
+<span class="linenos">3459</span>        <span class="n">cls_or_fn</span><span class="o">.</span><span class="n">__dataclass_transform__</span> <span class="o">=</span> <span class="p">{</span>
+<span class="linenos">3460</span>            <span class="s2">&quot;eq_default&quot;</span><span class="p">:</span> <span class="n">eq_default</span><span class="p">,</span>
+<span class="linenos">3461</span>            <span class="s2">&quot;order_default&quot;</span><span class="p">:</span> <span class="n">order_default</span><span class="p">,</span>
+<span class="linenos">3462</span>            <span class="s2">&quot;kw_only_default&quot;</span><span class="p">:</span> <span class="n">kw_only_default</span><span class="p">,</span>
+<span class="linenos">3463</span>            <span class="s2">&quot;field_specifiers&quot;</span><span class="p">:</span> <span class="n">field_specifiers</span><span class="p">,</span>
+<span class="linenos">3464</span>            <span class="s2">&quot;kwargs&quot;</span><span class="p">:</span> <span class="n">kwargs</span><span class="p">,</span>
+<span class="linenos">3465</span>        <span class="p">}</span>
+<span class="linenos">3466</span>        <span class="k">return</span> <span class="n">cls_or_fn</span>
+<span class="linenos">3467</span>    <span class="k">return</span> <span class="n">decorator</span>
 </pre></div>
 
                 </article>
@@ -3997,15 +3977,11 @@ <h1>Source code for typing</h1><div class="highlight"><pre>
       
         <div class="footer-item">
   <p class="sphinx-version">
-    Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5.
+     Created with <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5, with some help from <a href="https://chat.openai.com/"> ChatGPT</a> (GPT 4).
     <br/>
   </p>
 </div>
       
-        <div class="footer-item"><p class="theme-version">
-  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
-</p></div>
-      
     </div>
   
   
diff --git a/_sources/.DS_Store b/_sources/.DS_Store
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GIT binary patch
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diff --git a/_sources/api/abc.rst b/_sources/api/abc.rst
index f4a30d02..ecb5e505 100644
--- a/_sources/api/abc.rst
+++ b/_sources/api/abc.rst
@@ -1,19 +1,13 @@
 pyxu.abc
 ========
 
-.. Solver-Related -------------------------------------------------------------
-.. autoclass:: pyxu.abc.Solver
-
-   .. autoattribute:: _mstate
+.. contents:: Table of Contents
+   :local:
+   :depth: 2
 
-   .. autoattribute:: _astate
-
-.. autoclass:: pyxu.abc.SolverMode
+pyxu.abc.arithmetic
+-------------------
 
-.. autoclass:: pyxu.abc.StoppingCriterion
-
-
-.. Arithmetic Rules -----------------------------------------------------------
 .. autoclass:: pyxu.abc.arithmetic.Rule
    :members: op
    :no-members:
@@ -39,7 +33,9 @@ pyxu.abc
 .. autoclass:: pyxu.abc.arithmetic.TransposeRule
    :no-members:
 
-.. Operator-Related -----------------------------------------------------------
+pyxu.abc.operator
+-----------------
+
 .. autoclass:: pyxu.abc.Property
 
 .. autoclass:: pyxu.abc.Operator
@@ -101,3 +97,16 @@ pyxu.abc
 
 .. autoclass:: pyxu.abc.LinFunc
    :no-members:
+
+pyxu.abc.solver
+---------------
+
+.. autoclass:: pyxu.abc.Solver
+
+   .. autoattribute:: _mstate
+
+   .. autoattribute:: _astate
+
+.. autoclass:: pyxu.abc.SolverMode
+
+.. autoclass:: pyxu.abc.StoppingCriterion
diff --git a/_sources/api/experimental.rst b/_sources/api/experimental.rst
deleted file mode 100644
index 998ad46f..00000000
--- a/_sources/api/experimental.rst
+++ /dev/null
@@ -1,4 +0,0 @@
-pyxu.experimental
-=================
-
-.. automodule:: pyxu.experimental.sampler
diff --git a/_sources/api/index.rst b/_sources/api/index.rst
index 8a4b3038..c571d24d 100644
--- a/_sources/api/index.rst
+++ b/_sources/api/index.rst
@@ -430,8 +430,10 @@ Array Backend-Related
 
 .. autosummary::
 
+   ~pyxu.util.compute
    ~pyxu.util.get_array_module
    ~pyxu.util.redirect
+   ~pyxu.util.to_NUMPY
 
 Complex Number Handling
 ^^^^^^^^^^^^^^^^^^^^^^^
@@ -456,7 +458,6 @@ Misc
 
 .. autosummary::
 
-   ~pyxu.util.compute
    ~pyxu.util.copy_if_unsafe
    ~pyxu.util.import_module
    ~pyxu.util.infer_composition_shape
@@ -464,7 +465,6 @@ Misc
    ~pyxu.util.next_fast_len
    ~pyxu.util.parse_params
    ~pyxu.util.read_only
-   ~pyxu.util.to_NUMPY
 
 .. rubric:: Low-lever Helpers
 
@@ -479,7 +479,7 @@ Misc
    :maxdepth: 2
    :hidden:
 
-   abc/index
+   abc
    info.deps
    info.ptype
    info.warning
@@ -489,6 +489,6 @@ Misc
    opt.stop
    runtime
    math
-   util/index
+   util
    experimental.sampler
    ../references
diff --git a/_sources/api/info.deps.rst b/_sources/api/info.deps.rst
index ab346d37..117cefd9 100644
--- a/_sources/api/info.deps.rst
+++ b/_sources/api/info.deps.rst
@@ -3,5 +3,9 @@ pyxu.info.deps
 
 .. automodule:: pyxu.info.deps
    :members:
+   :exclude-members: CUPY_ENABLED
    :undoc-members:
    :show-inheritance:
+
+   .. autodata:: CUPY_ENABLED
+      :no-value:
diff --git a/_sources/api/info.ptype.rst b/_sources/api/info.ptype.rst
index 652a3ebb..a0c23519 100644
--- a/_sources/api/info.ptype.rst
+++ b/_sources/api/info.ptype.rst
@@ -1,4 +1,52 @@
 pyxu.info.ptype
 ===============
 
+.. [Sepand, 2023.09.15]
+.. `pyxu.info.ptype` contains alias types for Python type checkers.  When auto-documented via Sphinx, alias types
+.. contain "alias of ..." as part of their docstring, which depends on the machine config.  (Was unable to remove them
+.. via Sphinx's `autodoc-process-docstring` event.) To avoid machine-dependant outputs in HTML docs, we provide custom
+.. machine-agnostic documentation for some aliases as required. Provided descriptions match those given as comments in
+.. `pyxu.info.ptype`.
+
+
 .. automodule:: pyxu.info.ptype
+   :exclude-members: NDArray, ArrayModule, SparseArray, SparseModule, OpT, Property, SolverT, SolverM, Real, DType
+
+   .. class:: NDArray
+
+      Supported dense array types.
+
+   .. class:: ArrayModule
+
+      Supported dense array modules.
+
+   .. class:: SparseArray
+
+      Supported sparse array types.
+
+   .. class:: SparseModule
+
+      Supported sparse array modules.
+
+   .. class:: OpT
+
+      Top-level abstract :py:class:`~pyxu.abc.Operator` interface exposed to users.
+
+   .. autodata:: Property
+      :no-value:
+
+   .. class:: SolverT
+
+      Top-level abstract :py:class:`~pyxu.abc.Solver` interface exposed to users.
+
+   .. class:: SolverM
+
+      Solver run-mode(s).
+
+   .. class:: Real
+
+      Alias of :py:class:`numbers.Real`.
+
+   .. data:: DType
+
+      :py:attr:`~pyxu.info.ptype.NDArray` dtype specifier.
diff --git a/_sources/api/info.rst b/_sources/api/info.rst
deleted file mode 100644
index 7337a2a8..00000000
--- a/_sources/api/info.rst
+++ /dev/null
@@ -1,26 +0,0 @@
-pyxu.info
-=========
-
-.. contents:: Table of Contents
-   :local:
-   :depth: 1
-   
-pyxu.info.ptype
----------------
-
-.. automodule:: pyxu.info.ptype
-
-pyxu.info.deps
---------------
-
-.. automodule:: pyxu.info.deps
-   :members:
-   :undoc-members:
-   :show-inheritance:
-
-pyxu.info.warning
------------------
-
-.. automodule:: pyxu.info.warning
-   :no-special-members:
-   :exclude-members: add_note, args, with_traceback
diff --git a/_sources/api/operator.rst b/_sources/api/operator.rst
deleted file mode 100644
index c8a06615..00000000
--- a/_sources/api/operator.rst
+++ /dev/null
@@ -1,245 +0,0 @@
-pyxu.operator
-=============
-
-.. pyxu.operator.map.base -----------------------------------------------------
-
-.. autofunction:: pyxu.operator.ConstantValued
-
-.. pyxu.operator.func.norm ----------------------------------------------------
-
-.. autoclass:: pyxu.operator.L1Norm
-   :no-members:
-
-.. autoclass:: pyxu.operator.L2Norm
-   :no-members:
-
-.. autoclass:: pyxu.operator.SquaredL2Norm
-   :no-members:
-
-.. autoclass:: pyxu.operator.SquaredL1Norm
-   :no-members:
-   :members: prox
-   :special-members: __init__
-
-.. autofunction:: pyxu.operator.shift_loss
-
-.. autoclass:: pyxu.operator.KLDivergence
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.operator.LInfinityNorm
-   :no-members:
-
-.. autoclass:: pyxu.operator.L21Norm
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.operator.PositiveL1Norm
-   :no-members:
-
-.. pyxu.operator.func.indicator -----------------------------------------------
-
-.. autofunction:: pyxu.operator.L1Ball
-
-.. autofunction:: pyxu.operator.L2Ball
-
-.. autofunction:: pyxu.operator.LInfinityBall
-
-.. autoclass:: pyxu.operator.PositiveOrthant
-   :no-members:
-
-.. autoclass:: pyxu.operator.HyperSlab
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.operator.RangeSet
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.operator.AffineSet
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.operator.ConvexSetIntersection
-   :no-members:
-   :members: prox
-   :special-members: __init__
-
-.. pyxu.operator.blocks -------------------------------------------------------
-
-.. autofunction:: pyxu.operator.stack
-
-.. autofunction:: pyxu.operator.vstack
-
-.. autofunction:: pyxu.operator.hstack
-
-.. autofunction:: pyxu.operator.block_diag
-
-.. autofunction:: pyxu.operator.block
-
-.. autofunction:: pyxu.operator.coo_block
-
-.. pyxu.operator.map.ufunc ----------------------------------------------------
-
-.. autofunction:: pyxu.operator.sin
-
-.. autofunction:: pyxu.operator.cos
-
-.. autofunction:: pyxu.operator.tan
-
-.. autofunction:: pyxu.operator.arcsin
-
-.. autofunction:: pyxu.operator.arccos
-
-.. autofunction:: pyxu.operator.arctan
-
-.. autofunction:: pyxu.operator.sinh
-
-.. autofunction:: pyxu.operator.cosh
-
-.. autofunction:: pyxu.operator.tanh
-
-.. autofunction:: pyxu.operator.arcsinh
-
-.. autofunction:: pyxu.operator.arccosh
-
-.. autofunction:: pyxu.operator.arctanh
-
-.. autofunction:: pyxu.operator.exp
-
-.. autofunction:: pyxu.operator.log
-
-.. autofunction:: pyxu.operator.clip
-
-.. autofunction:: pyxu.operator.sqrt
-
-.. autofunction:: pyxu.operator.cbrt
-
-.. autofunction:: pyxu.operator.square
-
-.. autofunction:: pyxu.operator.abs
-
-.. autofunction:: pyxu.operator.sign
-
-.. autofunction:: pyxu.operator.gaussian
-
-.. autofunction:: pyxu.operator.sigmoid
-
-.. autofunction:: pyxu.operator.softplus
-
-.. autofunction:: pyxu.operator.leakyrelu
-
-.. autofunction:: pyxu.operator.relu
-
-.. autofunction:: pyxu.operator.silu
-
-.. autofunction:: pyxu.operator.softmax
-
-.. pyxu.operator.linop.select -------------------------------------------------
-
-.. autoclass:: pyxu.operator.SubSample
-   :no-members:
-   :members: apply, adjoint, TrimSpec, IndexSpec
-   :special-members: __init__
-
-.. autofunction:: pyxu.operator.Trim
-
-.. pyxu.operator.linop.reduce -------------------------------------------------
-
-.. autofunction:: pyxu.operator.Sum
-
-.. pyxu.operator.linop.kron ---------------------------------------------------
-
-.. autofunction:: pyxu.operator.kron
-
-.. autofunction:: pyxu.operator.khatri_rao
-
-.. pyxu.operator.linop.base ---------------------------------------------------
-
-.. autoclass:: pyxu.operator.IdentityOp
-   :no-members:
-
-.. autoclass:: pyxu.operator.NullOp
-   :no-members:
-
-.. autofunction:: pyxu.operator.NullFunc
-
-.. autofunction:: pyxu.operator.HomothetyOp
-
-.. autofunction:: pyxu.operator.DiagonalOp
-
-.. pyxu.operator.linop.pad ----------------------------------------------------
-
-.. autoclass:: pyxu.operator.Pad
-   :no-members:
-   :members: WidthSpec, ModeSpec
-   :special-members: __init__
-
-.. pyxu.operator.linop.stencil ------------------------------------------------
-
-.. autoclass:: pyxu.operator._Stencil
-   :no-members:
-   :members: init, apply, IndexSpec
-
-.. autoclass:: pyxu.operator.Stencil
-   :no-members:
-   :members: KernelSpec, configure_dispatcher, kernel, center, relative_indices, visualize
-   :special-members: __init__
-
-.. autoclass:: pyxu.operator.Correlate
-
-.. autofunction:: pyxu.operator.Convolve
-
-.. pyxu.operator.linop.fft ----------------------------------------------------
-
-.. autoclass:: pyxu.operator.FFT
-   :no-members:
-   :members: apply, adjoint
-   :special-members: __init__
-
-.. autoclass:: pyxu.operator.NUFFT
-   :no-members:
-   :members: type1, type2, type3, apply, adjoint, ascomplexarray, mesh, plot_kernel, params, auto_chunk, allocate, diagnostic_plot, stats
-
-.. pyxu.operator.linop.diff ---------------------------------------------------
-
-.. autoclass:: pyxu.operator.PartialDerivative
-   :members: finite_difference, gaussian_derivative
-
-.. autofunction:: pyxu.operator.Gradient
-
-.. autofunction:: pyxu.operator.Jacobian
-
-.. autofunction:: pyxu.operator.Divergence
-
-.. autofunction:: pyxu.operator.Hessian
-
-.. autofunction:: pyxu.operator.Laplacian
-
-.. autofunction:: pyxu.operator.DirectionalDerivative
-
-.. autofunction:: pyxu.operator.DirectionalGradient
-
-.. autofunction:: pyxu.operator.DirectionalLaplacian
-
-.. autofunction:: pyxu.operator.DirectionalHessian
-
-.. pyxu.operator.linop.filter -------------------------------------------------
-
-.. autofunction:: pyxu.operator.MovingAverage
-
-.. autofunction:: pyxu.operator.Gaussian
-
-.. autofunction:: pyxu.operator.DifferenceOfGaussians
-
-.. autofunction:: pyxu.operator.DoG
-
-.. autofunction:: pyxu.operator.Laplace
-
-.. autofunction:: pyxu.operator.Sobel
-
-.. autofunction:: pyxu.operator.Prewitt
-
-.. autofunction:: pyxu.operator.Scharr
-
-.. autoclass:: pyxu.operator.StructureTensor
diff --git a/_sources/api/operator/interop.rst b/_sources/api/operator/interop.rst
deleted file mode 100644
index d4192034..00000000
--- a/_sources/api/operator/interop.rst
+++ /dev/null
@@ -1,34 +0,0 @@
-pyxu.operator.interop
-=====================
-
-.. contents:: Table of Contents
-   :local:
-   :depth: 1
-
-Generic Constructor
--------------------
-
-.. autofunction:: pyxu.operator.interop.source.from_source
-
-SciPy Interoperability
-----------------------
-
-.. autofunction:: pyxu.operator.interop.sciop.from_sciop
-
-JAX Interoperability
---------------------
-
-.. autofunction:: pyxu.operator.interop.jax.from_jax
-
-.. autofunction:: pyxu.operator.interop.jax._from_jax
-
-.. autofunction:: pyxu.operator.interop.jax._to_jax
-
-PyTorch Interoperability
-------------------------
-
-.. autofunction:: pyxu.operator.interop.torch.from_torch
-
-.. autofunction:: pyxu.operator.interop.torch.astensor
-
-.. autofunction:: pyxu.operator.interop.torch.asarray
diff --git a/_sources/api/opt.rst b/_sources/api/opt.rst
deleted file mode 100644
index ff06006f..00000000
--- a/_sources/api/opt.rst
+++ /dev/null
@@ -1,94 +0,0 @@
-pyxu.opt
-========
-
-.. contents:: Table of Contents
-   :local:
-   :depth: 1
-
-pyxu.opt.stop
--------------
-
-.. autoclass:: pyxu.opt.stop.MaxIter
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.opt.stop.ManualStop
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.opt.stop.MaxDuration
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.opt.stop.MaxCarbon
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.opt.stop.Memorize
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.opt.stop.AbsError
-   :no-members:
-   :special-members: __init__
-
-.. autoclass:: pyxu.opt.stop.RelError
-   :no-members:
-   :special-members: __init__
-
-pyxu.opt.solver
----------------
-
-.. autoclass:: pyxu.opt.solver.pgd.PGD
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.cg.CG
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.nlcg.NLCG
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.adam.Adam
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.pds.CondatVu
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.pds.CV
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.pds.PD3O
-   :no-members:
-
-.. autofunction:: pyxu.opt.solver.pds.ChambollePock
-
-.. autofunction:: pyxu.opt.solver.pds.CP
-
-.. autoclass:: pyxu.opt.solver.pds.LorisVerhoeven
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.pds.LV
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.pds.DavisYin
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.pds.DY
-   :no-members:
-
-.. autofunction:: pyxu.opt.solver.pds.DouglasRachford
-
-.. autofunction:: pyxu.opt.solver.pds.DR
-
-.. autoclass:: pyxu.opt.solver.pds.ForwardBackward
-   :no-members:
-
-.. autoclass:: pyxu.opt.solver.pds.FB
-   :no-members:
-
-.. autofunction:: pyxu.opt.solver.pds.ProximalPoint
-
-.. autofunction:: pyxu.opt.solver.pds.PP
-
-.. autoclass:: pyxu.opt.solver.pds.ADMM
-   :no-members:
diff --git a/_sources/api/util.rst b/_sources/api/util.rst
index d3d99d53..3b9dcff5 100644
--- a/_sources/api/util.rst
+++ b/_sources/api/util.rst
@@ -1,14 +1,60 @@
 pyxu.util
 =========
 
-.. automodule:: pyxu.util
+.. contents:: Table of Contents
+   :local:
+   :depth: 2
 
-   .. Force document of some non-public functions.
+pyxu.util.array_module
+----------------------
 
-   .. autofunction:: pyxu.util.misc.peaks
+.. autofunction:: pyxu.util.get_array_module
 
-   .. autofunction:: pyxu.util.misc.star_like_sample
+.. autofunction:: pyxu.util.redirect
 
-   .. autofunction:: pyxu.util.operator._dask_zip
+.. autofunction:: pyxu.util.compute
 
-   .. autofunction:: pyxu.util.operator._array_ize
+.. autofunction:: pyxu.util.to_NUMPY
+
+pyxu.util.complex
+-----------------
+
+.. autofunction:: pyxu.util.view_as_complex_mat
+
+.. autofunction:: pyxu.util.view_as_complex
+
+.. autofunction:: pyxu.util.view_as_real_mat
+
+.. autofunction:: pyxu.util.view_as_real
+
+pyxu.util.misc
+--------------
+
+.. autofunction:: pyxu.util.copy_if_unsafe
+
+.. autofunction:: pyxu.util.import_module
+
+.. autofunction:: pyxu.util.infer_composition_shape
+
+.. autofunction:: pyxu.util.infer_sum_shape
+
+.. autofunction:: pyxu.util.next_fast_len
+
+.. autofunction:: pyxu.util.parse_params
+
+.. autofunction:: pyxu.util.read_only
+
+.. autofunction:: pyxu.util.misc.peaks
+
+.. autofunction:: pyxu.util.misc.star_like_sample
+
+pyxu.util.operator
+------------------
+
+.. autofunction:: pyxu.util.as_canonical_shape
+
+.. autofunction:: pyxu.util.vectorize
+
+.. autofunction:: pyxu.util.operator._array_ize
+
+.. autofunction:: pyxu.util.operator._dask_zip
diff --git a/_sources/api/util/array_module.rst b/_sources/api/util/array_module.rst
index a3067b44..9d48670d 100644
--- a/_sources/api/util/array_module.rst
+++ b/_sources/api/util/array_module.rst
@@ -4,3 +4,7 @@ pyxu.util.array_module
 .. autofunction:: pyxu.util.get_array_module
 
 .. autofunction:: pyxu.util.redirect
+
+.. autofunction:: pyxu.util.compute
+
+.. autofunction:: pyxu.util.to_NUMPY
diff --git a/_sources/api/util/misc.rst b/_sources/api/util/misc.rst
index f1ef45d8..ca8bfff7 100644
--- a/_sources/api/util/misc.rst
+++ b/_sources/api/util/misc.rst
@@ -1,8 +1,6 @@
 pyxu.util.misc
 ==============
 
-.. autofunction:: pyxu.util.compute
-
 .. autofunction:: pyxu.util.copy_if_unsafe
 
 .. autofunction:: pyxu.util.import_module
@@ -17,8 +15,6 @@ pyxu.util.misc
 
 .. autofunction:: pyxu.util.read_only
 
-.. autofunction:: pyxu.util.to_NUMPY
-
 .. autofunction:: pyxu.util.misc.peaks
 
 .. autofunction:: pyxu.util.misc.star_like_sample
diff --git a/_sources/examples/contributing.ipynb b/_sources/examples/contributing.ipynb
new file mode 100644
index 00000000..817f3fd3
--- /dev/null
+++ b/_sources/examples/contributing.ipynb
@@ -0,0 +1,134 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "92ed2e98",
+   "metadata": {},
+   "source": [
+    "# Using Contributed Plugins in Pyxu\n",
+    "\n",
+    "In this notebook, we will explore how to use contributed plugins in the Pyxu software framework. We will focus on the `pyxu-gradient-descent` plugin. \n",
+    "\n",
+    "## Step 1: Attempting to Import Before Installation\n",
+    "\n",
+    "Before installing the plugin, let's try importing an object from the `pyxu-gradient-descent` namespace to see what happens.\n",
+    "```python\n",
+    "try:\n",
+    "    from pyxu.opt.solver import GradientDescent\n",
+    "except ImportError as e:\n",
+    "    print(e)\n",
+    "```\n",
+    "\n",
+    "<div style=\"border:1px solid #ccc; padding: 10px; background-color: #f9f9f9; font-family: monospace;\">\n",
+    "\n",
+    "cannot import name 'GradientDescent' from 'pyxu.opt.solver' (pyxu/opt/solver/__init__.py)\n",
+    "\n",
+    "    \n",
+    "</div>\n",
+    "\n",
+    "\n",
+    "You should see an *ImportError*, indicating that the objects are not available because the plugin is not installed yet.\n",
+    "\n",
+    "## Step 2: Installing the Plugin\n",
+    "\n",
+    "To install the pyxu-gradient-descent plugin, use the following magic command:\n",
+    "\n",
+    "```python\n",
+    "!pip install pyxu-gradient-descent\n",
+    "```\n",
+    "\n",
+    "## Step 3: Importing the Necessary Objects\n",
+    "\n",
+    "Now that we have installed the plugin, let's import the necessary objects:\n",
+    "\n",
+    "```python\n",
+    "from pyxu.operator import SquaredL2Norm\n",
+    "from pyxu.opt.solver import GradientDescent\n",
+    "import numpy as np\n",
+    "```\n",
+    "<div style=\" padding: 10px; background-color: #ffe6e6;\">\n",
+    "pyxu/info/plugin.py:69: ContributionWarning: Plugin `GradientDescent` loaded, use with caution.\n",
+    "  warnings.warn(f\"Plugin `{name}` loaded, use with caution.\", pxw.ContributionWarning)\n",
+    "</div>\n",
+    "\n",
+    "The warning signals that a class or function has been imported from external code into the core Pyxu codebase, and should be used with caution. \n",
+    "\n",
+    "## Step 4: Using the Gradient Descent Algorithm\n",
+    "\n",
+    "In this step, we will use the gradient descent algorithm to minimize a function defined by the squared L2 norm. Here is how you can do it:\n",
+    "\n",
+    "```python\n",
+    "# Define the dimension\n",
+    "N = 100\n",
+    "\n",
+    "# Generate random data\n",
+    "rng = np.random.default_rng(seed=0)\n",
+    "y = rng.uniform(size=N)\n",
+    "\n",
+    "# Define the loss function\n",
+    "loss = SquaredL2Norm(dim=N).asloss(y)\n",
+    "\n",
+    "# Initialize the gradient descent algorithm\n",
+    "gd = GradientDescent(f=loss)\n",
+    "\n",
+    "# Define the initial point\n",
+    "x0 = np.random.randn(N)\n",
+    "\n",
+    "# Run the gradient descent algorithm\n",
+    "gd.fit(x0=x0, acceleration=True)\n",
+    "\n",
+    "# Check the solution\n",
+    "assert np.allclose(gd.solution(), y)\n",
+    "```\n",
+    "<div style=\"border:1px solid #ccc; padding: 10px; background-color: #f9f9f9; font-family: monospace;\">\n",
+    "\n",
+    "INFO -- [2023-09-13 09:28:52.933466] Iteration 0\n",
+    "    \n",
+    "\titeration: 0\n",
+    "    RelError[x]: 0.0\n",
+    "\n",
+    "INFO -- [2023-09-13 09:28:52.934287] Iteration 1\n",
+    "\n",
+    "    iteration: 1\n",
+    "    RelError[x]: 1.1798071385920126\n",
+    "\n",
+    "INFO -- [2023-09-13 09:28:52.934882] Iteration 2\n",
+    "\n",
+    "    iteration: 2\n",
+    "    RelError[x]: 9.55411637565644e-17\n",
+    "\n",
+    "INFO -- [2023-09-13 09:28:52.935515] Stopping Criterion satisfied -> END\n",
+    "\n",
+    "</div>\n",
+    "\n",
+    "\n",
+    "If everything runs without errors, it means that the gradient descent algorithm has successfully found a solution that is close to the input data.\n",
+    "\n",
+    "## Conclusion\n",
+    "\n",
+    "In this notebook, we have seen how to use contributed plugins in the Pyxu software framework. We learned how to install a plugin and use it to run a gradient descent algorithm. We hope this guide has been helpful, and encourage you to explore other plugins available for the Pyxu framework."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/_sources/examples/index.rst b/_sources/examples/index.rst
index 0af24139..6cf5bb3a 100644
--- a/_sources/examples/index.rst
+++ b/_sources/examples/index.rst
@@ -4,12 +4,12 @@ Example Gallery
 .. nblinkgallery::
     :name: rst-link-gallery
 
-    Stencils
-    DifferentialOperators
+    stencils
 
 .. toctree::
    :maxdepth: 2
    :hidden:
 
-   Stencils
-   DifferentialOperators
+   contributing
+   stencils
+
diff --git a/_sources/examples/Stencils.ipynb b/_sources/examples/stencils.ipynb
similarity index 100%
rename from _sources/examples/Stencils.ipynb
rename to _sources/examples/stencils.ipynb
diff --git a/_sources/fair/howto.rst b/_sources/fair/howto.rst
index b52b4a9d..149e08db 100644
--- a/_sources/fair/howto.rst
+++ b/_sources/fair/howto.rst
@@ -26,7 +26,7 @@ For instance:
 
   .. code-block:: python
 
-     import pyxu.opt.solver.GradientDescent
+     from pyxu.opt.solver import GradientDescent
 
 - Without the installation of the plugin, the previous line of code would have raised an error.
 
@@ -55,9 +55,27 @@ as:
 * `pyxu.math <../api/math.html>`_
 * pyxu.contrib: for any other contribution
 
+To override a class or function in the core Pyxu framework, simply use the identical name as the target you wish to override.
+This process involves a critical step: specifying your intention in the setup.cfg file by prefixing the new entry point
+with an underscore (``_``).
+
+For example, to override the ``NullFunc`` class housed within the ``pyxu.operator.func`` namespace, insert the following
+directive in your setup.cfg file:
+
+.. code-block:: ini
+
+    [options.entry_points]
+       pyxu.operator.func =
+        _NullFunc = your_module_name:NullFunc
+
+
 Once ready, publish your plugin on `PyPI <https://pypi.org/>`_. The Pyxu-FAIR periodically scans PyPI for new plugins and
 `scores <./score.html>`_ them based on their popularity and quality. The higher the score, the higher the chances of your
 plugin being discovered by Pyxu users.
 
+If you believe your plugin enhances the Pyxu core codebase, we encourage you to reach out so we can evaluate the possibility
+of incorporating it. Even if you're uncertain, don't hesitate to open an issue on the `Pyxu GitHub repository <https://github.com/matthieumeo/pyxu>`_
+for feedback and guidance.
+
 🌟 No matter your expertise level, the Pyxu-FAIR ensures a smooth experience. Dive in, and may your Pyxu journey be
 FAIR and fantastic! 🌟
diff --git a/_sources/fair/index.rst b/_sources/fair/index.rst
index dfe44c09..436f3025 100644
--- a/_sources/fair/index.rst
+++ b/_sources/fair/index.rst
@@ -233,3 +233,4 @@ communicate with the main framework.
    dev_notes
    score
    plugins/index
+   plugins_preview/index
diff --git a/_sources/fair/plugins/index.rst b/_sources/fair/plugins/index.rst
index 04cfde22..4f97ef7d 100644
--- a/_sources/fair/plugins/index.rst
+++ b/_sources/fair/plugins/index.rst
@@ -181,937 +181,132 @@
     }
     </style>
 
-**************
-Plugin Catalog
-**************
+*********
+Catalogue
+*********
 
 
 .. raw:: html
 
-    <h2 style="font-size: 60px; font-weight: bold; display: inline"><span>Plugin Catalogue</span></h2>
+    <h2 style="font-size: 60px; font-weight: bold; display: inline"><span>Catalogue</span></h2>
 
 
-**Total Registered Plugin Packages: 17**
+**Total Registered Plugin Packages: 2**
 
 .. raw:: html
 
    <div class='globalsummary-box'>
         <div style="display: table;">
-
+            
             <span class="badge" style="display: table-row; line-height: 2;">
                 <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left blue" style="float: none; display: inline; text-align: right; border: none">Operator</span></span>
-                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">17 plugins in 12 packages </span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">0 plugins in 0 packages </span></span>
             </span>
-
+        
             <span class="badge" style="display: table-row; line-height: 2;">
                 <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left brown" style="float: none; display: inline; text-align: right; border: none">Solver</span></span>
-                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">14 plugins in 10 packages </span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">1 plugin in 1 package </span></span>
             </span>
-
+        
             <span class="badge" style="display: table-row; line-height: 2;">
                 <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left purple" style="float: none; display: inline; text-align: right; border: none">Stop</span></span>
-                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">18 plugins in 11 packages </span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">0 plugins in 0 packages </span></span>
             </span>
-
+        
             <span class="badge" style="display: table-row; line-height: 2;">
                 <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left green" style="float: none; display: inline; text-align: right; border: none">Math</span></span>
-                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">16 plugins in 10 packages </span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">1 plugin in 1 package </span></span>
             </span>
-
+        
             <span class="badge" style="display: table-row; line-height: 2;">
                 <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left orange" style="float: none; display: inline; text-align: right; border: none">Contrib</span></span>
-                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">20 plugins in 12 packages </span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">0 plugins in 0 packages </span></span>
             </span>
-
+        
         </div>
     </div>
 
-**Plugin in alphabetical order:**
+**Plugin list in alphabetical order**
 
 
 .. grid:: 2 2 3 3
     :gutter: 3
 
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="CSEEG.html">CSEEG</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/lbrooks/CSEEG" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://lbrooks.github.io/CSEEG/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 69.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left brown">Solver</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
+    
     .. grid-item-card::
 
         .. raw:: html
 
-            <h2 style="font-size: 30px;"><a href="DSP-Notebooks.html">DSP-Notebooks</a></h2>
+            <h2 style="font-size: 30px;"><a href="pyxu-eigh.html">pyxu-eigh</a></h2>
 
             <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+                
+                <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-1-007ec6.svg?logo=data:image/png;base64,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"></p>
 
             <ul class="plugin-info">
 
-
-                <li>
-                    <a href="https://github.com/sdunn/DSP-Notebooks" target="_blank">Home page</a>
-                </li>
-
-
-
+            
                 <li>
-                    <a href="https://sdunn.github.io/DSP-Notebooks/html/index" target="_blank">Documentation</a>
+                    <a href="https://github.com/AIR-Hub/pyxu-eigh" target="_blank">Home page</a>
                 </li>
+            
 
+            
 
-
+            
                 <li>
-                    <a> Score: 83.0 % </a>
+                    <a> Score: 1 % </a>
                 </li>
-
+            
             </ul>
 
             <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">2</span>
-                </span>
-
+                
                 <span class="badge">
                     <span class="badge-left green">Math</span>
-                    <span class="badge-right">3</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="EnvironTracker.html">EnvironTracker</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/cedwards/EnvironTracker" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://cedwards.github.io/EnvironTracker/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 79.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="HoughDetector.html">HoughDetector</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/abrick/HoughDetector" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://abrick.github.io/HoughDetector/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 56.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left brown">Solver</span>
                     <span class="badge-right">1</span>
                 </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">4</span>
-                </span>
-
+                
             </p>
 
-
+    
     .. grid-item-card::
 
         .. raw:: html
 
-            <h2 style="font-size: 30px;"><a href="HVOX.html">HVOX</a></h2>
+            <h2 style="font-size: 30px;"><a href="pyxu-gradient-descent.html">pyxu-gradient-descent</a></h2>
 
             <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Pre-alpha: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+                
+                <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-1-007ec6.svg?logo=data:image/png;base64,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"></p>
 
             <ul class="plugin-info">
 
-
+            
                 <li>
-                    <a href="https://github.com/snassar/HVOX" target="_blank">Home page</a>
+                    <a href="https://github.com/joanrue/pyxu-gradient-descent" target="_blank">Home page</a>
                 </li>
+            
 
+            
 
-
-                <li>
-                    <a href="https://snassar.github.io/HVOX/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
+            
                 <li>
-                    <a> Score: 80.0 % </a>
+                    <a> Score: 1 % </a>
                 </li>
-
+            
             </ul>
 
             <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">1</span>
-                </span>
-
+                
                 <span class="badge">
                     <span class="badge-left brown">Solver</span>
                     <span class="badge-right">1</span>
                 </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="OrientationPy.html">OrientationPy</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Mature: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/mmonteith/OrientationPy" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://mmonteith.github.io/OrientationPy/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 77.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="Palentologist.html">Palentologist</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/knaiman/Palentologist" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://knaiman.github.io/Palentologist/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 73.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left green">Math</span>
-                    <span class="badge-right">1</span>
-                </span>
-
+                
             </p>
 
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="PhaseRet.html">PhaseRet</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-inactive-bbbbbb.svg" title="Inactive: No longer maintained.">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/esequeira/PhaseRet" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://esequeira.github.io/PhaseRet/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">3</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">3</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="PycGSP.html">PycGSP</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/doliphant/PycGSP" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://doliphant.github.io/PycGSP/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 77.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left brown">Solver</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left green">Math</span>
-                    <span class="badge-right">3</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="pycNUFFT.html">pycNUFFT</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/csincell/pycNUFFT" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://csincell.github.io/pycNUFFT/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 78.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left brown">Solver</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left green">Math</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="PycSphere.html">PycSphere</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Pre-alpha: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAZCAYAAADE6YVjAAAACXBIWXMAAAHpAAAB6QHzJ3XIAAAAGXRFWHRTb2Z0d2FyZQB3d3cuaW5rc2NhcGUub3Jnm+48GgAAAzpJREFUSImtlU1oXFUUx3/nzVemWq1pbQXXIpSaEiPUtiCSTdK4qAhVLFh0VXChKAbSVbCiUFFxoSAB3ZmKH2C0aivigBpR/AJxERS1hGATg9F2JhN999x7XMx7Ly/TaQmZHvhzLoc793e+eCNmxuVsYXT/9vLmwhNRNXqUqpSlGiFVSRQhFWldNAY2DZ7+vtMbUafgWx9/dt/cYt3mFutWFFkwz2jwVsYD3mj55JzmKHzXrA3bSm1oz2UhJ0/Vnvl5dtH29ve/AVAZHyb/sHnDMr96zpshX63UDsx1hEyeqtmeW3cf21TtYX7+XCs5b7nM233u3GaG3ZgHRQlgvlgoUC6VODh8Jw/efw+//n42ybStAgXUEiXn0BnUrA0NABST2I59t/UDcGz8ae69e4Tfzs6yM30oFkLdQwEoCVISpJIoXYCeVjzaWkCqkg7qW0Ciyfdr7+YzuH3vfmYXzlMulSASzEFoBsxoDTlVyPlcJeGCJyz5bFaNz0eujxAOXlws7Np58+rEDEhX3SwREJJWWW7L0p80WzHR8EsUQsA5pd5YXnNpZmaGl2463N7ovOasINNW4SMry5SU+JrSWpT9ZwhcK6+9fdpCCIQQODB4R3bhi+lpAJaW/uHv8xfYtvU6jh45JKzTlj+86wZEz0lFKKoqKSSOHeVyKemKIUBv7xZ6e7fgnM6vFwBw1cgH84CsfDq0L1JVVBV1yntnPskuRVGEmWHJDFTjuUs/eWmrDp75MvJeH1CnuAQ2+c4U3/zwI7v7+hARSEA9PdWBjUAAxMx4buJkMhdP8K3W+RCIm3VEJNPxsUfWPZO8FQFU3Z8h2PbgfQZIt04EQBK/MYsAxh4+skNdq10uNyPnHLFzOOdwsdswJP2s4FR/CsHvCiFkLVNVDOiiiNVKAJ4aPXpLWkG6cS6rSHHOxruGAGisY2sA6nHaatsrL4wfvyKQ5598/EQKWFluZBVpsL82CoDcTFJzzrsQfCmOYywEzIzXJ57d1g3kov94r3pYVfHqUe/p8cVrugFAh0qi5h9TjXA13nsolvtfnThRv+KQRqG3z7t/oeo2v/nyi41uAQDZRzDVoYcea7bHutX/c3lfgmmbsZoAAAAASUVORK5CYII="></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/jhawk/PycSphere" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://jhawk.github.io/PycSphere/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 79.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left brown">Solver</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="pycWavelet.html">pycWavelet</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/cpark/pycWavelet" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://cpark.github.io/pycWavelet/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 68.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left brown">Solver</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">3</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left green">Math</span>
-                    <span class="badge-right">3</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="PYFW.html">PYFW</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Mature: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAZCAYAAADE6YVjAAAACXBIWXMAAAHpAAAB6QHzJ3XIAAAAGXRFWHRTb2Z0d2FyZQB3d3cuaW5rc2NhcGUub3Jnm+48GgAAAzpJREFUSImtlU1oXFUUx3/nzVemWq1pbQXXIpSaEiPUtiCSTdK4qAhVLFh0VXChKAbSVbCiUFFxoSAB3ZmKH2C0aivigBpR/AJxERS1hGATg9F2JhN999x7XMx7Ly/TaQmZHvhzLoc793e+eCNmxuVsYXT/9vLmwhNRNXqUqpSlGiFVSRQhFWldNAY2DZ7+vtMbUafgWx9/dt/cYt3mFutWFFkwz2jwVsYD3mj55JzmKHzXrA3bSm1oz2UhJ0/Vnvl5dtH29ve/AVAZHyb/sHnDMr96zpshX63UDsx1hEyeqtmeW3cf21TtYX7+XCs5b7nM233u3GaG3ZgHRQlgvlgoUC6VODh8Jw/efw+//n42ybStAgXUEiXn0BnUrA0NABST2I59t/UDcGz8ae69e4Tfzs6yM30oFkLdQwEoCVISpJIoXYCeVjzaWkCqkg7qW0Ciyfdr7+YzuH3vfmYXzlMulSASzEFoBsxoDTlVyPlcJeGCJyz5bFaNz0eujxAOXlws7Np58+rEDEhX3SwREJJWWW7L0p80WzHR8EsUQsA5pd5YXnNpZmaGl2463N7ovOasINNW4SMry5SU+JrSWpT9ZwhcK6+9fdpCCIQQODB4R3bhi+lpAJaW/uHv8xfYtvU6jh45JKzTlj+86wZEz0lFKKoqKSSOHeVyKemKIUBv7xZ6e7fgnM6vFwBw1cgH84CsfDq0L1JVVBV1yntnPskuRVGEmWHJDFTjuUs/eWmrDp75MvJeH1CnuAQ2+c4U3/zwI7v7+hARSEA9PdWBjUAAxMx4buJkMhdP8K3W+RCIm3VEJNPxsUfWPZO8FQFU3Z8h2PbgfQZIt04EQBK/MYsAxh4+skNdq10uNyPnHLFzOOdwsdswJP2s4FR/CsHvCiFkLVNVDOiiiNVKAJ4aPXpLWkG6cS6rSHHOxruGAGisY2sA6nHaatsrL4wfvyKQ5598/EQKWFluZBVpsL82CoDcTFJzzrsQfCmOYywEzIzXJ57d1g3kov94r3pYVfHqUe/p8cVrugFAh0qi5h9TjXA13nsolvtfnThRv+KQRqG3z7t/oeo2v/nyi41uAQDZRzDVoYcea7bHutX/c3lfgmmbsZoAAAAASUVORK5CYII="></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/rshelton/PYFW" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://rshelton.github.io/PYFW/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 95.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left green">Math</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="TokemakRec.html">TokemakRec</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-beta-d6af23.svg" title="Beta: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/msmith/TokemakRec" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://msmith.github.io/TokemakRec/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 91.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left brown">Solver</span>
-                    <span class="badge-right">3</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">2</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left green">Math</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="TVDenoiser.html">TVDenoiser</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-inactive-bbbbbb.svg" title="Inactive: No longer maintained.">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/dbrown/TVDenoiser" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://dbrown.github.io/TVDenoiser/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left brown">Solver</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left green">Math</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">3</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="UncertaintyQuant.html">UncertaintyQuant</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/kdavis/UncertaintyQuant" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://kdavis.github.io/UncertaintyQuant/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 88.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left green">Math</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
-    .. grid-item-card::
-
-        .. raw:: html
-
-            <h2 style="font-size: 30px;"><a href="WaveProp.html">WaveProp</a></h2>
-
-            <p class="currentstate">
-
-                <img class="svg-badge" src="../../_static/plugins/status/status-beta-d6af23.svg" title="Beta: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-            <ul class="plugin-info">
-
-
-                <li>
-                    <a href="https://github.com/knix/WaveProp" target="_blank">Home page</a>
-                </li>
-
-
-
-                <li>
-                    <a href="https://knix.github.io/WaveProp/html/index" target="_blank">Documentation</a>
-                </li>
-
-
-
-                <li>
-                    <a> Score: 76.0 % </a>
-                </li>
-
-            </ul>
-
-            <p class="summaryinfo">
-
-                <span class="badge">
-                    <span class="badge-left blue">Operator</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left brown">Solver</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left purple">Stop</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left green">Math</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-                <span class="badge">
-                    <span class="badge-left orange">Contrib</span>
-                    <span class="badge-right">1</span>
-                </span>
-
-            </p>
-
-
+    
 
 
 
@@ -1119,20 +314,6 @@ Plugin Catalog
    :maxdepth: 1
    :hidden:
 
-   CSEEG
-   DSP-Notebooks
-   EnvironTracker
-   HoughDetector
-   HVOX
-   OrientationPy
-   Palentologist
-   PhaseRet
-   PycGSP
-   pycNUFFT
-   PycSphere
-   pycWavelet
-   PYFW
-   TokemakRec
-   TVDenoiser
-   UncertaintyQuant
-   WaveProp
+   pyxu-eigh
+   pyxu-gradient-descent
+   
\ No newline at end of file
diff --git a/_sources/fair/plugins/pyxu-eigh.rst b/_sources/fair/plugins/pyxu-eigh.rst
new file mode 100644
index 00000000..65006100
--- /dev/null
+++ b/_sources/fair/plugins/pyxu-eigh.rst
@@ -0,0 +1,244 @@
+.. _plugins-page:
+
+.. |br| raw:: html
+
+   </br>
+
+.. raw:: html
+
+    <!-- CSS overrides on the pyxu-fair only -->
+    <style>
+
+    .summaryinfo {
+        color: #000;
+        font-size: 80%;
+        margin-bottom: 12px;
+        margin-top: 12px;
+    }
+
+    .entrypointraw {
+        color: #777;
+    }
+    .badge {
+        white-space: nowrap;
+        display: inline-block;
+        vertical-align: middle;
+        /*vertical-align: baseline;*/
+        font-family: "DejaVu Sans", Verdana, Geneva, sans-serif;
+        /*font-size: 90%;*/
+    }
+    .currentstate {
+        color: #666;
+        font-size: 90%;
+        margin-bottom: 12px;
+    }
+    span.badge-left {
+        border-radius: .25rem;
+        border-top-right-radius: 0;
+        border-bottom-right-radius: 0;
+        color: #212529;
+        background-color: #A2CBFF;
+        /* color: #ffffff; */
+        text-shadow: 1px 1px 1px rgba(0,0,0,0.3);
+
+        padding: .25em .4em;
+        line-height: 1;
+        text-align: center;
+        white-space: nowrap;
+        float: left;
+        display: block;
+    }
+
+    span.badge-right {
+        border-radius: .25rem;
+        border-top-left-radius: 0;
+        border-bottom-left-radius: 0;
+
+        color: #fff;
+        background-color: #343a40;
+
+        padding: .25em .4em;
+        line-height: 1;
+        text-align: center;
+        white-space: nowrap;
+        float: left;
+        display: block;
+    }
+
+    .badge-right.light-blue, .badge-left.light-blue {
+        background-color: #A2CBFF;
+        color: #212529;
+    }
+
+    .badge-right.light-red, .badge-left.light-red {
+        background-color: rgb(255, 162, 162);
+        color: rgb(43, 14, 14);
+    }
+
+    .badge-right.red, .badge-left.red {
+        background-color: #e41a1c;
+        color: #fff;
+    }
+
+    .badge-right.blue, .badge-left.blue {
+        background-color: #377eb8;
+        color: #fff;
+    }
+
+    .badge-right.green, .badge-left.green {
+        background-color: #4daf4a;
+        color: #fff;
+    }
+
+    .badge-right.purple, .badge-left.purple {
+        background-color: #984ea3;
+        color: #fff;
+    }
+
+    .badge-right.orange, .badge-left.orange {
+        background-color: #ff7f00;
+        color: #fff;
+    }
+
+    .badge-right.brown, .badge-left.brown {
+        background-color: #a65628;
+        color: #fff;
+    }
+
+    .badge-right.dark-gray, .badge-left.dark-gray {
+        color: #fff;
+        background-color: #343a40;
+    }
+
+
+    .badge a {
+        text-decoration: none;
+        padding: 0;
+        border: 0;
+        color: inherit;
+    }
+
+    .badge a:visited, .badge a:active {
+        color: inherit;
+      }
+
+    .badge a:focus, .badge a:hover {
+        color: rgba(255,255,255,0.5);
+        mix-blend-mode: difference;
+        text-decoration: none;
+        /* background-color: rgb(192, 219, 255); */
+    }
+
+
+    .svg-badge {
+        vertical-align: middle;
+    }
+
+    .tooltiptext {
+        visibility: hidden;
+        /* width: 120px; */
+        background-color: rgb(255, 247, 175);
+        color: #000;
+        text-align: center;
+        border-radius: 6px;
+        padding: 5px;
+
+        /* Position the tooltip */
+        position: absolute;
+        z-index: 1;
+    }
+
+    .tooltip:hover .tooltiptext {
+        visibility: visible;
+    }
+    </style>
+
+*********
+pyxu-eigh
+*********
+
+
+Description
+===========
+
+.. raw:: html
+    Pyxu plugin to compute the eigenvectors and eigenvalues of a real symmetric matrix
+
+
+
+General information
+===================
+
+.. raw:: html
+
+    
+    <p>
+        <strong>Short description</strong>: Pyxu plugin to compute the eigenvectors and eigenvalues of a real symmetric matrix
+    </p>
+    
+
+    <p class="currentstate">
+        
+        <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!"></p>
+    
+
+    <p>
+        <strong>Source code</strong>: <a href="https://github.com/AIR-Hub/pyxu-eigh" target="_blank">Go to the source code repository</a>
+    </p>
+
+    
+    <p>
+        <strong>Documentation</strong>: No documentation provided by the package author
+    <p>
+    
+
+
+Detailed information
+====================
+
+.. raw:: html
+    
+    <p>
+        <strong>Author(s)</strong>: Joan Rue Queralt
+    </p>
+    
+    
+    <p>
+        <strong>Contact</strong>: <a href="mailto:joan.rue.q@gmail.com">joan.rue.q@gmail.com</a>
+    </p>
+    
+    
+    <p>
+        <strong>Most recent version</strong>: 0.1.0
+    </p>
+    <p>
+        <strong>Compatibility</strong>:
+        <img class="svg-badge" title="Compatible with Pyxu 1" src="https://img.shields.io/badge/Pyxu-1-007ec6.svg?logo=data:image/png;base64,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">
+    </p>
+    
+
+
+Components contributed
+======================
+
+.. raw:: html
+    <p class="summaryinfo">
+        
+        <span class="badge">
+            <span class="badge-left green">Math</span>
+            <span class="badge-right">1</span>
+        </span>
+        
+    </p>
+    
+    
+    
+      Math <span class="entrypointraw">(pyxu.math)</span>
+    
+    <ul>
+    
+    <li><code>eigh</code>
+    
+    </ul>
+    
+    
\ No newline at end of file
diff --git a/_sources/fair/plugins/pyxu-gradient-descent.rst b/_sources/fair/plugins/pyxu-gradient-descent.rst
new file mode 100644
index 00000000..758cbacc
--- /dev/null
+++ b/_sources/fair/plugins/pyxu-gradient-descent.rst
@@ -0,0 +1,244 @@
+.. _plugins-page:
+
+.. |br| raw:: html
+
+   </br>
+
+.. raw:: html
+
+    <!-- CSS overrides on the pyxu-fair only -->
+    <style>
+
+    .summaryinfo {
+        color: #000;
+        font-size: 80%;
+        margin-bottom: 12px;
+        margin-top: 12px;
+    }
+
+    .entrypointraw {
+        color: #777;
+    }
+    .badge {
+        white-space: nowrap;
+        display: inline-block;
+        vertical-align: middle;
+        /*vertical-align: baseline;*/
+        font-family: "DejaVu Sans", Verdana, Geneva, sans-serif;
+        /*font-size: 90%;*/
+    }
+    .currentstate {
+        color: #666;
+        font-size: 90%;
+        margin-bottom: 12px;
+    }
+    span.badge-left {
+        border-radius: .25rem;
+        border-top-right-radius: 0;
+        border-bottom-right-radius: 0;
+        color: #212529;
+        background-color: #A2CBFF;
+        /* color: #ffffff; */
+        text-shadow: 1px 1px 1px rgba(0,0,0,0.3);
+
+        padding: .25em .4em;
+        line-height: 1;
+        text-align: center;
+        white-space: nowrap;
+        float: left;
+        display: block;
+    }
+
+    span.badge-right {
+        border-radius: .25rem;
+        border-top-left-radius: 0;
+        border-bottom-left-radius: 0;
+
+        color: #fff;
+        background-color: #343a40;
+
+        padding: .25em .4em;
+        line-height: 1;
+        text-align: center;
+        white-space: nowrap;
+        float: left;
+        display: block;
+    }
+
+    .badge-right.light-blue, .badge-left.light-blue {
+        background-color: #A2CBFF;
+        color: #212529;
+    }
+
+    .badge-right.light-red, .badge-left.light-red {
+        background-color: rgb(255, 162, 162);
+        color: rgb(43, 14, 14);
+    }
+
+    .badge-right.red, .badge-left.red {
+        background-color: #e41a1c;
+        color: #fff;
+    }
+
+    .badge-right.blue, .badge-left.blue {
+        background-color: #377eb8;
+        color: #fff;
+    }
+
+    .badge-right.green, .badge-left.green {
+        background-color: #4daf4a;
+        color: #fff;
+    }
+
+    .badge-right.purple, .badge-left.purple {
+        background-color: #984ea3;
+        color: #fff;
+    }
+
+    .badge-right.orange, .badge-left.orange {
+        background-color: #ff7f00;
+        color: #fff;
+    }
+
+    .badge-right.brown, .badge-left.brown {
+        background-color: #a65628;
+        color: #fff;
+    }
+
+    .badge-right.dark-gray, .badge-left.dark-gray {
+        color: #fff;
+        background-color: #343a40;
+    }
+
+
+    .badge a {
+        text-decoration: none;
+        padding: 0;
+        border: 0;
+        color: inherit;
+    }
+
+    .badge a:visited, .badge a:active {
+        color: inherit;
+      }
+
+    .badge a:focus, .badge a:hover {
+        color: rgba(255,255,255,0.5);
+        mix-blend-mode: difference;
+        text-decoration: none;
+        /* background-color: rgb(192, 219, 255); */
+    }
+
+
+    .svg-badge {
+        vertical-align: middle;
+    }
+
+    .tooltiptext {
+        visibility: hidden;
+        /* width: 120px; */
+        background-color: rgb(255, 247, 175);
+        color: #000;
+        text-align: center;
+        border-radius: 6px;
+        padding: 5px;
+
+        /* Position the tooltip */
+        position: absolute;
+        z-index: 1;
+    }
+
+    .tooltip:hover .tooltiptext {
+        visibility: visible;
+    }
+    </style>
+
+*********************
+pyxu-gradient-descent
+*********************
+
+
+Description
+===========
+
+.. raw:: html
+    An accelerated gradient descent optimizer for Pyxu
+
+
+
+General information
+===================
+
+.. raw:: html
+
+    
+    <p>
+        <strong>Short description</strong>: An accelerated gradient descent optimizer for Pyxu
+    </p>
+    
+
+    <p class="currentstate">
+        
+        <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!"></p>
+    
+
+    <p>
+        <strong>Source code</strong>: <a href="https://github.com/joanrue/pyxu-gradient-descent" target="_blank">Go to the source code repository</a>
+    </p>
+
+    
+    <p>
+        <strong>Documentation</strong>: No documentation provided by the package author
+    <p>
+    
+
+
+Detailed information
+====================
+
+.. raw:: html
+    
+    <p>
+        <strong>Author(s)</strong>: Joan Rue Queralt
+    </p>
+    
+    
+    <p>
+        <strong>Contact</strong>: <a href="mailto:joan.rue.q@gmail.com">joan.rue.q@gmail.com</a>
+    </p>
+    
+    
+    <p>
+        <strong>Most recent version</strong>: 0.1.0
+    </p>
+    <p>
+        <strong>Compatibility</strong>:
+        <img class="svg-badge" title="Compatible with Pyxu 1" src="https://img.shields.io/badge/Pyxu-1-007ec6.svg?logo=data:image/png;base64,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">
+    </p>
+    
+
+
+Components contributed
+======================
+
+.. raw:: html
+    <p class="summaryinfo">
+        
+        <span class="badge">
+            <span class="badge-left brown">Solver</span>
+            <span class="badge-right">1</span>
+        </span>
+        
+    </p>
+    
+    
+    
+      Solver <span class="entrypointraw">(pyxu.solver)</span>
+    
+    <ul>
+    
+    <li><code>GradientDescent</code>
+    
+    </ul>
+    
+    
\ No newline at end of file
diff --git a/_sources/fair/plugins/CSEEG.rst b/_sources/fair/plugins_preview/CSEEG.rst
similarity index 100%
rename from _sources/fair/plugins/CSEEG.rst
rename to _sources/fair/plugins_preview/CSEEG.rst
diff --git a/_sources/fair/plugins/DSP-Notebooks.rst b/_sources/fair/plugins_preview/DSP-Notebooks.rst
similarity index 100%
rename from _sources/fair/plugins/DSP-Notebooks.rst
rename to _sources/fair/plugins_preview/DSP-Notebooks.rst
diff --git a/_sources/fair/plugins/EnvironTracker.rst b/_sources/fair/plugins_preview/EnvironTracker.rst
similarity index 100%
rename from _sources/fair/plugins/EnvironTracker.rst
rename to _sources/fair/plugins_preview/EnvironTracker.rst
diff --git a/_sources/fair/plugins/HVOX.rst b/_sources/fair/plugins_preview/HVOX.rst
similarity index 100%
rename from _sources/fair/plugins/HVOX.rst
rename to _sources/fair/plugins_preview/HVOX.rst
diff --git a/_sources/fair/plugins/HoughDetector.rst b/_sources/fair/plugins_preview/HoughDetector.rst
similarity index 100%
rename from _sources/fair/plugins/HoughDetector.rst
rename to _sources/fair/plugins_preview/HoughDetector.rst
diff --git a/_sources/fair/plugins/OrientationPy.rst b/_sources/fair/plugins_preview/OrientationPy.rst
similarity index 100%
rename from _sources/fair/plugins/OrientationPy.rst
rename to _sources/fair/plugins_preview/OrientationPy.rst
diff --git a/_sources/fair/plugins/PYFW.rst b/_sources/fair/plugins_preview/PYFW.rst
similarity index 100%
rename from _sources/fair/plugins/PYFW.rst
rename to _sources/fair/plugins_preview/PYFW.rst
diff --git a/_sources/fair/plugins/Palentologist.rst b/_sources/fair/plugins_preview/Palentologist.rst
similarity index 100%
rename from _sources/fair/plugins/Palentologist.rst
rename to _sources/fair/plugins_preview/Palentologist.rst
diff --git a/_sources/fair/plugins/PhaseRet.rst b/_sources/fair/plugins_preview/PhaseRet.rst
similarity index 100%
rename from _sources/fair/plugins/PhaseRet.rst
rename to _sources/fair/plugins_preview/PhaseRet.rst
diff --git a/_sources/fair/plugins/PycGSP.rst b/_sources/fair/plugins_preview/PycGSP.rst
similarity index 100%
rename from _sources/fair/plugins/PycGSP.rst
rename to _sources/fair/plugins_preview/PycGSP.rst
diff --git a/_sources/fair/plugins/PycSphere.rst b/_sources/fair/plugins_preview/PycSphere.rst
similarity index 100%
rename from _sources/fair/plugins/PycSphere.rst
rename to _sources/fair/plugins_preview/PycSphere.rst
diff --git a/_sources/fair/plugins/TVDenoiser.rst b/_sources/fair/plugins_preview/TVDenoiser.rst
similarity index 100%
rename from _sources/fair/plugins/TVDenoiser.rst
rename to _sources/fair/plugins_preview/TVDenoiser.rst
diff --git a/_sources/fair/plugins/TokemakRec.rst b/_sources/fair/plugins_preview/TokemakRec.rst
similarity index 100%
rename from _sources/fair/plugins/TokemakRec.rst
rename to _sources/fair/plugins_preview/TokemakRec.rst
diff --git a/_sources/fair/plugins/UncertaintyQuant.rst b/_sources/fair/plugins_preview/UncertaintyQuant.rst
similarity index 100%
rename from _sources/fair/plugins/UncertaintyQuant.rst
rename to _sources/fair/plugins_preview/UncertaintyQuant.rst
diff --git a/_sources/fair/plugins/WaveProp.rst b/_sources/fair/plugins_preview/WaveProp.rst
similarity index 100%
rename from _sources/fair/plugins/WaveProp.rst
rename to _sources/fair/plugins_preview/WaveProp.rst
diff --git a/_sources/fair/plugins_preview/index.rst b/_sources/fair/plugins_preview/index.rst
new file mode 100644
index 00000000..aee37f61
--- /dev/null
+++ b/_sources/fair/plugins_preview/index.rst
@@ -0,0 +1,1138 @@
+:html_theme.sidebar_secondary.remove:
+:sd_hide_title: true
+
+.. |br| raw:: html
+
+   </br>
+
+.. raw:: html
+
+    <!-- CSS overrides on the pyxu-fair only -->
+    <style>
+    .globalsummary-box {
+        width:95%;
+        padding:10px;
+        margin: 20px;
+        padding-left: 40px;
+        padding-right: 40px;
+        background-color: rgba(255,255,255,0.19);
+        border:1px solid rgba(50,50,50,0.4);
+        border-radius:4px;
+        -webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,.05);
+        box-shadow:inset 0 1px 1px rgba(0,0,0,.05);
+        line-height: 1.5;
+    }
+    .summaryinfo {
+        color: #000;
+        font-size: 80%;
+        margin-bottom: 12px;
+        margin-top: 12px;
+    }
+    .submenu-entry {
+        width:90%;
+        min-height:140px;
+        padding:10px;
+        margin: 20px;
+        padding-left: 40px;
+        padding-right: 40px;
+        background-color:rgba(245,245,245,.19);
+        border:1px solid rgba(227,227,227,.31);
+        border-radius:4px;
+        -webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,.05);
+        box-shadow:inset 0 1px 1px rgba(0,0,0,.05);
+    }
+    .badge {
+        white-space: nowrap;
+        display: inline-block;
+        vertical-align: middle;
+        /*vertical-align: baseline;*/
+        font-family: "DejaVu Sans", Verdana, Geneva, sans-serif;
+        /*font-size: 90%;*/
+    }
+    .currentstate {
+        color: #666;
+        font-size: 90%;
+        margin-bottom: 12px;
+    }
+    span.badge-left {
+        border-radius: .25rem;
+        border-top-right-radius: 0;
+        border-bottom-right-radius: 0;
+        color: #212529;
+        background-color: #A2CBFF;
+        /* color: #ffffff; */
+        text-shadow: 1px 1px 1px rgba(0,0,0,0.3);
+
+        padding: .25em .4em;
+        line-height: 1;
+        text-align: center;
+        white-space: nowrap;
+        float: left;
+        display: block;
+    }
+
+    span.badge-right {
+        border-radius: .25rem;
+        border-top-left-radius: 0;
+        border-bottom-left-radius: 0;
+
+        color: #fff;
+        background-color: #343a40;
+
+        padding: .25em .4em;
+        line-height: 1;
+        text-align: center;
+        white-space: nowrap;
+        float: left;
+        display: block;
+    }
+
+    .badge-right.light-blue, .badge-left.light-blue {
+        background-color: #A2CBFF;
+        color: #212529;
+    }
+
+    .badge-right.light-red, .badge-left.light-red {
+        background-color: rgb(255, 162, 162);
+        color: rgb(43, 14, 14);
+    }
+
+    .badge-right.red, .badge-left.red {
+        background-color: #e41a1c;
+        color: #fff;
+    }
+
+    .badge-right.blue, .badge-left.blue {
+        background-color: #377eb8;
+        color: #fff;
+    }
+
+    .badge-right.green, .badge-left.green {
+        background-color: #4daf4a;
+        color: #fff;
+    }
+
+    .badge-right.purple, .badge-left.purple {
+        background-color: #984ea3;
+        color: #fff;
+    }
+
+    .badge-right.orange, .badge-left.orange {
+        background-color: #ff7f00;
+        color: #fff;
+    }
+
+    .badge-right.brown, .badge-left.brown {
+        background-color: #a65628;
+        color: #fff;
+    }
+
+    .badge-right.dark-gray, .badge-left.dark-gray {
+        color: #fff;
+        background-color: #343a40;
+    }
+
+
+    .badge a {
+        text-decoration: none;
+        padding: 0;
+        border: 0;
+        color: inherit;
+    }
+
+    .badge a:visited, .badge a:active {
+        color: inherit;
+      }
+
+    .badge a:focus, .badge a:hover {
+        color: rgba(255,255,255,0.5);
+        mix-blend-mode: difference;
+        text-decoration: none;
+        /* background-color: rgb(192, 219, 255); */
+    }
+
+
+    .svg-badge {
+        vertical-align: middle;
+    }
+
+    .tooltip {
+        position: relative;
+        display: inline-block;
+        border-bottom: 1px dotted black;
+    }
+
+    .tooltip .tooltiptext {
+        visibility: hidden;
+        /* width: 120px; */
+        background-color: rgb(255, 247, 175);
+        color: #000;
+        text-align: center;
+        border-radius: 6px;
+        padding: 5px;
+
+        /* Position the tooltip */
+        position: absolute;
+        z-index: 1;
+    }
+
+    .tooltip:hover .tooltiptext {
+        visibility: visible;
+    }
+    </style>
+
+**********************
+Plugin Preview Catalog
+**********************
+
+
+.. raw:: html
+
+    <h2 style="font-size: 60px; font-weight: bold; display: inline"><span>Plugin Catalogue</span></h2>
+
+
+**Total Registered Plugin Packages: 17**
+
+.. raw:: html
+
+   <div class='globalsummary-box'>
+        <div style="display: table;">
+
+            <span class="badge" style="display: table-row; line-height: 2;">
+                <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left blue" style="float: none; display: inline; text-align: right; border: none">Operator</span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">17 plugins in 12 packages </span></span>
+            </span>
+
+            <span class="badge" style="display: table-row; line-height: 2;">
+                <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left brown" style="float: none; display: inline; text-align: right; border: none">Solver</span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">14 plugins in 10 packages </span></span>
+            </span>
+
+            <span class="badge" style="display: table-row; line-height: 2;">
+                <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left purple" style="float: none; display: inline; text-align: right; border: none">Stop</span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">18 plugins in 11 packages </span></span>
+            </span>
+
+            <span class="badge" style="display: table-row; line-height: 2;">
+                <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left green" style="float: none; display: inline; text-align: right; border: none">Math</span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">16 plugins in 10 packages </span></span>
+            </span>
+
+            <span class="badge" style="display: table-row; line-height: 2;">
+                <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left orange" style="float: none; display: inline; text-align: right; border: none">Contrib</span></span>
+                <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">20 plugins in 12 packages </span></span>
+            </span>
+
+        </div>
+    </div>
+
+**Plugin in alphabetical order:**
+
+
+.. grid:: 2 2 3 3
+    :gutter: 3
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="CSEEG.html">CSEEG</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/lbrooks/CSEEG" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://lbrooks.github.io/CSEEG/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 69.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="DSP-Notebooks.html">DSP-Notebooks</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/sdunn/DSP-Notebooks" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://sdunn.github.io/DSP-Notebooks/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 83.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">3</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="EnvironTracker.html">EnvironTracker</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/cedwards/EnvironTracker" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://cedwards.github.io/EnvironTracker/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 79.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="HoughDetector.html">HoughDetector</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/abrick/HoughDetector" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://abrick.github.io/HoughDetector/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 56.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">4</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="HVOX.html">HVOX</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Pre-alpha: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/snassar/HVOX" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://snassar.github.io/HVOX/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 80.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="OrientationPy.html">OrientationPy</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Mature: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/mmonteith/OrientationPy" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://mmonteith.github.io/OrientationPy/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 77.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="Palentologist.html">Palentologist</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/knaiman/Palentologist" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://knaiman.github.io/Palentologist/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 73.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="PhaseRet.html">PhaseRet</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-inactive-bbbbbb.svg" title="Inactive: No longer maintained.">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/esequeira/PhaseRet" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://esequeira.github.io/PhaseRet/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">3</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">3</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="PycGSP.html">PycGSP</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/doliphant/PycGSP" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://doliphant.github.io/PycGSP/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 77.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">3</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="pycNUFFT.html">pycNUFFT</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/csincell/pycNUFFT" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://csincell.github.io/pycNUFFT/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 78.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="PycSphere.html">PycSphere</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Pre-alpha: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/jhawk/PycSphere" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://jhawk.github.io/PycSphere/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 79.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="pycWavelet.html">pycWavelet</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/cpark/pycWavelet" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://cpark.github.io/pycWavelet/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 68.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">3</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">3</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="PYFW.html">PYFW</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Mature: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/rshelton/PYFW" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://rshelton.github.io/PYFW/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 95.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="TokemakRec.html">TokemakRec</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-beta-d6af23.svg" title="Beta: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAZCAYAAADE6YVjAAAACXBIWXMAAAHpAAAB6QHzJ3XIAAAAGXRFWHRTb2Z0d2FyZQB3d3cuaW5rc2NhcGUub3Jnm+48GgAAAzpJREFUSImtlU1oXFUUx3/nzVemWq1pbQXXIpSaEiPUtiCSTdK4qAhVLFh0VXChKAbSVbCiUFFxoSAB3ZmKH2C0aivigBpR/AJxERS1hGATg9F2JhN999x7XMx7Ly/TaQmZHvhzLoc793e+eCNmxuVsYXT/9vLmwhNRNXqUqpSlGiFVSRQhFWldNAY2DZ7+vtMbUafgWx9/dt/cYt3mFutWFFkwz2jwVsYD3mj55JzmKHzXrA3bSm1oz2UhJ0/Vnvl5dtH29ve/AVAZHyb/sHnDMr96zpshX63UDsx1hEyeqtmeW3cf21TtYX7+XCs5b7nM233u3GaG3ZgHRQlgvlgoUC6VODh8Jw/efw+//n42ybStAgXUEiXn0BnUrA0NABST2I59t/UDcGz8ae69e4Tfzs6yM30oFkLdQwEoCVISpJIoXYCeVjzaWkCqkg7qW0Ciyfdr7+YzuH3vfmYXzlMulSASzEFoBsxoDTlVyPlcJeGCJyz5bFaNz0eujxAOXlws7Np58+rEDEhX3SwREJJWWW7L0p80WzHR8EsUQsA5pd5YXnNpZmaGl2463N7ovOasINNW4SMry5SU+JrSWpT9ZwhcK6+9fdpCCIQQODB4R3bhi+lpAJaW/uHv8xfYtvU6jh45JKzTlj+86wZEz0lFKKoqKSSOHeVyKemKIUBv7xZ6e7fgnM6vFwBw1cgH84CsfDq0L1JVVBV1yntnPskuRVGEmWHJDFTjuUs/eWmrDp75MvJeH1CnuAQ2+c4U3/zwI7v7+hARSEA9PdWBjUAAxMx4buJkMhdP8K3W+RCIm3VEJNPxsUfWPZO8FQFU3Z8h2PbgfQZIt04EQBK/MYsAxh4+skNdq10uNyPnHLFzOOdwsdswJP2s4FR/CsHvCiFkLVNVDOiiiNVKAJ4aPXpLWkG6cS6rSHHOxruGAGisY2sA6nHaatsrL4wfvyKQ5598/EQKWFluZBVpsL82CoDcTFJzzrsQfCmOYywEzIzXJ57d1g3kov94r3pYVfHqUe/p8cVrugFAh0qi5h9TjXA13nsolvtfnThRv+KQRqG3z7t/oeo2v/nyi41uAQDZRzDVoYcea7bHutX/c3lfgmmbsZoAAAAASUVORK5CYII="></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/msmith/TokemakRec" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://msmith.github.io/TokemakRec/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 91.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">3</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">2</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="TVDenoiser.html">TVDenoiser</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-inactive-bbbbbb.svg" title="Inactive: No longer maintained.">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/dbrown/TVDenoiser" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://dbrown.github.io/TVDenoiser/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">3</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="UncertaintyQuant.html">UncertaintyQuant</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/kdavis/UncertaintyQuant" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://kdavis.github.io/UncertaintyQuant/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 88.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+    .. grid-item-card::
+
+        .. raw:: html
+
+            <h2 style="font-size: 30px;"><a href="WaveProp.html">WaveProp</a></h2>
+
+            <p class="currentstate">
+
+                <img class="svg-badge" src="../../_static/plugins/status/status-beta-d6af23.svg" title="Beta: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+            <ul class="plugin-info">
+
+
+                <li>
+                    <a href="https://github.com/knix/WaveProp" target="_blank">Home page</a>
+                </li>
+
+
+
+                <li>
+                    <a href="https://knix.github.io/WaveProp/html/index" target="_blank">Documentation</a>
+                </li>
+
+
+
+                <li>
+                    <a> Score: 76.0 % </a>
+                </li>
+
+            </ul>
+
+            <p class="summaryinfo">
+
+                <span class="badge">
+                    <span class="badge-left blue">Operator</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left brown">Solver</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left purple">Stop</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left green">Math</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+                <span class="badge">
+                    <span class="badge-left orange">Contrib</span>
+                    <span class="badge-right">1</span>
+                </span>
+
+            </p>
+
+
+
+
+
+.. toctree::
+   :maxdepth: 1
+   :hidden:
+
+   CSEEG
+   DSP-Notebooks
+   EnvironTracker
+   HoughDetector
+   HVOX
+   OrientationPy
+   Palentologist
+   PhaseRet
+   PycGSP
+   pycNUFFT
+   PycSphere
+   pycWavelet
+   PYFW
+   TokemakRec
+   TVDenoiser
+   UncertaintyQuant
+   WaveProp
diff --git a/_sources/fair/plugins/pycNUFFT.rst b/_sources/fair/plugins_preview/pycNUFFT.rst
similarity index 100%
rename from _sources/fair/plugins/pycNUFFT.rst
rename to _sources/fair/plugins_preview/pycNUFFT.rst
diff --git a/_sources/fair/plugins/pycWavelet.rst b/_sources/fair/plugins_preview/pycWavelet.rst
similarity index 100%
rename from _sources/fair/plugins/pycWavelet.rst
rename to _sources/fair/plugins_preview/pycWavelet.rst
diff --git a/_sources/fair/score.rst b/_sources/fair/score.rst
index 70a9e4e8..34fdd4f5 100644
--- a/_sources/fair/score.rst
+++ b/_sources/fair/score.rst
@@ -1,15 +1,21 @@
 Pyxu Score Explained
 ====================
 
-The **Pyxu Score** is a quantitative measure we use to rank and evaluate Pyxu plugins. The score takes into account
-multiple criteria, ensuring you get a holistic understanding of a plugin's standing. Here's a breakdown:
+The **Pyxu Score** is a quantitative measure we use to rank and evaluate `Pyxu plugins <./plugins/index.html>`_.
 
-The Pyxu Score is calculated using the following criteria:
+.. warning::
 
-1. **Version Matching**: If a plugin's version matches the latest Pyxu version, it gets a point.
-2. **Pyxu Principles Adherence**: Plugins abiding by key Pyxu principles, namely:
+    While the Pyxu Score offers insights into a plugin's quality and popularity, it's just one of many metrics.
+    Users are encouraged to explore plugins individually and consider other factors before making a decision.
+
+The score takes into account multiple criteria, ensuring you get a holistic understanding of a plugin's standing. Here's
+a breakdown:
+
+1. **Version Matching**: If a plugin's version matches the latest Pyxu version, and the latest Python version it gets a point.
+2. **Pyxu Principles Adherence**: Plugins abiding by key `Pyxu principles <./dev_notes.html>`_, namely:
 
    * Input shape agnosticity (i.e., support for NDArrays),
+
    * Complete backend-agnosticity (i.e., support for Numpy, Cupy and Dask arrays),
    * Precision management (i.e., allow selection between computation at both single and double precision)
 
@@ -17,18 +23,16 @@ The Pyxu Score is calculated using the following criteria:
 
 3. **Development Stage Weight**:
 
-   * **Early stages** (Planning 📑, Pre-Alpha 🌒, Alpha 🌓) contribute 0.5 points.
-   * **Advanced stages** (Beta 🌔, Production/Stable ✔️, Mature 🌟) contribute 1 point.
-   * **Inactive 🚫** plugins do not recieive a score.
+   * **Early stages** (Planning, Pre-Alpha, Alpha) contribute 0.5 points.
+   * **Advanced stages** (Beta, Production/Stable, Mature) contribute 1 point.
+   * **Inactive** plugins do not recieive a score.
+   See `the PyPI classifiers <https://pypi.org/classifiers/>`_ for more information on the development stages.
 
-4. **Downloads ⬇️**: Plugins get points based on the number of downloads in the last month, up to a maximum of 1 point
+4. **Downloads**: Plugins get points based on the number of downloads in the last month, up to a maximum of 1 point
    for 1000 downloads.
 
 The final score is then normalized by the number of criteria used (6 in this case) and presented as a percentage.
 
-**Note**: While the Pyxu Score offers insights into a plugin's quality and popularity, it's just one of many metrics.
-Users are encouraged to explore plugins individually and consider other factors before making a decision.
-
 
 .. raw:: html
 
@@ -37,8 +41,8 @@ Users are encouraged to explore plugins individually and consider other factors
 Your insights matter! If you're a developer with ideas on how we can further refine the Pyxu Score, we'd love to hear
 from you. 💡
 
-We invite you to **open an issue** suggesting novel metrics or criteria that, in your opinion, would better represent
-the value and quality of Pyxu plugins. By contributing your thoughts, you play an integral role in refining and shaping
-the Pyxu community's standards.
+We invite you to `open an issue <https://github.com/matthieumeo/pyxu/issues>`_ suggesting novel metrics or criteria
+that, in your opinion, would better represent the value and quality of Pyxu plugins. By contributing your thoughts, you
+play an integral role in refining and shaping the Pyxu community's standards.
 
 Together, let's make the Pyxu Score the best reflection of plugin excellence! 🌟
diff --git a/_sources/guide/algebra.ipynb b/_sources/guide/algebra.ipynb
index f4d56d58..267c042a 100644
--- a/_sources/guide/algebra.ipynb
+++ b/_sources/guide/algebra.ipynb
@@ -27,24 +27,24 @@
     "\n",
     "Every time you perform an arithmetic operation, Pyxu automatically infers the output type based on the properties of the operators involved in the operation. This type inference is super convenient because it saves you from manual calculations! \n",
     "\n",
-    "For example, Pyxu takes care of updating as needed methods like `apply()`, `jacobian()`, `grad()`, `prox()`, and `adjoint()` according to arithmetic rules. This means you can plug these composite operators directly into proximal gradient algorithms without sweating the details of implementing gradients or proximal steps.\n",
+    "For example, Pyxu takes care of updating as needed methods like `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply), `jacobian()`[🔗](../api/abc.html#pyxu.abc.DiffMap.jacobian), `grad()`[🔗](../api/abc.html#pyxu.abc.DiffFunc.grad), `prox()`[🔗](../api/abc.html#pyxu.abc.ProxFunc.prox), and `adjoint()`[🔗](../api/abc.html#pyxu.abc.LinOp.adjoint) according to arithmetic rules. This means you can plug these composite operators directly into proximal gradient algorithms without sweating the details of implementing gradients or proximal steps.\n",
     "\n",
     "## Behind the Scenes: Arithmetic Rules\n",
     "\n",
-    "For those who love to peek under the hood, Pyxu utilizes a set of arithmetic rules located in the `pyxu.abc.arithmetic` module:\n",
+    "For those who love to peek under the hood, Pyxu utilizes a set of arithmetic rules located in the `pyxu.abc.arithmetic`[🔗](../api/abc/arithmetic.html) module:\n",
     "\n",
-    "- `Rule`: The base class for all arithmetic rules.\n",
-    "- `ScaleRule`: Handles scaling of operators by scalars.\n",
-    "- `ArgScaleRule`: Manages the dilation of the arguments of operators.\n",
-    "- `ArgShiftRule`: Takes care of shifting the arguments of operators.\n",
-    "- `AddRule`: Manages the addition of two operators.\n",
-    "- `ChainRule`: Deals with the composition of two operators.\n",
-    "- `PowerRule`: Handles exponentiation of an operator.\n",
-    "- `TransposeRule`: Takes care of transposing a linear operator.\n",
+    "- `Rule`[🔗](../api/abc.html#pyxu.abc.arithmetic.Rule): The base class for all arithmetic rules.\n",
+    "- `ScaleRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.ScaleRule): Handles scaling of operators by scalars.\n",
+    "- `ArgScaleRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.ArgScaleRule): Manages the dilation of the arguments of operators.\n",
+    "- `ArgShiftRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.ArgShiftRule): Takes care of shifting the arguments of operators.\n",
+    "- `AddRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.AddRule): Manages the addition of two operators.\n",
+    "- `ChainRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.ChainRule): Deals with the composition of two operators.\n",
+    "- `PowerRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.PowerRule): Handles exponentiation of an operator.\n",
+    "- `TransposeRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.TransposeRule): Takes care of transposing a linear operator.\n",
     "\n",
     "### Working Example 🎯\n",
     "\n",
-    "Consider the composition of a `DiffFunc` with a `DiffMap`. Let `f` be a `DiffFunc` and `L` be a `DiffMap`. Then their composition `h` is another `DiffFunc`, and the gradient is given by:\n",
+    "Consider the composition of a `DiffFunc`[🔗](../api/abc.html#pyxu.abc.DiffFunc) with a `DiffMap`[🔗](../api/abc.html#pyxu.abc.DiffMap). Let `f` be a `DiffFunc` and `L` be a `DiffMap`. Then their composition `h` is another `DiffFunc`, and the gradient is given by:\n",
     "\n",
     "```python\n",
     ">> h = f * L\n",
@@ -85,7 +85,7 @@
     "\n",
     "## Building Block-Operators \n",
     "\n",
-    "You can even define block-operators using the `coo_block` function. Alternatively, higher-level functions like `block`, `block_diag`, `stack`, `vstack`, and `hstack` can also be used.\n",
+    "You can even define block-operators using the `coo_block`[🔗](../api/operator/blocks.html#pyxu.operator.coo_block) function. Alternatively, higher-level functions like `block`[🔗](../api/operator/blocks.html#pyxu.operator.block), `block_diag`[🔗](../api/operator/blocks.html#pyxu.operator.block_diag), `stack`[🔗](../api/operator/blocks.html#pyxu.operator.stack), `vstack`[🔗](../api/operator/blocks.html#pyxu.operator.vstack), and `hstack`[🔗](../api/operator/blocks.html#pyxu.operator.hstack) can also be used.\n",
     "\n",
     "For example, the following code snippet: \n",
     "\n",
diff --git a/_sources/guide/algorithms.ipynb b/_sources/guide/algorithms.ipynb
index 3f937752..b6de671f 100644
--- a/_sources/guide/algorithms.ipynb
+++ b/_sources/guide/algorithms.ipynb
@@ -11,7 +11,7 @@
     "\n",
     "## Algorithms Overview\n",
     "\n",
-    "### Conjugate Gradient (CG)\n",
+    "### Conjugate Gradient (CG) [🔗](../api/opt.solver.html#pyxu.opt.solver.CG)\n",
     "👉 **Use case:** Quadratic problems, particularly when you have a well-conditioned matrix $A$.\n",
     "\n",
     "**Mathematical Form:**\n",
@@ -19,7 +19,7 @@
     "\\min_{x\\in\\mathbb{R}^{N}} \\frac{1}{2} \\mathbf{x}^{T} \\mathbf{A} \\mathbf{x} - \\mathbf{x}^{T} \\mathbf{b}\n",
     "$$\n",
     "\n",
-    "### Accelerated Proximal Gradient Descent (APGD)\n",
+    "### Accelerated Proximal Gradient Descent (APGD)  [🔗](../api/opt.solver.html#pyxu.opt.solver.PGD)\n",
     "👉 **Use case:** Problems that separate into smooth and non-smooth components. \n",
     "\n",
     "**Mathematical Form:**\n",
@@ -31,7 +31,7 @@
     "> **Note:** With acceleration, `APGD` can be shown to be an *optimal* first-order method, with the fastest possible convergence rate!\n",
     "\n",
     "\n",
-    "### Primal-Dual Splitting (PDS) Methods\n",
+    "### Primal-Dual Splitting (PDS) Methods \n",
     "👉 **Use case:** Multi-term problems, with smooth and non-smooth terms, possibly composed with a linear operator $K$.\n",
     "\n",
     "**Mathematical Form:**\n",
@@ -40,7 +40,7 @@
     "$$\n",
     "where $\\mathcal{F}$ is differentiable, $\\mathcal{G}$ and $\\mathcal{H}$ are proximable, and $K$ is a linear operator.\n",
     "\n",
-    "Methods under this category include `CondatVu`, `PD3O`, `ADMM`, `ChambollePock`, and more.\n",
+    "Methods under this category include `CondatVu` [🔗](../api/opt.solver.html#pyxu.opt.solver.CondatVu), `PD3O` [🔗](../api/opt.solver.html#pyxu.opt.solver.PD3O), `ADMM` [🔗](../api/opt.solver.html#pyxu.opt.solver.ADMM), `ChambollePock` [🔗](../api/opt.solver.html#pyxu.opt.solver.ChambollePock), and more.\n",
     "\n",
     "Note that, although implemented for three-term objective functionals, PDS methods can easilybe generalized to objective functionals of the form:\n",
     "$${\\min_{\\mathbf{x}\\in\\mathbb{R}^N} \\;\\mathcal{F}(\\mathbf{x})\\;\\;+\\;\\;\\mathcal{G}(\\mathbf{x})\\;\\;+\\;\\;\\sum_{i=1}^J\\mathcal{H}_i(K_i\\mathbf{x})}$$\n",
@@ -53,9 +53,9 @@
     "\n",
     "## Choosing the Right Algorithm\n",
     "\n",
-    "The golden rule is to **choose the most specific algorithm** —i.e., the one that makes the most assumptions consistent with your problem. This often results in faster convergence. For example, if your objective functional has a gradient, a gradient-based method like `APGD` will generally be more efficient than a generic proximal-based method like `DouglasRachford`.\n",
+    "The golden rule is to **choose the most specific algorithm** —i.e., the one that makes the most assumptions consistent with your problem. This often results in faster convergence. For example, if your objective functional has a gradient, a gradient-based method like `APGD` will generally be more efficient than a generic proximal-based method like `DouglasRachford` [🔗](../api/opt.solver.html#pyxu.opt.solver.DouglasRachford).\n",
     "\n",
-    "The most generic algorithms in Pyxu are `PD3O` and `CondatVu`, but they are also the least efficient, so use them only when simpler methods like `ADMM`, `APGD` or `CG` cannot be used. Note that `ADAM` can also be useful when step sizes are too complex to compute. \n",
+    "The most generic algorithms in Pyxu are `PD3O` and `CondatVu`, but they are also the least efficient, so use them only when simpler methods like `ADMM`, `APGD` or `CG` cannot be used. Note that `ADAM` [🔗](../api/opt.solver.html#pyxu.opt.solver.Adam) can also be useful when step sizes are too complex to compute. \n",
     "\n",
     "## Hyperparameter Tuning\n",
     "\n",
@@ -105,7 +105,7 @@
     "\n",
     "## Advanced Usage: Guru Interface \n",
     "\n",
-    "For those who want even more control, we provide a guru interface allowing you to overload default settings, including the stopping criteria (see module `pyxu.opt.stop` for available stopping criteria).\n",
+    "For those who want even more control, we provide a guru interface allowing you to overload default settings, including the stopping criteria (see module `pyxu.opt.stop`[🔗](../api/opt.stop.html) for available stopping criteria).\n",
     "\n",
     "For example, overloading the default stopping criterion of the `CondatVu` solver initialized above can be achieved as follows:\n",
     "\n",
@@ -121,12 +121,12 @@
     "\n",
     "## Implementing New Algorithms \n",
     "\n",
-    "To implement a new iterative solver, users need to sub-class `pyxu.abc.solver.Solver` and overwrite some of its core methods, such as `m_init()`,  and `m_step()`, which describe the initalization and update step of iterative algorithms (see the API Reference for more details). \n",
+    "To implement a new iterative solver, users need to sub-class `pyxu.abc.solver.Solver`[🔗](../api/abc.html#pyxu.abc.Solver) and overwrite some of its core methods, such as `m_init()`[🔗](../api/abc.html#pyxu.abc.Solver.m_init),  and `m_step()`[🔗](../api/abc.html#pyxu.abc.Solver.m_step), which describe the initalization and update step of iterative algorithms (see the API Reference for more details). \n",
     "\n",
     "\n",
     "Sub-classes of `Solver` inherit automatically from its very versatile API for solving optimisation problems, with the following notable features:\n",
     "\n",
-    " * manual/automatic/background execution of solver iterations via parameters provided to `fit()`. \n",
+    " * manual/automatic/background execution of solver iterations via parameters provided to `fit()`[🔗](../api/abc.html#pyxu.abc.Solver.fit). \n",
     " * automatic checkpointing of solver progress, providing a safe restore point in case of faulty numerical code. Each solver instance backs its state and final output to a folder on disk for post-analysis. In particular `fit()` will never crash: detailed exception information will always be available in a logfile for post-analysis.\n",
     " * solve for multiple initial points in parallel.\n",
     "\n",
diff --git a/_sources/examples/DifferentialOperators.ipynb b/_sources/guide/diff_ops.ipynb
similarity index 99%
rename from _sources/examples/DifferentialOperators.ipynb
rename to _sources/guide/diff_ops.ipynb
index 7495e98f..874d9f53 100644
--- a/_sources/examples/DifferentialOperators.ipynb
+++ b/_sources/guide/diff_ops.ipynb
@@ -1,62 +1,32 @@
 {
  "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "177a858e",
-   "metadata": {},
-   "source": [
-    "# Differential operators in Pyxu"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "ab2b2317",
    "metadata": {},
    "source": [
-    "The `pyxu.operator.linop.diff` module defines a set of classes and functions related to derivative operators. \n",
+    "# Differential Operators in Pyxu\n",
     "\n",
-    "In the context of inverse problems, derivative operators come handy when the spatial structure of the object or image be reconstructed can be leveraged. For example, common uses of derivatives are when the image is expected to be smooth in one or more directions, or in contrast, when it is  expected to have sharp edges and flat regions. In those cases, the derivative operators are used as part of regularization terms, adding prior knowledge to our solution (see example TODO).\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6e2d5017",
-   "metadata": {},
-   "source": [
-    "## 1. Partial derivatives"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7e401893",
-   "metadata": {},
-   "source": [
+    "The `pyxu.operator.linop.diff`[🔗](../api/operator/linop.html#derivatives)  module defines a set of classes and functions related to derivative operators. \n",
+    "\n",
+    "In the context of inverse problems, derivative operators come handy when the spatial structure of the object or image be reconstructed can be leveraged. For example, common uses of derivatives are when the image is expected to be smooth in one or more directions, or in contrast, when it is  expected to have sharp edges and flat regions. In those cases, the derivative operators are used as part of regularization terms, adding prior knowledge to our solution.\n",
+    "\n",
+    "## Partial Derivatives\n",
     "\n",
-    "The most basic differential operator is the **partial derivative**:\n",
     "\n",
+    "The most basic differential operator is the `PartialDerivative`[🔗](../api/operator/linop.html#pyxu.operator.PartialDerivative):\n",
     "\n",
-    "\\begin{align}\n",
-    "\\frac{\\partial^{n}}{\\partial x_0^{n_0} \\cdots \\partial x_{D-1}^{n_{D-1}}} \n",
-    "\\end{align}\n",
+    "$$\\frac{\\partial^{n}}{\\partial x_0^{n_0} \\cdots \\partial x_{D-1}^{n_{D-1}}}$$\n",
     "\n",
     "Which when applied to an given signal $\\mathbf{f}$, yields:\n",
     "\n",
-    "\\begin{align}\n",
-    "\\frac{\\partial^{n}}{\\partial x_0^{n_0} \\cdots \\partial x_{D-1}^{n_{D-1}}}\\mathbf{f} =\\mathbf{D}\\mathbf{f}\\in \\mathbb{R}^{N_0 \\times \\cdots \\times N_{D-1}}\n",
-    "\\end{align}\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e8617455",
-   "metadata": {},
-   "source": [
+    "$$\\frac{\\partial^{n}}{\\partial x_0^{n_0} \\cdots \\partial x_{D-1}^{n_{D-1}}}\\mathbf{f} =\\mathbf{D}\\mathbf{f}\\in \\mathbb{R}^{N_0 \\times \\cdots \\times N_{D-1}}$$\n",
+    "\n",
+    "\n",
     "Partial derivatives in `Pyxu` are computed via efficient **matrix-free** implementation, which is based on [JIT compiled stencils](https://numba.pydata.org/numba-doc/latest/user/stencil.html). For illustrative purposes, consider the following approximation to the partial derivatives:\n",
     "\n",
     "\n",
-    "\\begin{align}\n",
-    "\\mathbf{D} f [n] = f[n+1] - f[n]\n",
-    "\\end{align}\n",
+    "$$\\mathbf{D} f [n] = f[n+1] - f[n]$$\n",
     "\n",
     "\n",
     "As we will see below, this is the forward finite difference approximation. This could be implemented in **matrix-form**, in which case it would look like this:\n",
@@ -91,15 +61,14 @@
     "```\n",
     "\n",
     "\n",
-    "Despite Python being very slow when it comes to for loops, there are some ways to make them really efficient (see [HPC example](TODO)).\n",
+    "Despite Python being very slow when it comes to for-loops, Pyxu leverages existing tools to run them efficiently (see [HPC Features](./hpc.ipynb)).\n",
     "\n",
     "<!---\n",
-    " finite_difference = PartialDerivative.finite_difference(\n",
+    "finite_difference = PartialDerivative.finite_difference(\n",
     "            arg_shape=(10,), \n",
     "            order=(1, ),\n",
     "            scheme=\"forward\", \n",
     "            accuracy=1,)\n",
-    "\n",
     "fig, ax = plt.subplots(figsize=(5,5))\n",
     "im = ax.imshow(finite_difference.asarray(), cmap=\"RdYlBu\")\n",
     "ax.set_xticks(np.arange(cut - 1) + 0.5, [])\n",
@@ -109,22 +78,10 @@
     "plt.colorbar(im, ax=ax)\n",
     "fig.tight_layout()\n",
     "fig.savefig(\"data/images/matrix-form.png\", dpi=200)\n",
-    "--->"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0bdfbd20",
-   "metadata": {},
-   "source": [
-    "### 1.1. Parameters"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b795b197",
-   "metadata": {},
-   "source": [
+    "--->\n",
+    "\n",
+    "### Partial Derivative Parametrization\n",
+    "\n",
     "The `PartialDerivative` class implements two main approximations to the partial derivatives as methods:`finite_difference` and `gaussian_derivative`:\n",
     "\n",
     "```python\n",
@@ -138,8 +95,7 @@
     "        gpu: bool = False,\n",
     "        dtype: typ.Optional[pyct.DType] = None,\n",
     "        sampling: typ.Union[pyct.Real, cabc.Sequence[pyct.Real, ...]] = 1,\n",
-    "    ) -> pyct.OpT\n",
-    "    \n",
+    "    ) -> pyct.OpT:\n",
     "``` \n",
     "\n",
     "```python\n",
@@ -153,16 +109,15 @@
     "        gpu: bool = False,\n",
     "        dtype: typ.Optional[pyct.DType] = None,\n",
     "        sampling: typ.Union[pyct.Real, cabc.Sequence[pyct.Real, ...]] = 1,\n",
-    "    ) -> pyct.OpT\n",
-    "    \n",
+    "    ) -> pyct.OpT:\n",
     "```\n",
     "\n",
     "The common arguments are: \n",
     "        \n",
     "- `arg_shape`: Shape of the input image. This is information is necessary in case batch processing is intended.\n",
     "- `order`: Derivative order in each axis. For example, for a 2D image input: \n",
-    "    - `order=(1, 2)` would yield: $$\\frac{\\partial^{3} \\mathbf{f}}{\\partial x \\partial y^{2}}$$\n",
-    "    - `order=(2, 0)` would yield: $$\\frac{\\partial^{2} \\mathbf{f}}{\\partial x^{2}}$$\n",
+    "    - `order=(1, 2)` would yield: $\\frac{\\partial^{3} \\mathbf{f}}{\\partial x \\partial y^{2}}$\n",
+    "    - `order=(2, 0)` would yield: $\\frac{\\partial^{2} \\mathbf{f}}{\\partial x^{2}}$\n",
     "\n",
     "- `mode`: Padding mode to define boundary conditions. Pre-padding and post-trimming are computed to yield an output array of the same shape as the input. It can be defined in general (with a `string`) or per axis (with a `tuple`). The available modes are: \n",
     "    - 'constant'\n",
@@ -176,44 +131,21 @@
     "- `sampling`: Spacing between pixels. It can be defined in general (with a `float/int`) or per axis (with a `tuple`)\n",
     "        \n",
     "        \n",
-    "The sections below it is explained the differences between these two methods and their specific arguments."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "80b3cc9c",
-   "metadata": {},
-   "source": [
+    "The sections below it is explained the differences between these two methods and their specific arguments.\n",
+    "\n",
     "<div class=\"alert alert-block alert-warning\">  \n",
     "<b>Important:</b> Differential operators are not backend nor dtype agnostic! The arguments `gpu` and `dtype` must be chosen adequately.\n",
-    "</div>\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "fe4582cd",
-   "metadata": {},
-   "source": [
-    "### 1.2. Finite differences"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b3dc5538",
-   "metadata": {},
-   "source": [
+    "</div>\n",
+    "\n",
+    "\n",
+    "### Finite Differences Approximation to the Partial Derivative\n",
+    "\n",
     "Finite differences approximate the derivatives by computing the difference between pixel values in the image. There are different variations of finite differences, such as forward differences, backward differences, and central differences.\n",
     "\n",
     "* *Forward Differences*: $\\mathbf{D}_{F} f [n] = \\frac{f[n+1] - f[n]}{h}$\n",
     "* *Backward Differences*: $\\mathbf{D}_{B} f [n] = \\frac{f[n] - f[n-1]}{h}$\n",
-    "* *Central Differences*: $\\mathbf{D}_{C} f [n] = \\frac{f[n+1] - f[n-1]}{2h}$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8198e968",
-   "metadata": {},
-   "source": [
+    "* *Central Differences*: $\\mathbf{D}_{C} f [n] = \\frac{f[n+1] - f[n-1]}{2h}$\n",
+    "\n",
     "Another important parameter for finite difference is the accuracy, which defines the number of digits used for the approximation. \n",
     "\n",
     "These are some kernels generated by different parameterizations: the (parenthesis) indicates the central element.\n",
@@ -353,7 +285,7 @@
    "id": "1dd0f18f",
    "metadata": {},
    "source": [
-    "### 1.3.Gaussian derivative"
+    "### Gaussian Derivative Approximation to the Partial Derivative"
    ]
   },
   {
@@ -514,7 +446,7 @@
    "id": "52dcd0e8",
    "metadata": {},
    "source": [
-    "### 1.4. How to choose?"
+    "### How to choose between Finite Differences and Gaussian Derivative?"
    ]
   },
   {
@@ -523,8 +455,9 @@
    "metadata": {},
    "source": [
     "The choice between *finite difference* and *Gaussian derivative* can be seen as a **trade-off between bias and variance**:\n",
-    "- When estimating partial derivatives, the Gaussian derivative robustly captures the true behavior of the derivative of the smoothed signal, thus introducing bias in the estimation. \n",
-    "- On the other hand, finite differences, especially when using a small accuracy value, can be highly sensitive to noise and can produce unstable estimates of the derivative (variance). Gaussian derivatives, on the other hand, tend to be smoother and less affected by noise.\n",
+    "\n",
+    "* When estimating partial derivatives, the Gaussian derivative robustly captures the true behavior of the derivative of the smoothed signal, thus introducing bias in the estimation. \n",
+    "* On the other hand, finite differences, especially when using a small accuracy value, can be highly sensitive to noise and can produce unstable estimates of the derivative (variance). Gaussian derivatives, on the other hand, tend to be smoother and less affected by noise.\n",
     "\n",
     "As a rule of thumb, it is recommended to try both approaches and to use the Gaussian derivative for very noisy signals."
    ]
@@ -534,7 +467,7 @@
    "id": "eb92f038",
    "metadata": {},
    "source": [
-    "## 2. Stacks of partial derivatives"
+    "## Stacks of Partial Derivatives"
    ]
   },
   {
@@ -544,28 +477,24 @@
    "source": [
     "There are two main classes of stacks of partial derivative:\n",
     "\n",
-    "* `Gradient`: stack of all first order derivatives (one per axis), \n",
+    "* `Gradient`[🔗](../api/operator/linop.html#pyxu.operator.Gradient): stack of all first order derivatives (one per axis), \n",
     "\n",
     "\n",
-    "\\begin{align}\n",
-    "\\mathbf{f} = \\begin{bmatrix}\n",
+    "$$\\mathbf{f} = \\begin{bmatrix}\n",
     "   \\frac{\\partial \\mathbf{f}}{\\partial x_0} \\\\\n",
     "   \\vdots \\\\\n",
     "   \\frac{\\partial \\mathbf{f}}{\\partial x_{D-1}}\n",
-    "   \\end{bmatrix} \\in \\mathbb{R}^{D \\times N_{0} \\times \\cdots \\times N_{D-1}}\n",
-    "\\end{align}\n",
+    "   \\end{bmatrix} \\in \\mathbb{R}^{D \\times N_{0} \\times \\cdots \\times N_{D-1}}$$\n",
     "\n",
     "\n",
-    "* `Hessian`: stack of all second order derivatives,\n",
+    "* `Hessian`[🔗](../api/operator/linop.html#pyxu.operator.Hessian): stack of all second order derivatives,\n",
     "\n",
-    "\\begin{align}\n",
-    " \\mathbf{H} \\mathbf{f} = \\begin{bmatrix}\n",
+    "$$\\mathbf{H} \\mathbf{f} = \\begin{bmatrix}\n",
     "   \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{0}^{2} } &  \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{0}\\,\\partial x_{1} } & \\cdots & \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{0} \\, \\partial x_{D-1} } \\\\\n",
     "   \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{1} \\, \\partial x_{0} } & \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{1}^{2} } & \\cdots & \\dfrac{ \\partial^{2}\\mathbf{f} }{\\partial x_{1} \\,\\partial x_{D-1}} \\\\\n",
     "   \\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
     "   \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{D-1} \\, \\partial x_{0} } & \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{D-1} \\, \\partial x_{1} } & \\cdots & \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{D-1}^{2}}\n",
-    "   \\end{bmatrix}\n",
-    "\\end{align}"
+    "   \\end{bmatrix}$$"
    ]
   },
   {
@@ -573,7 +502,7 @@
    "id": "1eca7161",
    "metadata": {},
    "source": [
-    "### 2.1. Parameters"
+    "### Parameters"
    ]
   },
   {
@@ -616,9 +545,9 @@
     "\n",
     "There are some common arguments that we didn't see in the previous `PartialDerivative` class:\n",
     "        \n",
-    "- `diff_method`: This will select between `finite_difference` ('fd') or `gaussian_derivative` ('gd') type of partial derivatives.\n",
-    "- `parallel`: If `True`, it will compute the different partial derivatives in parrellalel on different threads.\n",
-    "- `diff_kwargs`: Placeholder to specify arguments that are specific to `finite_difference` and `gaussian_derivative`.\n",
+    "* `diff_method`: This will select between `finite_difference` ('fd') or `gaussian_derivative` ('gd') type of partial derivatives.\n",
+    "* `parallel`: If `True`, it will compute the different partial derivatives in parrellalel on different threads.\n",
+    "* `diff_kwargs`: Placeholder to specify arguments that are specific to `finite_difference` and `gaussian_derivative`.\n",
     "        \n",
     "The sections below it is explained the differences between these two methods and their specific arguments."
    ]
@@ -638,7 +567,7 @@
    "id": "816838de",
    "metadata": {},
    "source": [
-    "### 2.2. Gradient"
+    "### Gradient"
    ]
   },
   {
@@ -650,12 +579,10 @@
     "\n",
     "For example, in the case of a 2-dimensional image, the gradient operator implements:\n",
     "\n",
-    "\\begin{align}\n",
-    "\\boldsymbol{\\nabla} \\mathbf{f} = \\begin{bmatrix}\n",
+    "$$\\boldsymbol{\\nabla} \\mathbf{f} = \\begin{bmatrix}\n",
     "    \\frac{\\partial \\mathbf{f}}{\\partial x} \\\\\n",
     "    \\frac{\\partial \\mathbf{f}}{\\partial y}\n",
-    "    \\end{bmatrix} \\in \\mathbb{R}^{2 \\times N_{x} \\times N_{y}}\n",
-    "\\end{align}\n",
+    "    \\end{bmatrix} \\in \\mathbb{R}^{2 \\times N_{x} \\times N_{y}}$$\n",
     "\n"
    ]
   },
@@ -742,7 +669,7 @@
    "id": "9bdfc5cb",
    "metadata": {},
    "source": [
-    "### 2.3. Hessian"
+    "### Hessian"
    ]
   },
   {
diff --git a/_sources/guide/funcs.ipynb b/_sources/guide/funcs.ipynb
index c6dc7dab..b22ac70f 100644
--- a/_sources/guide/funcs.ipynb
+++ b/_sources/guide/funcs.ipynb
@@ -21,13 +21,12 @@
     "> \n",
     "> 1. **Subclassing**: Extend these classes to create customized functionals tailored to your problem. \n",
     "> \n",
-    "> 2. **Generic Constructor Routine**: Utilize the `from_source` method to define new functionals from their core methods, like `apply()`, `grad()`, or `prox()`.\n",
+    "> 2. **Generic Constructor Routine**: Utilize the `from_source`[🔗](../api/operator.interop.html#general) method to define new functionals from their core methods, like `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply), `grad()`[🔗](../api/abc.html#pyxu.abc.DiffFunc.grad), or `prox()`[🔗](../api/abc.html#pyxu.abc.ProxFunc.prox).\n",
     ">\n",
     "> Additionally, don't forget to explore our comprehensive Reference API. It features pre-implemented versions of many commonly used functionals, serving as both a shortcut for common tasks and a useful learning resource.\n",
     "\n",
     "### `Func`: The Foundation Stone 🧱\n",
-    "\n",
-    "The `Func` class is the base class in the functional hierarchy. Its core method is `apply()`, which computes the value of the functional at a given input.\n",
+    "The `Func`[🔗](../api/abc.html#pyxu.abc.Func) class is the base class in the functional hierarchy. Its core method is `apply()`, which computes the value of the functional at a given input.\n",
     "\n",
     "Here's a simplified example, implementing the squared $L_2$ norm:\n",
     "\n",
@@ -54,7 +53,7 @@
     "\n",
     "### `DiffFunc`: Differentiable Functionals 🎯\n",
     "\n",
-    "The `DiffFunc` class extends `Func` for functionals that have a well-defined gradient. It introduces an additional method, `grad()`, for gradient computation.\n",
+    "The `DiffFunc`[🔗](../api/abc.html#pyxu.abc.DiffFunc) class extends `Func` for functionals that have a well-defined gradient. It introduces an additional method, `grad()`, for gradient computation.\n",
     "\n",
     "```python\n",
     "from pyxu.abc import DiffFunc\n",
@@ -67,11 +66,11 @@
     "        return 2 * x\n",
     "```\n",
     "\n",
-    ">🌈Tip: With Pyxu, you can use `from_torch` or `from_jax` to automatically compute the gradient if you have a PyTorch or JAX implementation of your functional.\n",
+    ">🌈Tip: With Pyxu, you can use `from_torch`[🔗](../api/operator.interop.html#pyxu.operator.interop.from_torch) or `from_jax`[🔗](../api/operator.interop.html#pyxu.operator.interop.from_jax) to automatically compute the gradient if you have a PyTorch or JAX implementation of your functional.\n",
     "\n",
     "### `ProxFunc`: Proximable Functionals 🛡️\n",
     "\n",
-    "For functionals with a simple proximal operator, you'll find `ProxFunc` extremely useful. It offers the `prox()` method, which evaluates the proximal operator of the functional. Here's an example using the $L_1$ norm:\n",
+    "For functionals with a simple proximal operator, you'll find `ProxFunc`[🔗](../api/abc.html#pyxu.abc.ProxFunc) extremely useful. It offers the `prox()` method, which evaluates the proximal operator of the functional. Here's an example using the $L_1$ norm:\n",
     "\n",
     "```python\n",
     "from pyxu.abc import ProxFunc\n",
@@ -86,7 +85,7 @@
     "\n",
     "#### Moreau Envelope for Smoothing\n",
     "\n",
-    "You can also smooth out a proximable functional using the `moreau_envelope()` method. For example, you can smooth the L1 norm to create the [Huber loss function](https://www.wikiwand.com/en/Huber_loss) as follows:\n",
+    "You can also smooth out a proximable functional using the `moreau_envelope()`[🔗](../api/abc.html#pyxu.abc.ProxFunc.moreau_envelope) method. For example, you can smooth the L1 norm to create the [Huber loss function](https://www.wikiwand.com/en/Huber_loss) as follows:\n",
     "\n",
     "```python\n",
     "huber = L1Norm(dim).moreau_envelope(mu=0.1)\n",
@@ -110,7 +109,7 @@
     "\n",
     "### Specialized Classes: `ProxDiffFunc`, `LinFunc`, `QuadraticFunc` 🎨\n",
     "\n",
-    "These classes are for functionals that offer even more, like being both proximable and differentiable (`ProxDiffFunc`), or being linear (`LinFunc`) or quadratic (`QuadraticFunc`). Quadratic functionals are especially important in primal-dual methods for faster convergence, so do use them when you can! \n",
+    "These classes are for functionals that offer even more, like being both proximable and differentiable (`ProxDiffFunc`[🔗](../api/abc.html#pyxu.abc.ProxDiffFunc)), or being linear (`LinFunc`[🔗](../api/abc.html#pyxu.abc.LinFunc)) or quadratic (`QuadraticFunc`[🔗](../api/abc.html#pyxu.abc.QuadraticFunc)). Quadratic functionals are especially important in primal-dual methods for faster convergence, so do use them when you can! \n",
     "\n",
     "> Note: when dealing with `ProxDiffFunc` instances, it can be hard to decide whether the gradient or proximal operator should be used for optimization purposes. The general rule-of-thumb is to use the gradient as much as possible, as the latter requires more regularity on the objective functional, which can be leveraged by solvers for fatser convergence. \n",
     "\n",
diff --git a/_sources/guide/fwdops.ipynb b/_sources/guide/fwdops.ipynb
index 9c31a608..03d47405 100644
--- a/_sources/guide/fwdops.ipynb
+++ b/_sources/guide/fwdops.ipynb
@@ -8,7 +8,7 @@
     "# Forward Operators\n",
     "\n",
     "In computational imaging, the ability to accurately model the acquisition system is cornerstone to solving inverse\n",
-    "problems. The `LinOp()` class in Pyxu serves as a foundational abstraction for defining linear forward operators,\n",
+    "problems. The `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) class in Pyxu serves as a foundational abstraction for defining linear forward operators,\n",
     "essentially mapping the original signal or image to the data we observe. This guide distills the knowledge needed to\n",
     "implement custom forward operators using the `LinOp()` class, as well as related classes in the Pyxu library.\n",
     "\n",
@@ -16,9 +16,9 @@
     "> \n",
     "> 1. **Subclassing**: Extend these classes to create customized operators tailored to your problem. \n",
     "> \n",
-    "> 2. **Generic Constructor Routine**: Utilize the `from_source` method to define new operators from their core methods, like `apply()`, `adjoint()`, or `jacobian()`.\n",
+    "> 2. **Generic Constructor Routine**: Utilize the `from_source`[🔗](../api/operator.interop.html#general) method to define new operators from their core methods, like `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply), `adjoint()`[🔗](../api/abc.html#pyxu.abc.LinOp.adjoint), or `jacobian()`[🔗](../api/abc.html#pyxu.abc.DiffMap.jacobian).\n",
     ">\n",
-    "> Additionally, don't forget to explore our comprehensive Reference API. It features pre-implemented versions of many commonly used forward operators, serving as both a shortcut for common tasks and a useful learning resource.\n",
+    "> Additionally, don't forget to explore our comprehensive (Reference API)[../api/index.html]. It features pre-implemented versions of many commonly used forward operators, serving as both a shortcut for common tasks and a useful learning resource.\n",
     "\n",
     "## The Importance of Matrix-Free Operators\n",
     "\n",
@@ -47,31 +47,31 @@
     "    class Sum(LinOp):\n",
     "        pass\n",
     "    ```\n",
-    "    Here, a new class called `Sum()` is defined, inheriting from Pyxu's `LinOp()` base class, the primary abstraction\n",
+    "    Here, a new class called `Sum()` is defined, inheriting from Pyxu's `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) base class, the primary abstraction\n",
     "    for designing real-valued linear operators. This inheritance means that `Sum()` is expected to implement certain\n",
     "    core methods, namely `apply()` and `adjoint()`. \n",
     "\n",
     "\n",
-    "- **The ``apply()`` Method:**\n",
+    "- **The** ``apply()`` **Method:**\n",
     "  \n",
     "    ```python\n",
     "        def apply(self, arr):\n",
     "            return arr.sum(keepdims=True)\n",
     "    ```\n",
-    "    The `apply()` method takes an array `arr` as input and returns the sum of its elements. This is the core\n",
+    "    The `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply) method takes an array `arr` as input and returns the sum of its elements. This is the core\n",
     "    functionality of the operator. Instead of representing the sum operation as a matrix and performing matrix-vector\n",
     "    multiplication, the method directly computes the sum, making it \"matrix-free.\"\n",
     "\n",
     "    > **Note**: `keepdims=True` is required since, as per the `LinOp.apply()` signature, it must return an NDArray, and\n",
     "    > not a scalar.\n",
     "\n",
-    "- **The ``adjoint()`` Method:**\n",
+    "- **The** ``adjoint()`` **Method:**\n",
     "  \n",
     "    ```python\n",
     "        def adjoint(self, arr):\n",
     "            return arr * np.ones(self.shape[1])\n",
     "    ```\n",
-    "    The `adjoint()` method also takes an array `arr` as input. The adjoint operation for this sum operator is\n",
+    "    The `adjoint()`[🔗](../api/abc.html#pyxu.abc.LinOp.adjoint) method also takes an array `arr` as input. The adjoint operation for this sum operator is\n",
     "    effectively a *broadcast* operation, mapping a scalar to a vector with the same dimension of the original array\n",
     "    space.\n",
     "\n",
@@ -127,24 +127,24 @@
     "\n",
     "## Additional Features of LinOp: Batteries Included \n",
     "\n",
-    "Pyxu's `LinOp()` is designed to be as versatile and useful as possible for computational imaging. Here are some of the\n",
+    "Pyxu's `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) is designed to be as versatile and useful as possible for computational imaging. Here are some of the\n",
     "extra capabilities baked right into the class to facilitate both simple and complex tasks:\n",
     "\n",
     "- **Lipschitz Constant**: Knowing the Lipschitz constant of an operator is invaluable for optimization routines. If you\n",
-    "  know it, you can directly store it in the `lipschitz` property. Don't know it? No problem! The `estimate_lipschitz()`\n",
+    "  know it, you can directly store it in the `lipschitz`[🔗](../api/abc.html#pyxu.abc.Map.lipschitz) property. Don't know it? No problem! The `estimate_lipschitz()`[🔗](../api/abc.html#pyxu.abc.Map.estimate_lipschitz)\n",
     "  method will compute it for you, offering various methods to balance accuracy and execution time.\n",
     "\n",
     "```python\n",
     "my_operator.lipschitz = my_operator.estimate_lipschitz()\n",
     "```\n",
     "\n",
-    "- **Singular Value Decomposition**: Ever needed to compute the singular values of your operator? Use the `svdvals()`\n",
+    "- **Singular Value Decomposition**: Ever needed to compute the singular values of your operator? Use the `svdvals()`[🔗](../api/abc.html#pyxu.abc.LinOp.svdvals)\n",
     "  method which employs the Arnoldi algorithm to get the job done without breaking the matrix-free paradigm.\n",
     "\n",
-    "- **Trace of Operator**: Sometimes you may need to compute the trace of an operator. The `trace()` method uses a\n",
+    "- **Trace of Operator**: Sometimes you may need to compute the trace of an operator. The `trace()`[🔗](../api/abc.html#pyxu.abc.SquareOp.trace) method uses a\n",
     "  stochastic approximation with the Hutch++ algorithm to efficiently it.\n",
     "\n",
-    "- **Pseudo-Inverse**: If you're looking to solve an inverse problem, the `pinv()` method helps you evaluate the\n",
+    "- **Pseudo-Inverse**: If you're looking to solve an inverse problem, the `pinv()`[🔗](../api/abc.html#pyxu.abc.LinOp.pinv) method helps you evaluate the\n",
     "  pseudo-inverse by solving the (dampened) normal equations, making it the most straightforward way to reverse your\n",
     "  operations.\n",
     "\n",
@@ -152,30 +152,30 @@
     "pseudo_inv_result = my_operator.pinv(my_array, damp=value)\n",
     "```\n",
     "\n",
-    "- **Support for Explicit Matrices**: Though `LinOp()` is primarily built for matrix-free operations, you are not\n",
-    "  restricted to them. If you prefer, you can work with explicit matrices using the `from_array()` method, supporting a\n",
+    "- **Support for Explicit Matrices**: Though `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) is primarily built for matrix-free operations, you are not\n",
+    "  restricted to them. If you prefer, you can work with explicit matrices using the `from_array()`[🔗](../api/abc.html#pyxu.abc.LinOp.from_array) method, supporting a\n",
     "  variety of array formats including `numpy`, `cupy`, `sparse`, and `dask`.\n",
     "\n",
     "```python\n",
     "op = LinOp.from_array(np.ones((N, N)))\n",
     "```\n",
     "\n",
-    "With all these tools and methods at your disposal, `LinOp()` aims to be your go-to solution for implementing linear\n",
+    "With all these tools and methods at your disposal, `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) aims to be your go-to solution for implementing linear\n",
     "operators in computational imaging tasks.\n",
     "\n",
     "## DiffMap for Non-linear Forward Operators \n",
     "\n",
     "Linear models are often an idealized representation. In some situations forward operators are inherently non-linear.\n",
     "Take phase retrieval or some forms of tomography as examples: these are scenarios where the relationship between the\n",
-    "object and its measurements isn't just a linear transformation. For such cases, Pyxu provides the `DiffMap()` class to\n",
+    "object and its measurements isn't just a linear transformation. For such cases, Pyxu provides the `DiffMap()`[🔗](../api/abc.html#pyxu.abc.DiffMap) class to\n",
     "implement these non-linear forward operators.\n",
     "\n",
     "### Core Methods\n",
     "\n",
-    "- **`apply()`**: This method is where you'll implement your forward model. Just like in `LinOp()`, you override this\n",
+    "- `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply): This method is where you'll implement your forward model. Just like in `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp), you override this\n",
     "  function to define how your specific forward model operates on an input array.\n",
     "\n",
-    "- **`jacobian`**: In calculus, the Jacobian matrix represents the best linear approximation to a function at a given\n",
+    "- `jacobian()`[🔗](../api/abc.html#pyxu.abc.DiffMap.jacobian): In calculus, the Jacobian matrix represents the best linear approximation to a function at a given\n",
     "  point. For a function $\\mathbf{f}: \\mathbb{R}^{M} \\to \\mathbb{R}^{N}$, the Jacobian\n",
     "  $\\mathbf{J}_{\\mathbf{f}}(\\mathbf{x})$ at a point $\\mathbf{x}$ is an $N \\times M$ matrix where the entry $(i, j)$ is\n",
     "  $\\frac{\\partial f_{i}}{\\partial x_{j}}$. When the forward operator is non-linear, knowing the Jacobian is crucial for\n",
@@ -190,17 +190,17 @@
     "Libraries like JAX or PyTorch offer automatic differentiation techniques (autograd) to compute derivatives, which you\n",
     "can use to obtain the Jacobian efficiently in matrix-free fashion.\n",
     "\n",
-    "In Pyxu, methods `from_torch()` and `from_jax()` allow you to define operators whose Jacobians are computed via\n",
+    "In Pyxu, methods `from_torch`[🔗](../api/operator.interop.html#pyxu.operator.interop.from_torch) and `from_jax`[🔗](../api/operator.interop.html#pyxu.operator.interop.from_jax) allow you to define operators whose Jacobians are computed via\n",
     "autograd.  This means you can utilize the power of these deep learning libraries to implement non-linear operators\n",
     "seamlessly.\n",
     "\n",
-    "With `DiffMap()`, you're well-equipped to tackle the challenges posed by non-linear forward operators in computational\n",
+    "With `DiffMap()`[🔗](../api/abc.html#pyxu.abc.DiffMap), you're well-equipped to tackle the challenges posed by non-linear forward operators in computational\n",
     "imaging.\n",
     "\n",
     "## Wrapping Up\n",
     "\n",
     "Pyxu offers a robust and scalable framework for computational imaging professionals to deal with both linear and\n",
-    "non-linear forward operators. With the abstraction provided by classes like `LinOp()` and `DiffMap()`, you can focus on\n",
+    "non-linear forward operators. With the abstraction provided by classes like `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) and `DiffMap()`[🔗](../api/abc.html#pyxu.abc.DiffMap), you can focus on\n",
     "the problem you're solving rather than computational limitations. These classes are meant to be subclassed to tailor to\n",
     "your specific problem domain. Happy coding! 🚀\n"
    ]
diff --git a/_sources/guide/hpc.ipynb b/_sources/guide/hpc.ipynb
index 5438dabd..89add656 100644
--- a/_sources/guide/hpc.ipynb
+++ b/_sources/guide/hpc.ipynb
@@ -185,7 +185,7 @@
    ],
    "source": [
     "import time as t\n",
-    "from pyxu.util.deps import supported_array_modules\n",
+    "from pyxu.info.deps import supported_array_modules\n",
     "from pyxu.util import compute\n",
     "\n",
     "timings = dict()\n",
@@ -208,7 +208,7 @@
     }
    },
    "source": [
-    "If called from within the context manager ``Precision``, the decorated apply method will automatically coerce the input/output to the user-specified precision:"
+    "If called from within the context manager ``Precision``[🔗](../api/runtime.html#pyxu.runtime.Precision), the decorated apply method will automatically coerce the input/output to the user-specified precision:"
    ]
   },
   {
diff --git a/_sources/guide/index.rst b/_sources/guide/index.rst
index 9dba494b..cbc0a4ec 100644
--- a/_sources/guide/index.rst
+++ b/_sources/guide/index.rst
@@ -16,3 +16,4 @@ essential aspects of the library, helping you harness its full power for your re
    algorithms.ipynb
    lipschitz.ipynb
    hpc.ipynb
+   diff_ops.ipynb
diff --git a/_sources/guide/lipschitz.ipynb b/_sources/guide/lipschitz.ipynb
index f74f0803..0296bebe 100644
--- a/_sources/guide/lipschitz.ipynb
+++ b/_sources/guide/lipschitz.ipynb
@@ -23,7 +23,7 @@
     "\n",
     "## Accessing Lipschitz Constants\n",
     "\n",
-    "Pyxu operators come equipped with attributes `lipschitz` and `diff_lipschitz` for storing the Lipschitz constants of a map and its derivative (if defined), respectively. These constants are leveraged under the hood by Pyxu to auto-tune the step sizes in various optimization algorithms.\n",
+    "Pyxu operators come equipped with attributes `lipschitz`[🔗](../api/abc.html#pyxu.abc.Map.lipschitz) and `diff_lipschitz`[🔗](../api/abc.html#pyxu.abc.DiffMap.diff_lipschitz) for storing the Lipschitz constants of a map and its derivative (if defined), respectively. These constants are leveraged under the hood by Pyxu to auto-tune the step sizes in various optimization algorithms.\n",
     "\n",
     "```python\n",
     "# Access Lipschitz constant of an operator 'op'\n",
@@ -32,7 +32,7 @@
     "\n",
     "## Estimating Lipschitz Constants\n",
     "\n",
-    "For user-defined or complicated operators where Lipschitz constants are unknown, you can estimate them using Pyxu's `estimate_lipschitz()` method.\n",
+    "For user-defined or complicated operators where Lipschitz constants are unknown, you can estimate them using Pyxu's `estimate_lipschitz()`[🔗](../api/abc.html#pyxu.abc.Map.estimate_lipschitz) method.\n",
     "\n",
     "```python\n",
     "# Estimate Lipschitz constant and update the attribute\n",
@@ -43,7 +43,7 @@
     "\n",
     "Pyxu offers two methods to estimate Lipschitz constants:\n",
     "\n",
-    "1. **Trace Method (`trace`)**: This is the default and computationally lighter option. It computes a rough estimate using the Frobenius norm of the operator, making use of the [Hutch++ stochastic algorithm](https://arxiv.org/abs/2010.09649):\n",
+    "1. **Trace Method (**`trace`**)**: This is the default and computationally lighter option. It computes a rough estimate using the Frobenius norm of the operator, making use of the [Hutch++ stochastic algorithm](https://arxiv.org/abs/2010.09649):\n",
     "\n",
     "    ```python\n",
     "    # Using trace method\n",
@@ -52,7 +52,7 @@
     "    ```\n",
     "\n",
     "\n",
-    "2. **SVD Method (`svd`)**: This method computes the spectral norm of the operator and generally provides a tighter Lipschitz constant. However, it can be computationally intensive for large operators. A reduced-accuracy mode is available for quicker but slightly overestimated constants:\n",
+    "2. **SVD Method (**`svd`**)**: This method computes the spectral norm of the operator and generally provides a tighter Lipschitz constant. However, it can be computationally intensive for large operators. A reduced-accuracy mode is available for quicker but slightly overestimated constants:\n",
     "\n",
     "    ```python\n",
     "    # Using SVD method with reduced accuracy\n",
@@ -208,7 +208,7 @@
     "... \n",
     "```\n",
     "\n",
-    "More details on this feature can be found in the API reference under `pyxu.abc.arithmetic`.\n",
+    "More details on this feature can be found in the [API reference](../api/index.html) under `pyxu.abc.arithmetic`[🔗](../api/abc/arithmetic.html#).\n",
     "\n",
     "> **Note 📝**: While the propagated constants are usually good enough for step size tuning, they may not always be the tightest estimates.\n",
     "\n",
diff --git a/_sources/references.rst b/_sources/references.rst
index 6aa449f4..3f671cbf 100644
--- a/_sources/references.rst
+++ b/_sources/references.rst
@@ -2,10 +2,10 @@
 ==============
 
 .. [ProxAdam] Melchior, Joseph, Moolekamp. "Proximal Adam: Robust Adaptive Update Scheme for Constrained Optimization" (2020).
-.. .. [ProxAlg] Parikh, Neal, and Stephen Boyd. "Proximal algorithms." Foundations and Trends in optimization 1.3 (2014): 127-239.
+.. [ProxAlg] Parikh, Neal, and Stephen Boyd. "Proximal algorithms." Foundations and Trends in optimization 1.3 (2014): 127-239.
 .. [FirstOrd] Beck, Amir. First-order methods in optimization. Society for Industrial and Applied Mathematics, 2017.
 .. [OnKerLearn] Martins, André FT, et al. "Online multiple kernel learning for structured prediction." arXiv preprint arXiv:1010.2770 (2010).
-.. .. [ProxSplit] Combettes, Patrick L., and Jean-Christophe Pesquet. "Proximal splitting methods in signal processing." Fixed-point algorithms for inverse problems in science and engineering. Springer, New York, NY, 2011. 185-212.
+.. [ProxSplit] Combettes, Patrick L., and Jean-Christophe Pesquet. "Proximal splitting methods in signal processing." Fixed-point algorithms for inverse problems in science and engineering. Springer, New York, NY, 2011. 185-212.
 .. [FuncSphere] Simeoni, Matthieu Martin Jean-Andre. Functional Inverse Problems on Spheres: Theory, Algorithms and Applications. No. THESIS. EPFL, 2020.
 .. [CVS] Condat, Laurent. "A primal–dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms." Journal of Optimization Theory and Applications 158.2 (2013): 460-479.
 .. [PD3O] Yan, Ming. "A new primal-dual algorithm for minimizing the sum of three functions with a linear operator." arXiv preprint arXiv:1611.09805 (2018).
@@ -16,9 +16,9 @@
 .. [APGD] Liang, Jingwei, Tao Luo, and Carola-Bibiane Schönlieb. "Improving" Fast Iterative Shrinkage-Thresholding Algorithm": Faster, Smarter and Greedier." arXiv preprint arXiv:1811.01430 (2018).
 .. [NLCP] Valkonen, Tuomo, "A primal-dual hybrid gradient method for nonlinear operators with applications to MRI." Inverse Problems 30 (2014), 055012, doi:10.1088/0266-5611/30/5/055012.
 .. [PP] Rockafellar, R. Tyrrell. "Monotone operators and the proximal point algorithm." SIAM journal on control and optimization 14.5 (1976): 877-898.
-.. .. [P2] Jain, Raj, and Imrich Chlamtac. "The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations." Communications of the ACM 28.10 (1985): 1076-1085.
-.. .. [GaussProcesses] Rasmussen, Carl Edward, and C. K. Williams. "Gaussian processes for machine learning, vol. 1." (2006).
-.. .. [SubGauss] Aziznejad, Shayan, and Michael Unser. "An L1 representer theorem for multiple-kernel regression." arXiv preprint arXiv:1811.00836 (2018).
+.. [P2] Jain, Raj, and Imrich Chlamtac. "The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations." Communications of the ACM 28.10 (1985): 1076-1085.
+.. [GaussProcesses] Rasmussen, Carl Edward, and C. K. Williams. "Gaussian processes for machine learning, vol. 1." (2006).
+.. [SubGauss] Aziznejad, Shayan, and Michael Unser. "An L1 representer theorem for multiple-kernel regression." arXiv preprint arXiv:1811.00836 (2018).
 .. [FINUFFT] Barnett, Alexander H., Jeremy Magland, and Ludvig af Klinteberg. "A parallel nonuniform fast Fourier transform library based on an “Exponential of semicircle" kernel." SIAM Journal on Scientific Computing 41.5 (2019): C479-C504.
 .. [cuFINUFFT] Shih, Yu-hsuan, et al. "cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs." 2021 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW). IEEE, 2021.
 .. [NumOpt_NocWri] Wright S, Nocedal J. "Numerical optimization". Springer Science. 1999 Apr 3;35(67-68):7.
@@ -26,4 +26,4 @@
 .. [WelfordAlg] Welford, B. P. "Note on a method for calculating corrected sums of squares and products." Technometrics 4.3 (1962): 419-420.
 .. [ULA] Alain Durmus, and Éric Moulines. "Nonasymptotic convergence analysis for the unadjusted Langevin algorithm." The Annals of Applied Probability 27(3) 1551-1587, 2017.
 .. [MYULA] Alain Durmus, Éric Moulines, and Marcelo Pereyra, "Efficient Bayesian Computation by Proximal Markov Chain Monte Carlo: When Langevin Meets Moreau", SIAM Journal of Imaging Science, 2018
-.. .. [UQ_MCMC] Cai, Xiaohao, Marcelo Pereyra, and Jason D. McEwen. "Uncertainty quantification for radio interferometric imaging–I. Proximal MCMC methods." Monthly Notices of the Royal Astronomical Society 480.3 (2018): 4154-4169.
+.. [UQ_MCMC] Cai, Xiaohao, Marcelo Pereyra, and Jason D. McEwen. "Uncertainty quantification for radio interferometric imaging–I. Proximal MCMC methods." Monthly Notices of the Royal Astronomical Society 480.3 (2018): 4154-4169.
diff --git a/_static/.DS_Store b/_static/.DS_Store
deleted file mode 100644
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diff --git a/_static/css/custom.css b/_static/css/custom.css
index 131512f3..651d6d3e 100644
--- a/_static/css/custom.css
+++ b/_static/css/custom.css
@@ -60,6 +60,11 @@ background: linear-gradient(to right, var(--pst-color-primary), rgb(245, 188, 71
 -webkit-text-fill-color: transparent;
 }
 
+h2 code {
+  -webkit-background-clip: initial;
+  -webkit-text-fill-color: initial;
+  color: var(--pst-color-primary);
+}
 
 .navbar-icon-links img.icon-link-image {
     border-radius: 0rem;
diff --git a/_static/documentation_options.js b/_static/documentation_options.js
index 612f5a96..ac6da9ee 100644
--- a/_static/documentation_options.js
+++ b/_static/documentation_options.js
@@ -1,5 +1,5 @@
 const DOCUMENTATION_OPTIONS = {
-    VERSION: '1.0.1.dev1',
+    VERSION: '1.0.1.dev58',
     LANGUAGE: 'en',
     COLLAPSE_INDEX: false,
     BUILDER: 'html',
diff --git a/_static/pygments.css b/_static/pygments.css
index f188c252..4f5fd852 100644
--- a/_static/pygments.css
+++ b/_static/pygments.css
@@ -22,7 +22,6 @@ html[data-theme="light"] .highlight .c1 { color: #8f5902; font-style: italic } /
 html[data-theme="light"] .highlight .cs { color: #8f5902; font-style: italic } /* Comment.Special */
 html[data-theme="light"] .highlight .gd { color: #a40000 } /* Generic.Deleted */
 html[data-theme="light"] .highlight .ge { color: #000000; font-style: italic } /* Generic.Emph */
-html[data-theme="light"] .highlight .ges { color: #000000; font-weight: bold; font-style: italic } /* Generic.EmphStrong */
 html[data-theme="light"] .highlight .gr { color: #ef2929 } /* Generic.Error */
 html[data-theme="light"] .highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
 html[data-theme="light"] .highlight .gi { color: #00A000 } /* Generic.Inserted */
diff --git a/api/abc.html b/api/abc.html
index ef9062d0..470de0ba 100644
--- a/api/abc.html
+++ b/api/abc.html
@@ -18,7 +18,7 @@
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" rel="preload" type="font/woff2"/>
-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
 <link href="../_static/sphinx-codeautolink.css?v=125d5c1c" rel="stylesheet" type="text/css"/>
 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -28,11 +28,11 @@
 <link href="../_static/sg_gallery-dataframe.css?v=2082cf3c" rel="stylesheet" type="text/css"/>
 <link href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" rel="stylesheet" type="text/css"/>
 <link href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" rel="stylesheet" type="text/css"/>
-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
 <!-- Pre-loaded scripts that we'll load fully later -->
 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
 <link as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" rel="preload"/>
-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
 <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -139,7 +139,7 @@
 <label class="sr-only">PyPI</label></a>
 </li>
 <li class="nav-item">
-<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="mailto: matthieu.simeoni@gmail.com" rel="noopener" target="_blank" title="Contact"><span><i class="fa-brands fa-telegram"></i></span>
+<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="mailto: contact@pyxu.org" rel="noopener" target="_blank" title="Contact"><span><i class="fa-brands fa-telegram"></i></span>
 <label class="sr-only">Contact</label></a>
 </li>
 <li class="nav-item">
@@ -212,7 +212,7 @@
 <label class="sr-only">PyPI</label></a>
 </li>
 <li class="nav-item">
-<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="mailto: matthieu.simeoni@gmail.com" rel="noopener" target="_blank" title="Contact"><span><i class="fa-brands fa-telegram"></i></span>
+<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="mailto: contact@pyxu.org" rel="noopener" target="_blank" title="Contact"><span><i class="fa-brands fa-telegram"></i></span>
 <label class="sr-only">Contact</label></a>
 </li>
 <li class="nav-item">
@@ -229,7 +229,13 @@
 <li class="toctree-l1"><a class="reference internal" href="info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1"><a class="reference internal" href="operator.html">pyxu.operator</a></li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="operator/blocks.html">pyxu.operator.blocks</a></li>
+<li class="toctree-l2"><a class="reference internal" href="operator/func.html">pyxu.operator.func</a></li>
+<li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
+<li class="toctree-l2"><a class="reference internal" href="operator/map.html">pyxu.operator.map</a></li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="operator.interop.html">pyxu.operator.interop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="opt.solver.html">pyxu.opt.solver</a></li>
 <li class="toctree-l1"><a class="reference internal" href="opt.stop.html">pyxu.opt.stop</a></li>
@@ -272,493 +278,149 @@
 <article class="bd-article" role="main">
 <section id="pyxu-abc">
 <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">#</a></h1>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.Solver">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Solver</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">folder</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">exist_ok</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stop_rate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">writeback_rate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">verbosity</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_progress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log_var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
-<p>Iterative solver for minimization problems of the form <span class="math notranslate nohighlight">\(\hat{x} = \arg\min_{x \in \mathbb{R}^{N}}
-\mathcal{F}(x)\)</span>, where the form of <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is solver-dependent.</p>
-<p>Solver provides a versatile API for solving optimisation problems, with the following features:</p>
-<ul class="simple">
-<li><p>manual/automatic/background execution of solver iterations via parameters provided to
-<a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>. (See below.)</p></li>
-<li><p>automatic checkpointing of solver progress, providing a safe restore point in case of faulty numerical code.  Each
-solver instance backs its state and final output to a folder on disk for post-analysis.  In particular
-<a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> will never crash: detailed exception information will always be available in a
-logfile for post-analysis.</p></li>
-<li><p>arbitrary specification of complex stopping criteria via the <a class="reference internal" href="#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a> class.</p></li>
-<li><p>solve for multiple initial points in parallel.</p></li>
-</ul>
-<p>To implement a new iterative solver, users need to sub-class <a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> and overwrite the methods
-below:</p>
+<nav class="contents local" id="table-of-contents">
+<p class="topic-title">Table of Contents</p>
 <ul class="simple">
-<li><p><a class="reference internal" href="#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code></a></p></li>
-<li><p><a class="reference internal" href="#pyxu.abc.Solver.m_init" title="pyxu.abc.Solver.m_init"><code class="xref py py-meth docutils literal notranslate"><span class="pre">m_init()</span></code></a>  [i.e. math-init()]</p></li>
-<li><p><a class="reference internal" href="#pyxu.abc.Solver.m_step" title="pyxu.abc.Solver.m_step"><code class="xref py py-meth docutils literal notranslate"><span class="pre">m_step()</span></code></a>  [i.e. math-step()]</p></li>
-<li><p><a class="reference internal" href="#pyxu.abc.Solver.default_stop_crit" title="pyxu.abc.Solver.default_stop_crit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">default_stop_crit()</span></code></a>  [optional; see method definition for details]</p></li>
-<li><p><a class="reference internal" href="#pyxu.abc.Solver.objective_func" title="pyxu.abc.Solver.objective_func"><code class="xref py py-meth docutils literal notranslate"><span class="pre">objective_func()</span></code></a>  [optional; see method definition for details]</p></li>
-</ul>
-<p>Advanced functionalities of <a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> are automatically inherited by sub-classes.</p>
-<p class="rubric">Examples</p>
-<p>Here are examples on how to solve minimization problems with this class:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">slvr</span> <span class="o">=</span> <span class="n">Solver</span><span class="p">()</span>
-
-<span class="c1">### 1. Blocking mode: .fit() does not return until solver has stopped.</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">mode</span><span class="o">=</span><span class="n">SolverMode</span><span class="o">.</span><span class="n">BLOCK</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="n">data</span><span class="p">,</span> <span class="n">hist</span> <span class="o">=</span> <span class="n">slvr</span><span class="o">.</span><span class="n">stats</span><span class="p">()</span>  <span class="c1"># final output of solver.</span>
-
-<span class="c1">### 2. Async mode: solver iterations run in the background.</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">mode</span><span class="o">=</span><span class="n">SolverMode</span><span class="o">.</span><span class="n">ASYNC</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="nb">print</span><span class="p">(</span><span class="s1">'test'</span><span class="p">)</span>  <span class="c1"># you can do something in between.</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">busy</span><span class="p">()</span>  <span class="c1"># or check whether the solver already stopped.</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">stop</span><span class="p">()</span>  <span class="c1"># and preemptively force it to stop.</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="n">data</span><span class="p">,</span> <span class="n">hist</span> <span class="o">=</span> <span class="n">slvr</span><span class="o">.</span><span class="n">stats</span><span class="p">()</span>  <span class="c1"># then query the result after a (potential) force-stop.</span>
-
-<span class="c1">### 3. Manual mode: fine-grain control of solver data per iteration.</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">mode</span><span class="o">=</span><span class="n">SolverMode</span><span class="o">.</span><span class="n">MANUAL</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="k">for</span> <span class="n">data</span> <span class="ow">in</span> <span class="n">slvr</span><span class="o">.</span><span class="n">steps</span><span class="p">():</span>
-<span class="o">...</span>     <span class="c1"># Do something with the logged variables after each iteration.</span>
-<span class="o">...</span>     <span class="k">pass</span>  <span class="c1"># solver has stopped after the loop.</span>
-<span class="o">&gt;&gt;&gt;</span> <span class="n">data</span><span class="p">,</span> <span class="n">hist</span> <span class="o">=</span> <span class="n">slvr</span><span class="o">.</span><span class="n">stats</span><span class="p">()</span>  <span class="c1"># final output of solver.</span>
-</pre></div>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>folder</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/pathlib.html#pathlib.Path" title="(in Python v3.11)"><em>Path</em></a>) – </p></li>
-<li><p><strong>exist_ok</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-<li><p><strong>stop_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p></li>
-<li><p><strong>writeback_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p></li>
-<li><p><strong>verbosity</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p></li>
-<li><p><strong>show_progress</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-<li><p><strong>log_var</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
+<li><p><a class="reference internal" href="#pyxu-abc-arithmetic" id="id3">pyxu.abc.arithmetic</a></p></li>
+<li><p><a class="reference internal" href="#pyxu-abc-operator" id="id4">pyxu.abc.operator</a></p></li>
+<li><p><a class="reference internal" href="#pyxu-abc-solver" id="id5">pyxu.abc.solver</a></p></li>
 </ul>
+</nav>
+<section id="pyxu-abc-arithmetic">
+<h2><a class="toc-backref" href="#id3" role="doc-backlink">pyxu.abc.arithmetic</a><a class="headerlink" href="#pyxu-abc-arithmetic" title="Link to this heading">#</a></h2>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.arithmetic.Rule">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Rule</span></span><a class="reference internal" href="../_modules/pyxu/abc/arithmetic.html#Rule"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.arithmetic.Rule" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
+<p>General arithmetic rule.</p>
+<p>This class defines default arithmetic rules applicable unless re-defined by sub-classes.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.arithmetic.Rule.op">
+<span class="sig-name descname"><span class="pre">op</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/arithmetic.html#Rule.op"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.arithmetic.Rule.op" title="Link to this definition">#</a></dt>
+<dd><dl class="field-list simple">
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>op</strong> – Synthesize operator.</p>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
 </dd>
 </dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.abc.Solver._mstate">
-<span class="sig-name descname"><span class="pre">_mstate</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><span class="pre">dict</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><span class="pre">Any</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#pyxu.abc.Solver._mstate" title="Link to this definition">#</a></dt>
-<dd><p>Mathematical state.</p>
 </dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.abc.Solver._astate">
-<span class="sig-name descname"><span class="pre">_astate</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><span class="pre">dict</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><span class="pre">Any</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#pyxu.abc.Solver._astate" title="Link to this definition">#</a></dt>
-<dd><p>Book-keeping (non-math) state.</p>
 </dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">folder</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">exist_ok</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stop_rate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">writeback_rate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">verbosity</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_progress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log_var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.arithmetic.ScaleRule">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ScaleRule</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cst</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/arithmetic.html#ScaleRule"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.arithmetic.ScaleRule" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.arithmetic.Rule" title="pyxu.abc.arithmetic.Rule"><code class="xref py py-class docutils literal notranslate"><span class="pre">Rule</span></code></a></p>
+<p>Arithmetic rules for element-wise scaling: <span class="math notranslate nohighlight">\(B(x) = \alpha A(x)\)</span>.</p>
+<p>Special Cases:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>\<span class="n">alpha</span> <span class="o">=</span> <span class="mi">0</span>  <span class="o">=&gt;</span> <span class="n">NullOp</span><span class="o">/</span><span class="n">NullFunc</span>
+\<span class="n">alpha</span> <span class="o">=</span> <span class="mi">1</span>  <span class="o">=&gt;</span> <span class="bp">self</span>
+</pre></div>
+</div>
+<p>Else:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>|--------------------------|-------------|--------------------------------------------------------------------|
+|         Property         |  Preserved? |                     Arithmetic Update Rule(s)                      |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| CAN_EVAL                 | yes         | op_new.apply(arr) = op_old.apply(arr) * \alpha                     |
+|                          |             | op_new.lipschitz = op_old.lipschitz * abs(\alpha)                  |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| FUNCTIONAL               | yes         | op_new.asloss(\beta) = op_old.asloss(\beta) * \alpha               |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| PROXIMABLE               | \alpha &gt; 0  | op_new.prox(arr, tau) = op_old.prox(arr, tau * \alpha)             |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| DIFFERENTIABLE           | yes         | op_new.jacobian(arr) = op_old.jacobian(arr) * \alpha               |
+|                          |             | op_new.diff_lipschitz = op_old.diff_lipschitz * abs(\alpha)        |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| DIFFERENTIABLE_FUNCTION  | yes         | op_new.grad(arr) = op_old.grad(arr) * \alpha                       |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| QUADRATIC                | \alpha &gt; 0  | Q, c, t = op_old._quad_spec()                                      |
+|                          |             | op_new._quad_spec() = (\alpha * Q, \alpha * c, \alpha * t)         |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| LINEAR                   | yes         | op_new.adjoint(arr) = op_old.adjoint(arr) * \alpha                 |
+|                          |             | op_new.asarray() = op_old.asarray() * \alpha                       |
+|                          |             | op_new.svdvals() = op_old.svdvals() * abs(\alpha)                  |
+|                          |             | op_new.pinv(x, damp) = op_old.pinv(x, damp / (\alpha**2)) / \alpha |
+|                          |             | op_new.gram() = op_old.gram() * (\alpha**2)                        |
+|                          |             | op_new.cogram() = op_old.cogram() * (\alpha**2)                    |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| LINEAR_SQUARE            | yes         | op_new.trace() = op_old.trace() * \alpha                           |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| LINEAR_NORMAL            | yes         |                                                                    |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| LINEAR_UNITARY           | \alpha = -1 |                                                                    |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| LINEAR_SELF_ADJOINT      | yes         |                                                                    |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| LINEAR_POSITIVE_DEFINITE | \alpha &gt; 0  |                                                                    |
+|--------------------------|-------------|--------------------------------------------------------------------|
+| LINEAR_IDEMPOTENT        | no          |                                                                    |
+|--------------------------|-------------|--------------------------------------------------------------------|
+</pre></div>
+</div>
+<dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>folder</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Path" title="pyxu.info.ptype.Path"><code class="xref py py-class docutils literal notranslate"><span class="pre">Path</span></code></a>) – Directory on disk where instance data should be stored.  A location will be automatically chosen if
-unspecified. (Default: OS-dependent tempdir.)</p></li>
-<li><p><strong>exist_ok</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="code docutils literal notranslate"><span class="pre">folder</span></code> is specified and <code class="code docutils literal notranslate"><span class="pre">exist_ok</span></code> is false (default), <a class="reference external" href="https://docs.python.org/3/library/exceptions.html#FileExistsError" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">FileExistsError</span></code></a> is raised if the
-target directory already exists.</p></li>
-<li><p><strong>stop_rate</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Rate at which solver evaluates stopping criteria.</p></li>
-<li><p><strong>writeback_rate</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Rate at which solver checkpoints are written to disk.  No checkpointing is done if unspecified: only the
-final solver output will be written back to disk.  Must be a multiple of <code class="code docutils literal notranslate"><span class="pre">stop_rate</span></code> if specified.</p></li>
-<li><p><strong>verbosity</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Rate at which stopping criteria statistics are logged.  Must be a multiple of <code class="code docutils literal notranslate"><span class="pre">stop_rate</span></code>.  Defaults to
-<code class="code docutils literal notranslate"><span class="pre">stop_rate</span></code> if unspecified.</p></li>
-<li><p><strong>show_progress</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If True (default) and <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> is run with mode=BLOCK, then statistics are also
-logged to stdout.</p></li>
-<li><p><strong>log_var</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variables from the solver’s math-state (<a class="reference internal" href="#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">_mstate</span></code></a>) to be logged per iteration.
-These are the variables made available when calling <a class="reference internal" href="#pyxu.abc.Solver.stats" title="pyxu.abc.Solver.stats"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stats()</span></code></a>.</p></li>
+<li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
+<li><p><strong>cst</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 </ul>
 </dd>
 </dl>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p>Partial device&lt;&gt;CPU synchronization takes place when stopping-criteria are evaluated.  Increasing <code class="code docutils literal notranslate"><span class="pre">stop_rate</span></code>
-is advised to reduce the effect of such transfers when applicable.</p></li>
-<li><p>Full device&lt;&gt;CPU synchronization takes place at checkpoint-time.  Increasing <code class="code docutils literal notranslate"><span class="pre">writeback_rate</span></code> is advised to
-reduce the effect of such transfers when applicable.</p></li>
-</ul>
 </dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.fit">
-<span class="sig-name descname"><span class="pre">fit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.fit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.fit" title="Link to this definition">#</a></dt>
-<dd><p>Solve minimization problem(s) defined in <a class="reference internal" href="#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code></a>, with the provided run-specifc
-parameters.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.arithmetic.ArgScaleRule">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ArgScaleRule</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cst</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/arithmetic.html#ArgScaleRule"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.arithmetic.ArgScaleRule" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.arithmetic.Rule" title="pyxu.abc.arithmetic.Rule"><code class="xref py py-class docutils literal notranslate"><span class="pre">Rule</span></code></a></p>
+<p>Arithmetic rules for element-wise parameter scaling: <span class="math notranslate nohighlight">\(B(x) = A(\alpha x)\)</span>.</p>
+<p>Special Cases:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>\<span class="n">alpha</span> <span class="o">=</span> <span class="mi">0</span>  <span class="o">=&gt;</span> <span class="n">ConstantValued</span> <span class="p">(</span><span class="n">w</span><span class="o">/</span> <span class="n">potential</span> <span class="n">vector</span><span class="o">-</span><span class="n">valued</span> <span class="n">output</span><span class="p">)</span>
+\<span class="n">alpha</span> <span class="o">=</span> <span class="mi">1</span>  <span class="o">=&gt;</span> <span class="bp">self</span>
+</pre></div>
+</div>
+<p>Else:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>|--------------------------|-------------|-----------------------------------------------------------------------------|
+|         Property         |  Preserved? |                          Arithmetic Update Rule(s)                          |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| CAN_EVAL                 | yes         | op_new.apply(arr) = op_old.apply(arr * \alpha)                              |
+|                          |             | op_new.lipschitz = op_old.lipschitz * abs(\alpha)                           |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| FUNCTIONAL               | yes         | op_new.asloss(\beta) = AMBIGUOUS -&gt; DISABLED                                |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| PROXIMABLE               | yes         | op_new.prox(arr, tau) = op_old.prox(\alpha * arr, \alpha**2 * tau) / \alpha |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| DIFFERENTIABLE           | yes         | op_new.diff_lipschitz = op_old.diff_lipschitz * (\alpha**2)                 |
+|                          |             | op_new.jacobian(arr) = op_old.jacobian(arr * \alpha) * \alpha               |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| DIFFERENTIABLE_FUNCTION  | yes         | op_new.grad(arr) = op_old.grad(\alpha * arr) * \alpha                       |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| QUADRATIC                | yes         | Q, c, t = op_old._quad_spec()                                               |
+|                          |             | op_new._quad_spec() = (\alpha**2 * Q, \alpha * c, t)                        |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| LINEAR                   | yes         | op_new.adjoint(arr) = op_old.adjoint(arr) * \alpha                          |
+|                          |             | op_new.asarray() = op_old.asarray() * \alpha                                |
+|                          |             | op_new.svdvals() = op_old.svdvals() * abs(\alpha)                           |
+|                          |             | op_new.pinv(x, damp) = op_old.pinv(x, damp / (\alpha**2)) / \alpha          |
+|                          |             | op_new.gram() = op_old.gram() * (\alpha**2)                                 |
+|                          |             | op_new.cogram() = op_old.cogram() * (\alpha**2)                             |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| LINEAR_SQUARE            | yes         | op_new.trace() = op_old.trace() * \alpha                                    |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| LINEAR_NORMAL            | yes         |                                                                             |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| LINEAR_UNITARY           | \alpha = -1 |                                                                             |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| LINEAR_SELF_ADJOINT      | yes         |                                                                             |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| LINEAR_POSITIVE_DEFINITE | \alpha &gt; 0  |                                                                             |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+| LINEAR_IDEMPOTENT        | no          |                                                                             |
+|--------------------------|-------------|-----------------------------------------------------------------------------|
+</pre></div>
+</div>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>kwargs</strong> – See class-level docstring for class-specific keyword parameters.</p></li>
-<li><p><strong>stop_crit</strong> (<a class="reference internal" href="#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a>) – Stopping criterion to end solver iterations.  If unspecified, defaults to
-<a class="reference internal" href="#pyxu.abc.Solver.default_stop_crit" title="pyxu.abc.Solver.default_stop_crit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">default_stop_crit()</span></code></a>.</p></li>
-<li><p><strong>mode</strong> (<a class="reference internal" href="#pyxu.abc.SolverMode" title="pyxu.abc.SolverMode"><code class="xref py py-class docutils literal notranslate"><span class="pre">SolverMode</span></code></a>) – <p>Execution mode.
-See <a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> for usage examples.</p>
-<p>Useful method pairs depending on the execution mode:</p>
-<ul>
-<li><p>BLOCK: <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a></p></li>
-<li><p>ASYNC: <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>, <a class="reference internal" href="#pyxu.abc.Solver.busy" title="pyxu.abc.Solver.busy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">busy()</span></code></a>, <a class="reference internal" href="#pyxu.abc.Solver.stop" title="pyxu.abc.Solver.stop"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stop()</span></code></a></p></li>
-<li><p>MANUAL: <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>, <a class="reference internal" href="#pyxu.abc.Solver.steps" title="pyxu.abc.Solver.steps"><code class="xref py py-meth docutils literal notranslate"><span class="pre">steps()</span></code></a></p></li>
-</ul>
-</p></li>
-<li><p><strong>track_objective</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Auto-compute objective function every time stopping criterion is evaluated.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.m_init">
-<span class="sig-name descname"><span class="pre">m_init</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.m_init"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.m_init" title="Link to this definition">#</a></dt>
-<dd><p>Set solver’s initial mathematical state based on kwargs provided to <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>.</p>
-<p>This method must only manipulate <a class="reference internal" href="#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">_mstate</span></code></a>.</p>
-<p>After calling this method, the solver must be able to complete its 1st iteration via a call to
-<a class="reference internal" href="#pyxu.abc.Solver.m_step" title="pyxu.abc.Solver.m_step"><code class="xref py py-meth docutils literal notranslate"><span class="pre">m_step()</span></code></a>.</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.m_step">
-<span class="sig-name descname"><span class="pre">m_step</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.m_step"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.m_step" title="Link to this definition">#</a></dt>
-<dd><p>Perform one (mathematical) step.</p>
-<p>This method must only manipulate <a class="reference internal" href="#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">_mstate</span></code></a>.</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.steps">
-<span class="sig-name descname"><span class="pre">steps</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.steps"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.steps" title="Link to this definition">#</a></dt>
-<dd><p>Generator of logged variables after each iteration.</p>
-<p>The i-th call to <a class="reference external" href="https://docs.python.org/3/library/functions.html#next" title="(in Python v3.11)"><code class="xref py py-func docutils literal notranslate"><span class="pre">next()</span></code></a> on this object returns the logged variables after the i-th solver iteration.</p>
-<p>This method is only usable after calling <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> with mode=MANUAL.  See
-<a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> for usage examples.</p>
-<p>There is no guarantee that a checkpoint on disk exists when the generator is exhausted.  (Reason: potential
-exceptions raised during solver’s progress.) Users should invoke <a class="reference internal" href="#pyxu.abc.Solver.writeback" title="pyxu.abc.Solver.writeback"><code class="xref py py-meth docutils literal notranslate"><span class="pre">writeback()</span></code></a>
-afterwards if needed.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>n</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – <p>Maximum number of <a class="reference external" href="https://docs.python.org/3/library/functions.html#next" title="(in Python v3.11)"><code class="xref py py-func docutils literal notranslate"><span class="pre">next()</span></code></a> calls allowed before exhausting the generator.  Defaults to infinity if
-unspecified.</p>
-<p>The generator will terminate prematurely if the solver naturally stops before <code class="code docutils literal notranslate"><span class="pre">n</span></code> calls to <a class="reference external" href="https://docs.python.org/3/library/functions.html#next" title="(in Python v3.11)"><code class="xref py py-func docutils literal notranslate"><span class="pre">next()</span></code></a>
-are made.</p>
-</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Generator" title="(in Python v3.11)"><em>Generator</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.stats">
-<span class="sig-name descname"><span class="pre">stats</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.stats"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.stats" title="Link to this definition">#</a></dt>
-<dd><p>Query solver state.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><ul class="simple">
-<li><p><strong>data</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Value(s) of <code class="docutils literal notranslate"><span class="pre">log_var</span></code> (s) after last iteration.</p></li>
-<li><p><strong>history</strong> (<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v1.25)"><code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – (N_iter,) records of stopping-criteria values per iteration.</p></li>
-</ul>
-</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)">tuple</a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)">dict</a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)">str</a>, <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a> | <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a> | None], <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v1.25)"><em>ndarray</em></a> | None]</p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>If any of the <code class="docutils literal notranslate"><span class="pre">log_var</span></code> (s) and/or <code class="docutils literal notranslate"><span class="pre">history</span></code> are not (yet) known at query time, <code class="docutils literal notranslate"><span class="pre">None</span></code> is returned.</p>
-</dd></dl>
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.workdir">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">workdir</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/pathlib.html#pathlib.Path" title="(in Python v3.11)"><span class="pre">Path</span></a></em><a class="headerlink" href="#pyxu.abc.Solver.workdir" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>wd</strong> – Absolute path to the directory on disk where instance data is stored.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Path" title="pyxu.info.ptype.Path"><code class="xref py py-class docutils literal notranslate"><span class="pre">Path</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.logfile">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">logfile</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/pathlib.html#pathlib.Path" title="(in Python v3.11)"><span class="pre">Path</span></a></em><a class="headerlink" href="#pyxu.abc.Solver.logfile" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>lf</strong> – Absolute path to the log file on disk where stopping criteria statistics are logged.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Path" title="pyxu.info.ptype.Path"><code class="xref py py-class docutils literal notranslate"><span class="pre">Path</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.datafile">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">datafile</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/pathlib.html#pathlib.Path" title="(in Python v3.11)"><span class="pre">Path</span></a></em><a class="headerlink" href="#pyxu.abc.Solver.datafile" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>df</strong> – Absolute path to the file on disk where <code class="docutils literal notranslate"><span class="pre">log_var</span></code> (s) are stored during checkpointing or after solver has
-stopped.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Path" title="pyxu.info.ptype.Path"><code class="xref py py-class docutils literal notranslate"><span class="pre">Path</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.busy">
-<span class="sig-name descname"><span class="pre">busy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.busy"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.busy" title="Link to this definition">#</a></dt>
-<dd><p>Test if an async-running solver has stopped.</p>
-<p>This method is only usable after calling <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> with mode=ASYNC.  See
-<a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> for usage examples.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>b</strong> – True if solver has stopped, False otherwise.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.solution">
-<span class="sig-name descname"><span class="pre">solution</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.solution"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.solution" title="Link to this definition">#</a></dt>
-<dd><p>Output the “solution” of the optimization problem.</p>
-<p>This is a helper method intended for novice users.  The return type is sub-class dependent, so don’t write an
-API using this: use <a class="reference internal" href="#pyxu.abc.Solver.stats" title="pyxu.abc.Solver.stats"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stats()</span></code></a> instead.</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.stop">
-<span class="sig-name descname"><span class="pre">stop</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.stop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.stop" title="Link to this definition">#</a></dt>
-<dd><p>Stop an async-running solver.</p>
-<p>This method is only usable after calling <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> with mode=ASYNC.  See
-<a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> for usage examples.</p>
-<p>This method will block until the solver has stopped.</p>
-<p>There is no guarantee that a checkpoint on disk exists once halted.  (Reason: potential exceptions raised during
-solver’s progress.) Users should invoke <a class="reference internal" href="#pyxu.abc.Solver.writeback" title="pyxu.abc.Solver.writeback"><code class="xref py py-meth docutils literal notranslate"><span class="pre">writeback()</span></code></a> afterwards if needed.</p>
-<p>Users must call this method to terminate an async-solver, even if <a class="reference internal" href="#pyxu.abc.Solver.busy" title="pyxu.abc.Solver.busy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">busy()</span></code></a> is False.</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.writeback">
-<span class="sig-name descname"><span class="pre">writeback</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.writeback"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.writeback" title="Link to this definition">#</a></dt>
-<dd><p>Checkpoint state to disk.</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.default_stop_crit">
-<span class="sig-name descname"><span class="pre">default_stop_crit</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.default_stop_crit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.default_stop_crit" title="Link to this definition">#</a></dt>
-<dd><p>Default stopping criterion for solver if unspecified in <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> calls.</p>
-<p>Sub-classes are expected to overwrite this method.  If not overridden, then omitting the <code class="code docutils literal notranslate"><span class="pre">stop_crit</span></code> parameter
-in <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> is forbidden.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><em>StoppingCriterion</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.Solver.objective_func">
-<span class="sig-name descname"><span class="pre">objective_func</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.objective_func"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.objective_func" title="Link to this definition">#</a></dt>
-<dd><p>Evaluate objective function given current math state.</p>
-<p>The output array must have shape:</p>
-<ul class="simple">
-<li><p>(1,) if evaluated at 1 point,</p></li>
-<li><p>(N, 1) if evaluated at N different points.</p></li>
-</ul>
-<p>Sub-classes are expected to overwrite this method.  If not overridden, then enabling <code class="code docutils literal notranslate"><span class="pre">track_objective</span></code> in
-<a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> is forbidden.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.SolverMode">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SolverMode</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">names</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">module</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">qualname</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">boundary</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#SolverMode"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SolverMode" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/enum.html#enum.Enum" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Enum</span></code></a></p>
-<p>Solver execution mode.</p>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.abc.SolverMode.BLOCK">
-<span class="sig-name descname"><span class="pre">BLOCK</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">1</span></em><a class="headerlink" href="#pyxu.abc.SolverMode.BLOCK" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.abc.SolverMode.MANUAL">
-<span class="sig-name descname"><span class="pre">MANUAL</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">2</span></em><a class="headerlink" href="#pyxu.abc.SolverMode.MANUAL" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.abc.SolverMode.ASYNC">
-<span class="sig-name descname"><span class="pre">ASYNC</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">3</span></em><a class="headerlink" href="#pyxu.abc.SolverMode.ASYNC" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.StoppingCriterion">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">StoppingCriterion</span></span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#StoppingCriterion"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.StoppingCriterion" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
-<p>State machines (SM) which decide when to stop iterative solvers by examining their mathematical state.</p>
-<p>SM decisions are always accompanied by at least one numerical statistic. These stats may be queried by solvers via
-<a class="reference internal" href="#pyxu.abc.StoppingCriterion.info" title="pyxu.abc.StoppingCriterion.info"><code class="xref py py-meth docutils literal notranslate"><span class="pre">info()</span></code></a> to provide diagnostic information to users.</p>
-<p>Composite stopping criteria can be implemented via the overloaded (and[<code class="docutils literal notranslate"><span class="pre">&amp;</span></code>], or[<code class="docutils literal notranslate"><span class="pre">|</span></code>]) operators.</p>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.StoppingCriterion.stop">
-<span class="sig-name descname"><span class="pre">stop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">state</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#StoppingCriterion.stop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.StoppingCriterion.stop" title="Link to this definition">#</a></dt>
-<dd><p>Compute a stop signal based on the current mathematical state.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>state</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – <p>Full mathematical state of solver at some iteration, i.e. <a class="reference internal" href="#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">_mstate</span></code></a>.</p>
-<p>Values from <code class="code docutils literal notranslate"><span class="pre">state</span></code> may be cached inside the instance to form complex stopping conditions.</p>
-</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>s</strong> – True if no further iterations should be performed, False otherwise.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.StoppingCriterion.info">
-<span class="sig-name descname"><span class="pre">info</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#StoppingCriterion.info"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.StoppingCriterion.info" title="Link to this definition">#</a></dt>
-<dd><p>Get statistics associated with the last call to <a class="reference internal" href="#pyxu.abc.StoppingCriterion.stop" title="pyxu.abc.StoppingCriterion.stop"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stop()</span></code></a>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>data</strong></p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.StoppingCriterion.clear">
-<span class="sig-name descname"><span class="pre">clear</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#StoppingCriterion.clear"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.StoppingCriterion.clear" title="Link to this definition">#</a></dt>
-<dd><p>Clear SM state (if any).</p>
-<p>This method is useful when a <a class="reference internal" href="#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a> instance must be reused in another call to
-<a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>.</p>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.arithmetic.Rule">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Rule</span></span><a class="reference internal" href="../_modules/pyxu/abc/arithmetic.html#Rule"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.arithmetic.Rule" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
-<p>General arithmetic rule.</p>
-<p>This class defines default arithmetic rules applicable unless re-defined by sub-classes.</p>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.arithmetic.Rule.op">
-<span class="sig-name descname"><span class="pre">op</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/arithmetic.html#Rule.op"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.arithmetic.Rule.op" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> – Synthesize operator.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.arithmetic.ScaleRule">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ScaleRule</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cst</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/arithmetic.html#ScaleRule"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.arithmetic.ScaleRule" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.arithmetic.Rule" title="pyxu.abc.arithmetic.Rule"><code class="xref py py-class docutils literal notranslate"><span class="pre">Rule</span></code></a></p>
-<p>Arithmetic rules for element-wise scaling: <span class="math notranslate nohighlight">\(B(x) = \alpha A(x)\)</span>.</p>
-<p>Special Cases:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>\<span class="n">alpha</span> <span class="o">=</span> <span class="mi">0</span>  <span class="o">=&gt;</span> <span class="n">NullOp</span><span class="o">/</span><span class="n">NullFunc</span>
-\<span class="n">alpha</span> <span class="o">=</span> <span class="mi">1</span>  <span class="o">=&gt;</span> <span class="bp">self</span>
-</pre></div>
-</div>
-<p>Else:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>|--------------------------|-------------|--------------------------------------------------------------------|
-|         Property         |  Preserved? |                     Arithmetic Update Rule(s)                      |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| CAN_EVAL                 | yes         | op_new.apply(arr) = op_old.apply(arr) * \alpha                     |
-|                          |             | op_new.lipschitz = op_old.lipschitz * abs(\alpha)                  |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| FUNCTIONAL               | yes         | op_new.asloss(\beta) = op_old.asloss(\beta) * \alpha               |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| PROXIMABLE               | \alpha &gt; 0  | op_new.prox(arr, tau) = op_old.prox(arr, tau * \alpha)             |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| DIFFERENTIABLE           | yes         | op_new.jacobian(arr) = op_old.jacobian(arr) * \alpha               |
-|                          |             | op_new.diff_lipschitz = op_old.diff_lipschitz * abs(\alpha)        |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| DIFFERENTIABLE_FUNCTION  | yes         | op_new.grad(arr) = op_old.grad(arr) * \alpha                       |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| QUADRATIC                | \alpha &gt; 0  | Q, c, t = op_old._quad_spec()                                      |
-|                          |             | op_new._quad_spec() = (\alpha * Q, \alpha * c, \alpha * t)         |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| LINEAR                   | yes         | op_new.adjoint(arr) = op_old.adjoint(arr) * \alpha                 |
-|                          |             | op_new.asarray() = op_old.asarray() * \alpha                       |
-|                          |             | op_new.svdvals() = op_old.svdvals() * abs(\alpha)                  |
-|                          |             | op_new.pinv(x, damp) = op_old.pinv(x, damp / (\alpha**2)) / \alpha |
-|                          |             | op_new.gram() = op_old.gram() * (\alpha**2)                        |
-|                          |             | op_new.cogram() = op_old.cogram() * (\alpha**2)                    |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| LINEAR_SQUARE            | yes         | op_new.trace() = op_old.trace() * \alpha                           |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| LINEAR_NORMAL            | yes         |                                                                    |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| LINEAR_UNITARY           | \alpha = -1 |                                                                    |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| LINEAR_SELF_ADJOINT      | yes         |                                                                    |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| LINEAR_POSITIVE_DEFINITE | \alpha &gt; 0  |                                                                    |
-|--------------------------|-------------|--------------------------------------------------------------------|
-| LINEAR_IDEMPOTENT        | no          |                                                                    |
-|--------------------------|-------------|--------------------------------------------------------------------|
-</pre></div>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
-<li><p><strong>cst</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.arithmetic.ArgScaleRule">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ArgScaleRule</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cst</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/arithmetic.html#ArgScaleRule"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.arithmetic.ArgScaleRule" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.arithmetic.Rule" title="pyxu.abc.arithmetic.Rule"><code class="xref py py-class docutils literal notranslate"><span class="pre">Rule</span></code></a></p>
-<p>Arithmetic rules for element-wise parameter scaling: <span class="math notranslate nohighlight">\(B(x) = A(\alpha x)\)</span>.</p>
-<p>Special Cases:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>\<span class="n">alpha</span> <span class="o">=</span> <span class="mi">0</span>  <span class="o">=&gt;</span> <span class="n">ConstantValued</span> <span class="p">(</span><span class="n">w</span><span class="o">/</span> <span class="n">potential</span> <span class="n">vector</span><span class="o">-</span><span class="n">valued</span> <span class="n">output</span><span class="p">)</span>
-\<span class="n">alpha</span> <span class="o">=</span> <span class="mi">1</span>  <span class="o">=&gt;</span> <span class="bp">self</span>
-</pre></div>
-</div>
-<p>Else:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>|--------------------------|-------------|-----------------------------------------------------------------------------|
-|         Property         |  Preserved? |                          Arithmetic Update Rule(s)                          |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| CAN_EVAL                 | yes         | op_new.apply(arr) = op_old.apply(arr * \alpha)                              |
-|                          |             | op_new.lipschitz = op_old.lipschitz * abs(\alpha)                           |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| FUNCTIONAL               | yes         | op_new.asloss(\beta) = AMBIGUOUS -&gt; DISABLED                                |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| PROXIMABLE               | yes         | op_new.prox(arr, tau) = op_old.prox(\alpha * arr, \alpha**2 * tau) / \alpha |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| DIFFERENTIABLE           | yes         | op_new.diff_lipschitz = op_old.diff_lipschitz * (\alpha**2)                 |
-|                          |             | op_new.jacobian(arr) = op_old.jacobian(arr * \alpha) * \alpha               |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| DIFFERENTIABLE_FUNCTION  | yes         | op_new.grad(arr) = op_old.grad(\alpha * arr) * \alpha                       |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| QUADRATIC                | yes         | Q, c, t = op_old._quad_spec()                                               |
-|                          |             | op_new._quad_spec() = (\alpha**2 * Q, \alpha * c, t)                        |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| LINEAR                   | yes         | op_new.adjoint(arr) = op_old.adjoint(arr) * \alpha                          |
-|                          |             | op_new.asarray() = op_old.asarray() * \alpha                                |
-|                          |             | op_new.svdvals() = op_old.svdvals() * abs(\alpha)                           |
-|                          |             | op_new.pinv(x, damp) = op_old.pinv(x, damp / (\alpha**2)) / \alpha          |
-|                          |             | op_new.gram() = op_old.gram() * (\alpha**2)                                 |
-|                          |             | op_new.cogram() = op_old.cogram() * (\alpha**2)                             |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| LINEAR_SQUARE            | yes         | op_new.trace() = op_old.trace() * \alpha                                    |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| LINEAR_NORMAL            | yes         |                                                                             |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| LINEAR_UNITARY           | \alpha = -1 |                                                                             |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| LINEAR_SELF_ADJOINT      | yes         |                                                                             |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| LINEAR_POSITIVE_DEFINITE | \alpha &gt; 0  |                                                                             |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-| LINEAR_IDEMPOTENT        | no          |                                                                             |
-|--------------------------|-------------|-----------------------------------------------------------------------------|
-</pre></div>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
-<li><p><strong>cst</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
+<li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
+<li><p><strong>cst</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -811,7 +473,7 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
-<li><p><strong>cst</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>) – </p></li>
+<li><p><strong>cst</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -1033,6 +695,9 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
 </dd>
 </dl>
 </dd></dl>
+</section>
+<section id="pyxu-abc-operator">
+<h2><a class="toc-backref" href="#id4" role="doc-backlink">pyxu.abc.operator</a><a class="headerlink" href="#pyxu-abc-operator" title="Link to this heading">#</a></h2>
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.Property">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Property</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">names</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">module</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">qualname</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">boundary</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#Property"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Property" title="Link to this definition">#</a></dt>
@@ -1451,7 +1116,7 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
 </dd></dl>
 <dl class="py property">
 <dt class="sig sig-object py" id="pyxu.abc.Map.lipschitz">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">lipschitz</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><span class="pre">Real</span></a></em><a class="headerlink" href="#pyxu.abc.Map.lipschitz" title="Link to this definition">#</a></dt>
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">lipschitz</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><span class="pre">Real</span></a></em><a class="headerlink" href="#pyxu.abc.Map.lipschitz" title="Link to this definition">#</a></dt>
 <dd><p>Return the last computed Lipschitz constant of <span class="math notranslate nohighlight">\(\mathbf{f}\)</span>.</p>
 <p class="rubric">Notes</p>
 <ul>
@@ -1495,7 +1160,7 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
 <dd class="field-odd"><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Class-specific kwargs to configure Lipschitz estimation.</p>
 </dd>
 <dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a></p>
+<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a></p>
 </dd>
 </dl>
 <p class="rubric">Notes</p>
@@ -1602,7 +1267,7 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
 </dd></dl>
 <dl class="py property">
 <dt class="sig sig-object py" id="pyxu.abc.DiffMap.diff_lipschitz">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">diff_lipschitz</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><span class="pre">Real</span></a></em><a class="headerlink" href="#pyxu.abc.DiffMap.diff_lipschitz" title="Link to this definition">#</a></dt>
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">diff_lipschitz</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><span class="pre">Real</span></a></em><a class="headerlink" href="#pyxu.abc.DiffMap.diff_lipschitz" title="Link to this definition">#</a></dt>
 <dd><p>Return the last computed Lipschitz constant of <span class="math notranslate nohighlight">\(\mathbf{J}_{\mathbf{f}}\)</span>.</p>
 <p class="rubric">Notes</p>
 <ul>
@@ -1646,7 +1311,7 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
 <dd class="field-odd"><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Class-specific kwargs to configure diff-Lipschitz estimation.</p>
 </dd>
 <dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a></p>
+<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a></p>
 </dd>
 </dl>
 <p class="rubric">Notes</p>
@@ -1931,7 +1596,7 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
 <li><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p></li>
 <li><p><strong>Q</strong> (<a class="reference internal" href="#pyxu.abc.PosDefOp" title="pyxu.abc.PosDefOp"><em>PosDefOp</em></a>) – </p></li>
 <li><p><strong>c</strong> (<a class="reference internal" href="#pyxu.abc.LinFunc" title="pyxu.abc.LinFunc"><em>LinFunc</em></a>) – </p></li>
-<li><p><strong>t</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
+<li><p><strong>t</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -2040,7 +1705,7 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
 </ul>
 </dd>
 <dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a></p>
+<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a></p>
 </dd>
 </dl>
 <p class="rubric">Notes</p>
@@ -2090,276 +1755,634 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
 <dd><p>Matrix representation of the linear operator.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>xp</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArrayModule</span></code></a>) – Which array module to use to represent the output. (Default: NumPy.)</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Precision of the array. (Default: current runtime precision.)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>A</strong> – (N, M) array-representation of the operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>xp</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArrayModule</span></code></a>) – Which array module to use to represent the output. (Default: NumPy.)</p></li>
+<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Precision of the array. (Default: current runtime precision.)</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>A</strong> – (N, M) array-representation of the operator.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+</dd>
+</dl>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>This generic implementation assumes the operator is backend-agnostic.  Thus, when defining a new
+backend-specific operator, <a class="reference internal" href="#pyxu.abc.LinOp.asarray" title="pyxu.abc.LinOp.asarray"><code class="xref py py-meth docutils literal notranslate"><span class="pre">asarray()</span></code></a> may need to be overriden.</p>
+</div>
+</dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.LinOp.gram">
+<span class="sig-name descname"><span class="pre">gram</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.gram"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.gram" title="Link to this definition">#</a></dt>
+<dd><p>Gram operator <span class="math notranslate nohighlight">\(\mathbf{A}^{\ast} \mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{M}\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>op</strong> – (M, M) Gram operator.</p>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
+</dd>
+</dl>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>By default the Gram is computed by the composition <code class="docutils literal notranslate"><span class="pre">self.T</span> <span class="pre">*</span> <span class="pre">self</span></code>.  This may not be the fastest way to
+compute the Gram operator.  If the Gram can be computed more efficiently (e.g. with a convolution), the user
+should re-define this method.</p>
+</div>
+</dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.LinOp.cogram">
+<span class="sig-name descname"><span class="pre">cogram</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.cogram"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.cogram" title="Link to this definition">#</a></dt>
+<dd><p>Co-Gram operator <span class="math notranslate nohighlight">\(\mathbf{A}\mathbf{A}^{\ast}:\mathbb{R}^{N} \to \mathbb{R}^{N}\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>op</strong> – (N, N) Co-Gram operator.</p>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
+</dd>
+</dl>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>By default the co-Gram is computed by the composition <code class="docutils literal notranslate"><span class="pre">self</span> <span class="pre">*</span> <span class="pre">self.T</span></code>.  This may not be the fastest way to
+compute the co-Gram operator.  If the co-Gram can be computed more efficiently (e.g. with a convolution), the
+user should re-define this method.</p>
+</div>
+</dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.LinOp.pinv">
+<span class="sig-name descname"><span class="pre">pinv</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">damp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_fit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.pinv"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.pinv" title="Link to this definition">#</a></dt>
+<dd><p>Evaluate the Moore-Penrose pseudo-inverse <span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger}\)</span> at specified point(s).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, N) input points.</p></li>
+<li><p><strong>damp</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive dampening factor regularizing the pseudo-inverse.</p></li>
+<li><p><strong>kwargs_init</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Optional kwargs to be passed to <a class="reference internal" href="opt.solver.html#pyxu.opt.solver.CG" title="pyxu.opt.solver.CG"><code class="xref py py-meth docutils literal notranslate"><span class="pre">CG()</span></code></a>’s <code class="docutils literal notranslate"><span class="pre">__init__()</span></code> method.</p></li>
+<li><p><strong>kwargs_fit</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Optional kwargs to be passed to <a class="reference internal" href="opt.solver.html#pyxu.opt.solver.CG" title="pyxu.opt.solver.CG"><code class="xref py py-meth docutils literal notranslate"><span class="pre">CG()</span></code></a>’s <code class="docutils literal notranslate"><span class="pre">fit()</span></code> method.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>out</strong> – (…, M) pseudo-inverse(s).</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+</dd>
+</dl>
+<p class="rubric">Notes</p>
+<p>The Moore-Penrose pseudo-inverse of an operator <span class="math notranslate nohighlight">\(\mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{N}\)</span> is defined
+as the operator <span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger}: \mathbb{R}^{N} \to \mathbb{R}^{M}\)</span> verifying the Moore-Penrose
+conditions:</p>
+<blockquote>
+<div><ol class="arabic simple">
+<li><p><span class="math notranslate nohighlight">\(\mathbf{A} \mathbf{A}^{\dagger} \mathbf{A} = \mathbf{A}\)</span>,</p></li>
+<li><p><span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger} \mathbf{A} \mathbf{A}^{\dagger} = \mathbf{A}^{\dagger}\)</span>,</p></li>
+<li><p><span class="math notranslate nohighlight">\((\mathbf{A}^{\dagger} \mathbf{A})^{\ast} = \mathbf{A}^{\dagger} \mathbf{A}\)</span>,</p></li>
+<li><p><span class="math notranslate nohighlight">\((\mathbf{A} \mathbf{A}^{\dagger})^{\ast} = \mathbf{A} \mathbf{A}^{\dagger}\)</span>.</p></li>
+</ol>
+</div></blockquote>
+<p>This operator exists and is unique for any finite-dimensional linear operator.  The action of the pseudo-inverse
+<span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger} \mathbf{y}\)</span> for every <span class="math notranslate nohighlight">\(\mathbf{y} \in \mathbb{R}^{N}\)</span> can be computed in
+matrix-free fashion by solving the <em>normal equations</em>:</p>
+<div class="math notranslate nohighlight">
+\[\mathbf{A}^{\ast} \mathbf{A} \mathbf{x} = \mathbf{A}^{\ast} \mathbf{y}
+\quad\Leftrightarrow\quad
+\mathbf{x} = \mathbf{A}^{\dagger} \mathbf{y},
+\quad
+\forall (\mathbf{x}, \mathbf{y}) \in \mathbb{R}^{M} \times \mathbb{R}^{N}.\]</div>
+<p>In the case of severe ill-conditioning, it is possible to consider the dampened normal equations for a
+numerically-stabler approximation of <span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger} \mathbf{y}\)</span>:</p>
+<div class="math notranslate nohighlight">
+\[(\mathbf{A}^{\ast} \mathbf{A} + \tau I) \mathbf{x} = \mathbf{A}^{\ast} \mathbf{y},\]</div>
+<p>where <span class="math notranslate nohighlight">\(\tau &gt; 0\)</span> corresponds to the <code class="code docutils literal notranslate"><span class="pre">damp</span></code> parameter.</p>
+</dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.LinOp.dagger">
+<span class="sig-name descname"><span class="pre">dagger</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">damp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_fit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.dagger"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.dagger" title="Link to this definition">#</a></dt>
+<dd><p>Return the Moore-Penrose pseudo-inverse operator <span class="math notranslate nohighlight">\(\mathbf{A}^\dagger\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>damp</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive dampening factor regularizing the pseudo-inverse.</p></li>
+<li><p><strong>kwargs_init</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Optional kwargs to be passed to <a class="reference internal" href="opt.solver.html#pyxu.opt.solver.CG" title="pyxu.opt.solver.CG"><code class="xref py py-meth docutils literal notranslate"><span class="pre">CG()</span></code></a>’s <code class="docutils literal notranslate"><span class="pre">__init__()</span></code> method.</p></li>
+<li><p><strong>kwargs_fit</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Optional kwargs to be passed to <a class="reference internal" href="opt.solver.html#pyxu.opt.solver.CG" title="pyxu.opt.solver.CG"><code class="xref py py-meth docutils literal notranslate"><span class="pre">CG()</span></code></a>’s <code class="docutils literal notranslate"><span class="pre">fit()</span></code> method.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>op</strong> – (M, N) Moore-Penrose pseudo-inverse operator.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
+</dd>
+</dl>
+</dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.LinOp.from_array">
+<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_array</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.from_array"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.from_array" title="Link to this definition">#</a></dt>
+<dd><p>Instantiate a <a class="reference internal" href="#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> from its array representation.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>A</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (N, M) array</p></li>
+<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>op</strong> – (N, M) linear operator</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
+</dd>
+</dl>
+</dd></dl>
+</dd></dl>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.SquareOp">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SquareOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#SquareOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SquareOp" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
+<p>Base class for <em>square</em> linear operators, i.e. <span class="math notranslate nohighlight">\(\mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{M}\)</span>
+(endomorphsisms).</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.SquareOp.trace">
+<span class="sig-name descname"><span class="pre">trace</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#SquareOp.trace"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SquareOp.trace" title="Link to this definition">#</a></dt>
+<dd><p>Compute trace of the operator.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>method</strong> (<code class="docutils literal notranslate"><span class="pre">"explicit"</span></code> | <code class="docutils literal notranslate"><span class="pre">"hutchpp"</span></code>) – <ul>
+<li><p>If <code class="code docutils literal notranslate"><span class="pre">explicit</span></code>, compute the exact trace.</p></li>
+<li><p>If <code class="code docutils literal notranslate"><span class="pre">hutchpp</span></code>, compute an approximation.</p></li>
+</ul>
+</p></li>
+<li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – <p>Optional kwargs passed to:</p>
+<ul>
+<li><p><code class="code docutils literal notranslate"><span class="pre">explicit</span></code>: <a class="reference internal" href="math.html#pyxu.math.trace" title="pyxu.math.trace"><code class="xref py py-func docutils literal notranslate"><span class="pre">trace()</span></code></a></p></li>
+<li><p><code class="code docutils literal notranslate"><span class="pre">hutchpp</span></code>: <a class="reference internal" href="math.html#pyxu.math.hutchpp" title="pyxu.math.hutchpp"><code class="xref py py-func docutils literal notranslate"><span class="pre">hutchpp()</span></code></a></p></li>
+</ul>
+</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>tr</strong> – Trace estimate.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a></p>
+</dd>
+</dl>
+</dd></dl>
+</dd></dl>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.NormalOp">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NormalOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#NormalOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.NormalOp" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.SquareOp" title="pyxu.abc.operator.SquareOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareOp</span></code></a></p>
+<p>Base class for <em>normal</em> operators.</p>
+<p>Normal operators satisfy the relation <span class="math notranslate nohighlight">\(\mathbf{A} \mathbf{A}^{\ast} = \mathbf{A}^{\ast} \mathbf{A}\)</span>.  It can
+be <a class="reference external" href="https://www.wikiwand.com/en/Spectral_theorem#/Normal_matrices">shown</a> that an operator is normal iff it is
+<em>unitarily diagonalizable</em>, i.e.  <span class="math notranslate nohighlight">\(\mathbf{A} = \mathbf{U} \mathbf{D} \mathbf{U}^{\ast}\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+</dd>
+</dl>
+</dd></dl>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.SelfAdjointOp">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SelfAdjointOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#SelfAdjointOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SelfAdjointOp" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.NormalOp" title="pyxu.abc.operator.NormalOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">NormalOp</span></code></a></p>
+<p>Base class for <em>self-adjoint</em> operators.</p>
+<p>Self-adjoint operators satisfy the relation <span class="math notranslate nohighlight">\(\mathbf{A}^{\ast} = \mathbf{A}\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+</dd>
+</dl>
+</dd></dl>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.UnitOp">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">UnitOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#UnitOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.UnitOp" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.NormalOp" title="pyxu.abc.operator.NormalOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">NormalOp</span></code></a></p>
+<p>Base class for <em>unitary</em> operators.</p>
+<p>Unitary operators satisfy the relation <span class="math notranslate nohighlight">\(\mathbf{A} \mathbf{A}^{\ast} = \mathbf{A}^{\ast} \mathbf{A} = I\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+</dd>
+</dl>
+</dd></dl>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.ProjOp">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ProjOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#ProjOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.ProjOp" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.SquareOp" title="pyxu.abc.operator.SquareOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareOp</span></code></a></p>
+<p>Base class for <em>projection</em> operators.</p>
+<p>Projection operators are <em>idempotent</em>, i.e. <span class="math notranslate nohighlight">\(\mathbf{A}^{2} = \mathbf{A}\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+</dd>
+</dl>
+</dd></dl>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.OrthProjOp">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">OrthProjOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#OrthProjOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.OrthProjOp" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.ProjOp" title="pyxu.abc.operator.ProjOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProjOp</span></code></a>, <a class="reference internal" href="#pyxu.abc.SelfAdjointOp" title="pyxu.abc.operator.SelfAdjointOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SelfAdjointOp</span></code></a></p>
+<p>Base class for <em>orthogonal projection</em> operators.</p>
+<p>Orthogonal projection operators are <em>idempotent</em> and <em>self-adjoint</em>, i.e.  <span class="math notranslate nohighlight">\(\mathbf{A}^{2} = \mathbf{A}\)</span> and
+<span class="math notranslate nohighlight">\(\mathbf{A}^{\ast} = \mathbf{A}\)</span>.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
 </dd>
 </dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This generic implementation assumes the operator is backend-agnostic.  Thus, when defining a new
-backend-specific operator, <a class="reference internal" href="#pyxu.abc.LinOp.asarray" title="pyxu.abc.LinOp.asarray"><code class="xref py py-meth docutils literal notranslate"><span class="pre">asarray()</span></code></a> may need to be overriden.</p>
-</div>
 </dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.LinOp.gram">
-<span class="sig-name descname"><span class="pre">gram</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.gram"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.gram" title="Link to this definition">#</a></dt>
-<dd><p>Gram operator <span class="math notranslate nohighlight">\(\mathbf{A}^{\ast} \mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{M}\)</span>.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.PosDefOp">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PosDefOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#PosDefOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.PosDefOp" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.SelfAdjointOp" title="pyxu.abc.operator.SelfAdjointOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SelfAdjointOp</span></code></a></p>
+<p>Base class for <em>positive-definite</em> operators.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> – (M, M) Gram operator.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
 </dd>
 </dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>By default the Gram is computed by the composition <code class="docutils literal notranslate"><span class="pre">self.T</span> <span class="pre">*</span> <span class="pre">self</span></code>.  This may not be the fastest way to
-compute the Gram operator.  If the Gram can be computed more efficiently (e.g. with a convolution), the user
-should re-define this method.</p>
-</div>
 </dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.LinOp.cogram">
-<span class="sig-name descname"><span class="pre">cogram</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.cogram"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.cogram" title="Link to this definition">#</a></dt>
-<dd><p>Co-Gram operator <span class="math notranslate nohighlight">\(\mathbf{A}\mathbf{A}^{\ast}:\mathbb{R}^{N} \to \mathbb{R}^{N}\)</span>.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.LinFunc">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">LinFunc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinFunc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinFunc" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.ProxDiffFunc" title="pyxu.abc.operator.ProxDiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxDiffFunc</span></code></a>, <a class="reference internal" href="#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
+<p>Base class for real-valued linear functionals <span class="math notranslate nohighlight">\(f: \mathbb{R}^{M} \to \mathbb{R}\)</span>.</p>
+<p>Instances of this class must implement <a class="reference internal" href="#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>, and <a class="reference internal" href="#pyxu.abc.LinOp.adjoint" title="pyxu.abc.LinOp.adjoint"><code class="xref py py-meth docutils literal notranslate"><span class="pre">adjoint()</span></code></a>.</p>
+<p>If known, the Lipschitz constant <span class="math notranslate nohighlight">\(L\)</span> should be stored in the <a class="reference internal" href="#pyxu.abc.Map.lipschitz" title="pyxu.abc.Map.lipschitz"><code class="xref py py-attr docutils literal notranslate"><span class="pre">lipschitz</span></code></a> property.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> – (N, N) Co-Gram operator.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
 </dd>
 </dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>By default the co-Gram is computed by the composition <code class="docutils literal notranslate"><span class="pre">self</span> <span class="pre">*</span> <span class="pre">self.T</span></code>.  This may not be the fastest way to
-compute the co-Gram operator.  If the co-Gram can be computed more efficiently (e.g. with a convolution), the
-user should re-define this method.</p>
-</div>
 </dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.LinOp.pinv">
-<span class="sig-name descname"><span class="pre">pinv</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">damp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_fit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.pinv"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.pinv" title="Link to this definition">#</a></dt>
-<dd><p>Evaluate the Moore-Penrose pseudo-inverse <span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger}\)</span> at specified point(s).</p>
+</section>
+<section id="pyxu-abc-solver">
+<h2><a class="toc-backref" href="#id5" role="doc-backlink">pyxu.abc.solver</a><a class="headerlink" href="#pyxu-abc-solver" title="Link to this heading">#</a></h2>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.Solver">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Solver</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">folder</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">exist_ok</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stop_rate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">writeback_rate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">verbosity</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_progress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log_var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
+<p>Iterative solver for minimization problems of the form <span class="math notranslate nohighlight">\(\hat{x} = \arg\min_{x \in \mathbb{R}^{N}}
+\mathcal{F}(x)\)</span>, where the form of <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is solver-dependent.</p>
+<p>Solver provides a versatile API for solving optimisation problems, with the following features:</p>
+<ul class="simple">
+<li><p>manual/automatic/background execution of solver iterations via parameters provided to
+<a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>. (See below.)</p></li>
+<li><p>automatic checkpointing of solver progress, providing a safe restore point in case of faulty numerical code.  Each
+solver instance backs its state and final output to a folder on disk for post-analysis.  In particular
+<a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> will never crash: detailed exception information will always be available in a
+logfile for post-analysis.</p></li>
+<li><p>arbitrary specification of complex stopping criteria via the <a class="reference internal" href="#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a> class.</p></li>
+<li><p>solve for multiple initial points in parallel.</p></li>
+</ul>
+<p>To implement a new iterative solver, users need to sub-class <a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> and overwrite the methods
+below:</p>
+<ul class="simple">
+<li><p><a class="reference internal" href="#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code></a></p></li>
+<li><p><a class="reference internal" href="#pyxu.abc.Solver.m_init" title="pyxu.abc.Solver.m_init"><code class="xref py py-meth docutils literal notranslate"><span class="pre">m_init()</span></code></a>  [i.e. math-init()]</p></li>
+<li><p><a class="reference internal" href="#pyxu.abc.Solver.m_step" title="pyxu.abc.Solver.m_step"><code class="xref py py-meth docutils literal notranslate"><span class="pre">m_step()</span></code></a>  [i.e. math-step()]</p></li>
+<li><p><a class="reference internal" href="#pyxu.abc.Solver.default_stop_crit" title="pyxu.abc.Solver.default_stop_crit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">default_stop_crit()</span></code></a>  [optional; see method definition for details]</p></li>
+<li><p><a class="reference internal" href="#pyxu.abc.Solver.objective_func" title="pyxu.abc.Solver.objective_func"><code class="xref py py-meth docutils literal notranslate"><span class="pre">objective_func()</span></code></a>  [optional; see method definition for details]</p></li>
+</ul>
+<p>Advanced functionalities of <a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> are automatically inherited by sub-classes.</p>
+<p class="rubric">Examples</p>
+<p>Here are examples on how to solve minimization problems with this class:</p>
+<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">slvr</span> <span class="o">=</span> <span class="n">Solver</span><span class="p">()</span>
+
+<span class="c1">### 1. Blocking mode: .fit() does not return until solver has stopped.</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">mode</span><span class="o">=</span><span class="n">SolverMode</span><span class="o">.</span><span class="n">BLOCK</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="n">data</span><span class="p">,</span> <span class="n">hist</span> <span class="o">=</span> <span class="n">slvr</span><span class="o">.</span><span class="n">stats</span><span class="p">()</span>  <span class="c1"># final output of solver.</span>
+
+<span class="c1">### 2. Async mode: solver iterations run in the background.</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">mode</span><span class="o">=</span><span class="n">SolverMode</span><span class="o">.</span><span class="n">ASYNC</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="nb">print</span><span class="p">(</span><span class="s1">'test'</span><span class="p">)</span>  <span class="c1"># you can do something in between.</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">busy</span><span class="p">()</span>  <span class="c1"># or check whether the solver already stopped.</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">stop</span><span class="p">()</span>  <span class="c1"># and preemptively force it to stop.</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="n">data</span><span class="p">,</span> <span class="n">hist</span> <span class="o">=</span> <span class="n">slvr</span><span class="o">.</span><span class="n">stats</span><span class="p">()</span>  <span class="c1"># then query the result after a (potential) force-stop.</span>
+
+<span class="c1">### 3. Manual mode: fine-grain control of solver data per iteration.</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="n">slvr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">mode</span><span class="o">=</span><span class="n">SolverMode</span><span class="o">.</span><span class="n">MANUAL</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="k">for</span> <span class="n">data</span> <span class="ow">in</span> <span class="n">slvr</span><span class="o">.</span><span class="n">steps</span><span class="p">():</span>
+<span class="o">...</span>     <span class="c1"># Do something with the logged variables after each iteration.</span>
+<span class="o">...</span>     <span class="k">pass</span>  <span class="c1"># solver has stopped after the loop.</span>
+<span class="o">&gt;&gt;&gt;</span> <span class="n">data</span><span class="p">,</span> <span class="n">hist</span> <span class="o">=</span> <span class="n">slvr</span><span class="o">.</span><span class="n">stats</span><span class="p">()</span>  <span class="c1"># final output of solver.</span>
+</pre></div>
+</div>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, N) input points.</p></li>
-<li><p><strong>damp</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive dampening factor regularizing the pseudo-inverse.</p></li>
-<li><p><strong>kwargs_init</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Optional kwargs to be passed to <a class="reference internal" href="opt.solver.html#pyxu.opt.solver.CG" title="pyxu.opt.solver.CG"><code class="xref py py-meth docutils literal notranslate"><span class="pre">CG()</span></code></a>’s <code class="docutils literal notranslate"><span class="pre">__init__()</span></code> method.</p></li>
-<li><p><strong>kwargs_fit</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Optional kwargs to be passed to <a class="reference internal" href="opt.solver.html#pyxu.opt.solver.CG" title="pyxu.opt.solver.CG"><code class="xref py py-meth docutils literal notranslate"><span class="pre">CG()</span></code></a>’s <code class="docutils literal notranslate"><span class="pre">fit()</span></code> method.</p></li>
+<li><p><strong>folder</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/pathlib.html#pathlib.Path" title="(in Python v3.11)"><em>Path</em></a>) – </p></li>
+<li><p><strong>exist_ok</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
+<li><p><strong>stop_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p></li>
+<li><p><strong>writeback_rate</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p></li>
+<li><p><strong>verbosity</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p></li>
+<li><p><strong>show_progress</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
+<li><p><strong>log_var</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
 </ul>
 </dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>out</strong> – (…, M) pseudo-inverse(s).</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
 </dl>
-<p class="rubric">Notes</p>
-<p>The Moore-Penrose pseudo-inverse of an operator <span class="math notranslate nohighlight">\(\mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{N}\)</span> is defined
-as the operator <span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger}: \mathbb{R}^{N} \to \mathbb{R}^{M}\)</span> verifying the Moore-Penrose
-conditions:</p>
-<blockquote>
-<div><ol class="arabic simple">
-<li><p><span class="math notranslate nohighlight">\(\mathbf{A} \mathbf{A}^{\dagger} \mathbf{A} = \mathbf{A}\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger} \mathbf{A} \mathbf{A}^{\dagger} = \mathbf{A}^{\dagger}\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\((\mathbf{A}^{\dagger} \mathbf{A})^{\ast} = \mathbf{A}^{\dagger} \mathbf{A}\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\((\mathbf{A} \mathbf{A}^{\dagger})^{\ast} = \mathbf{A} \mathbf{A}^{\dagger}\)</span>.</p></li>
-</ol>
-</div></blockquote>
-<p>This operator exists and is unique for any finite-dimensional linear operator.  The action of the pseudo-inverse
-<span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger} \mathbf{y}\)</span> for every <span class="math notranslate nohighlight">\(\mathbf{y} \in \mathbb{R}^{N}\)</span> can be computed in
-matrix-free fashion by solving the <em>normal equations</em>:</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{A}^{\ast} \mathbf{A} \mathbf{x} = \mathbf{A}^{\ast} \mathbf{y}
-\quad\Leftrightarrow\quad
-\mathbf{x} = \mathbf{A}^{\dagger} \mathbf{y},
-\quad
-\forall (\mathbf{x}, \mathbf{y}) \in \mathbb{R}^{M} \times \mathbb{R}^{N}.\]</div>
-<p>In the case of severe ill-conditioning, it is possible to consider the dampened normal equations for a
-numerically-stabler approximation of <span class="math notranslate nohighlight">\(\mathbf{A}^{\dagger} \mathbf{y}\)</span>:</p>
-<div class="math notranslate nohighlight">
-\[(\mathbf{A}^{\ast} \mathbf{A} + \tau I) \mathbf{x} = \mathbf{A}^{\ast} \mathbf{y},\]</div>
-<p>where <span class="math notranslate nohighlight">\(\tau &gt; 0\)</span> corresponds to the <code class="code docutils literal notranslate"><span class="pre">damp</span></code> parameter.</p>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="pyxu.abc.Solver._mstate">
+<span class="sig-name descname"><span class="pre">_mstate</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><span class="pre">dict</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><span class="pre">Any</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#pyxu.abc.Solver._mstate" title="Link to this definition">#</a></dt>
+<dd><p>Mathematical state.</p>
+</dd></dl>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="pyxu.abc.Solver._astate">
+<span class="sig-name descname"><span class="pre">_astate</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><span class="pre">dict</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><span class="pre">Any</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#pyxu.abc.Solver._astate" title="Link to this definition">#</a></dt>
+<dd><p>Book-keeping (non-math) state.</p>
 </dd></dl>
 <dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.LinOp.dagger">
-<span class="sig-name descname"><span class="pre">dagger</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">damp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_fit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.dagger"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.dagger" title="Link to this definition">#</a></dt>
-<dd><p>Return the Moore-Penrose pseudo-inverse operator <span class="math notranslate nohighlight">\(\mathbf{A}^\dagger\)</span>.</p>
-<dl class="field-list simple">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.__init__">
+<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">folder</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">exist_ok</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stop_rate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">writeback_rate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">verbosity</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_progress</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log_var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.__init__" title="Link to this definition">#</a></dt>
+<dd><dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>damp</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive dampening factor regularizing the pseudo-inverse.</p></li>
-<li><p><strong>kwargs_init</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Optional kwargs to be passed to <a class="reference internal" href="opt.solver.html#pyxu.opt.solver.CG" title="pyxu.opt.solver.CG"><code class="xref py py-meth docutils literal notranslate"><span class="pre">CG()</span></code></a>’s <code class="docutils literal notranslate"><span class="pre">__init__()</span></code> method.</p></li>
-<li><p><strong>kwargs_fit</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Optional kwargs to be passed to <a class="reference internal" href="opt.solver.html#pyxu.opt.solver.CG" title="pyxu.opt.solver.CG"><code class="xref py py-meth docutils literal notranslate"><span class="pre">CG()</span></code></a>’s <code class="docutils literal notranslate"><span class="pre">fit()</span></code> method.</p></li>
+<li><p><strong>folder</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Path" title="pyxu.info.ptype.Path"><code class="xref py py-class docutils literal notranslate"><span class="pre">Path</span></code></a>) – Directory on disk where instance data should be stored.  A location will be automatically chosen if
+unspecified. (Default: OS-dependent tempdir.)</p></li>
+<li><p><strong>exist_ok</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="code docutils literal notranslate"><span class="pre">folder</span></code> is specified and <code class="code docutils literal notranslate"><span class="pre">exist_ok</span></code> is false (default), <a class="reference external" href="https://docs.python.org/3/library/exceptions.html#FileExistsError" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">FileExistsError</span></code></a> is raised if the
+target directory already exists.</p></li>
+<li><p><strong>stop_rate</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Rate at which solver evaluates stopping criteria.</p></li>
+<li><p><strong>writeback_rate</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Rate at which solver checkpoints are written to disk.  No checkpointing is done if unspecified: only the
+final solver output will be written back to disk.  Must be a multiple of <code class="code docutils literal notranslate"><span class="pre">stop_rate</span></code> if specified.</p></li>
+<li><p><strong>verbosity</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Rate at which stopping criteria statistics are logged.  Must be a multiple of <code class="code docutils literal notranslate"><span class="pre">stop_rate</span></code>.  Defaults to
+<code class="code docutils literal notranslate"><span class="pre">stop_rate</span></code> if unspecified.</p></li>
+<li><p><strong>show_progress</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If True (default) and <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> is run with mode=BLOCK, then statistics are also
+logged to stdout.</p></li>
+<li><p><strong>log_var</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variables from the solver’s math-state (<a class="reference internal" href="#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">_mstate</span></code></a>) to be logged per iteration.
+These are the variables made available when calling <a class="reference internal" href="#pyxu.abc.Solver.stats" title="pyxu.abc.Solver.stats"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stats()</span></code></a>.</p></li>
 </ul>
 </dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (M, N) Moore-Penrose pseudo-inverse operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
 </dl>
+<p class="rubric">Notes</p>
+<ul class="simple">
+<li><p>Partial device&lt;&gt;CPU synchronization takes place when stopping-criteria are evaluated.  Increasing <code class="code docutils literal notranslate"><span class="pre">stop_rate</span></code>
+is advised to reduce the effect of such transfers when applicable.</p></li>
+<li><p>Full device&lt;&gt;CPU synchronization takes place at checkpoint-time.  Increasing <code class="code docutils literal notranslate"><span class="pre">writeback_rate</span></code> is advised to
+reduce the effect of such transfers when applicable.</p></li>
+</ul>
 </dd></dl>
 <dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.LinOp.from_array">
-<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_array</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinOp.from_array"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.from_array" title="Link to this definition">#</a></dt>
-<dd><p>Instantiate a <a class="reference internal" href="#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> from its array representation.</p>
+<dt class="sig sig-object py" id="pyxu.abc.Solver.fit">
+<span class="sig-name descname"><span class="pre">fit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.fit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.fit" title="Link to this definition">#</a></dt>
+<dd><p>Solve minimization problem(s) defined in <a class="reference internal" href="#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code></a>, with the provided run-specifc
+parameters.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (N, M) array</p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
+<li><p><strong>kwargs</strong> – See class-level docstring for class-specific keyword parameters.</p></li>
+<li><p><strong>stop_crit</strong> (<a class="reference internal" href="#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a>) – Stopping criterion to end solver iterations.  If unspecified, defaults to
+<a class="reference internal" href="#pyxu.abc.Solver.default_stop_crit" title="pyxu.abc.Solver.default_stop_crit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">default_stop_crit()</span></code></a>.</p></li>
+<li><p><strong>mode</strong> (<a class="reference internal" href="#pyxu.abc.SolverMode" title="pyxu.abc.SolverMode"><code class="xref py py-class docutils literal notranslate"><span class="pre">SolverMode</span></code></a>) – <p>Execution mode.
+See <a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> for usage examples.</p>
+<p>Useful method pairs depending on the execution mode:</p>
+<ul>
+<li><p>BLOCK: <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a></p></li>
+<li><p>ASYNC: <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>, <a class="reference internal" href="#pyxu.abc.Solver.busy" title="pyxu.abc.Solver.busy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">busy()</span></code></a>, <a class="reference internal" href="#pyxu.abc.Solver.stop" title="pyxu.abc.Solver.stop"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stop()</span></code></a></p></li>
+<li><p>MANUAL: <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>, <a class="reference internal" href="#pyxu.abc.Solver.steps" title="pyxu.abc.Solver.steps"><code class="xref py py-meth docutils literal notranslate"><span class="pre">steps()</span></code></a></p></li>
+</ul>
+</p></li>
+<li><p><strong>track_objective</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Auto-compute objective function every time stopping criterion is evaluated.</p></li>
 </ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (N, M) linear operator</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
 </dd>
 </dl>
 </dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.m_init">
+<span class="sig-name descname"><span class="pre">m_init</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.m_init"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.m_init" title="Link to this definition">#</a></dt>
+<dd><p>Set solver’s initial mathematical state based on kwargs provided to <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>.</p>
+<p>This method must only manipulate <a class="reference internal" href="#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">_mstate</span></code></a>.</p>
+<p>After calling this method, the solver must be able to complete its 1st iteration via a call to
+<a class="reference internal" href="#pyxu.abc.Solver.m_step" title="pyxu.abc.Solver.m_step"><code class="xref py py-meth docutils literal notranslate"><span class="pre">m_step()</span></code></a>.</p>
+</dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.m_step">
+<span class="sig-name descname"><span class="pre">m_step</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.m_step"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.m_step" title="Link to this definition">#</a></dt>
+<dd><p>Perform one (mathematical) step.</p>
+<p>This method must only manipulate <a class="reference internal" href="#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">_mstate</span></code></a>.</p>
 </dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.SquareOp">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SquareOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#SquareOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SquareOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
-<p>Base class for <em>square</em> linear operators, i.e. <span class="math notranslate nohighlight">\(\mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{M}\)</span>
-(endomorphsisms).</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.steps">
+<span class="sig-name descname"><span class="pre">steps</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.steps"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.steps" title="Link to this definition">#</a></dt>
+<dd><p>Generator of logged variables after each iteration.</p>
+<p>The i-th call to <a class="reference external" href="https://docs.python.org/3/library/functions.html#next" title="(in Python v3.11)"><code class="xref py py-func docutils literal notranslate"><span class="pre">next()</span></code></a> on this object returns the logged variables after the i-th solver iteration.</p>
+<p>This method is only usable after calling <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> with mode=MANUAL.  See
+<a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> for usage examples.</p>
+<p>There is no guarantee that a checkpoint on disk exists when the generator is exhausted.  (Reason: potential
+exceptions raised during solver’s progress.) Users should invoke <a class="reference internal" href="#pyxu.abc.Solver.writeback" title="pyxu.abc.Solver.writeback"><code class="xref py py-meth docutils literal notranslate"><span class="pre">writeback()</span></code></a>
+afterwards if needed.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+<dd class="field-odd"><p><strong>n</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – <p>Maximum number of <a class="reference external" href="https://docs.python.org/3/library/functions.html#next" title="(in Python v3.11)"><code class="xref py py-func docutils literal notranslate"><span class="pre">next()</span></code></a> calls allowed before exhausting the generator.  Defaults to infinity if
+unspecified.</p>
+<p>The generator will terminate prematurely if the solver naturally stops before <code class="code docutils literal notranslate"><span class="pre">n</span></code> calls to <a class="reference external" href="https://docs.python.org/3/library/functions.html#next" title="(in Python v3.11)"><code class="xref py py-func docutils literal notranslate"><span class="pre">next()</span></code></a>
+are made.</p>
+</p>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Generator" title="(in Python v3.11)"><em>Generator</em></a></p>
 </dd>
 </dl>
+</dd></dl>
 <dl class="py method">
-<dt class="sig sig-object py" id="pyxu.abc.SquareOp.trace">
-<span class="sig-name descname"><span class="pre">trace</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#SquareOp.trace"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SquareOp.trace" title="Link to this definition">#</a></dt>
-<dd><p>Compute trace of the operator.</p>
+<dt class="sig sig-object py" id="pyxu.abc.Solver.stats">
+<span class="sig-name descname"><span class="pre">stats</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.stats"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.stats" title="Link to this definition">#</a></dt>
+<dd><p>Query solver state.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>method</strong> (<code class="docutils literal notranslate"><span class="pre">"explicit"</span></code> | <code class="docutils literal notranslate"><span class="pre">"hutchpp"</span></code>) – <ul>
-<li><p>If <code class="code docutils literal notranslate"><span class="pre">explicit</span></code>, compute the exact trace.</p></li>
-<li><p>If <code class="code docutils literal notranslate"><span class="pre">hutchpp</span></code>, compute an approximation.</p></li>
-</ul>
-</p></li>
-<li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – <p>Optional kwargs passed to:</p>
-<ul>
-<li><p><code class="code docutils literal notranslate"><span class="pre">explicit</span></code>: <a class="reference internal" href="math.html#pyxu.math.trace" title="pyxu.math.trace"><code class="xref py py-func docutils literal notranslate"><span class="pre">trace()</span></code></a></p></li>
-<li><p><code class="code docutils literal notranslate"><span class="pre">hutchpp</span></code>: <a class="reference internal" href="math.html#pyxu.math.hutchpp" title="pyxu.math.hutchpp"><code class="xref py py-func docutils literal notranslate"><span class="pre">hutchpp()</span></code></a></p></li>
-</ul>
-</p></li>
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p><ul class="simple">
+<li><p><strong>data</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Value(s) of <code class="docutils literal notranslate"><span class="pre">log_var</span></code> (s) after last iteration.</p></li>
+<li><p><strong>history</strong> (<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v1.25)"><code class="xref py py-class docutils literal notranslate"><span class="pre">numpy.ndarray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – (N_iter,) records of stopping-criteria values per iteration.</p></li>
 </ul>
+</p>
 </dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>tr</strong> – Trace estimate.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a></p>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)">tuple</a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)">dict</a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)">str</a>, <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a> | <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a> | None], <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray" title="(in NumPy v1.25)"><em>ndarray</em></a> | None]</p>
 </dd>
 </dl>
+<p class="rubric">Notes</p>
+<p>If any of the <code class="docutils literal notranslate"><span class="pre">log_var</span></code> (s) and/or <code class="docutils literal notranslate"><span class="pre">history</span></code> are not (yet) known at query time, <code class="docutils literal notranslate"><span class="pre">None</span></code> is returned.</p>
 </dd></dl>
+<dl class="py property">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.workdir">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">workdir</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/pathlib.html#pathlib.Path" title="(in Python v3.11)"><span class="pre">Path</span></a></em><a class="headerlink" href="#pyxu.abc.Solver.workdir" title="Link to this definition">#</a></dt>
+<dd><dl class="field-list simple">
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>wd</strong> – Absolute path to the directory on disk where instance data is stored.</p>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Path" title="pyxu.info.ptype.Path"><code class="xref py py-class docutils literal notranslate"><span class="pre">Path</span></code></a></p>
+</dd>
+</dl>
 </dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.NormalOp">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NormalOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#NormalOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.NormalOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.SquareOp" title="pyxu.abc.operator.SquareOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareOp</span></code></a></p>
-<p>Base class for <em>normal</em> operators.</p>
-<p>Normal operators satisfy the relation <span class="math notranslate nohighlight">\(\mathbf{A} \mathbf{A}^{\ast} = \mathbf{A}^{\ast} \mathbf{A}\)</span>.  It can
-be <a class="reference external" href="https://www.wikiwand.com/en/Spectral_theorem#/Normal_matrices">shown</a> that an operator is normal iff it is
-<em>unitarily diagonalizable</em>, i.e.  <span class="math notranslate nohighlight">\(\mathbf{A} = \mathbf{U} \mathbf{D} \mathbf{U}^{\ast}\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+<dl class="py property">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.logfile">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">logfile</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/pathlib.html#pathlib.Path" title="(in Python v3.11)"><span class="pre">Path</span></a></em><a class="headerlink" href="#pyxu.abc.Solver.logfile" title="Link to this definition">#</a></dt>
+<dd><dl class="field-list simple">
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>lf</strong> – Absolute path to the log file on disk where stopping criteria statistics are logged.</p>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Path" title="pyxu.info.ptype.Path"><code class="xref py py-class docutils literal notranslate"><span class="pre">Path</span></code></a></p>
 </dd>
 </dl>
 </dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.SelfAdjointOp">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SelfAdjointOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#SelfAdjointOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SelfAdjointOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.NormalOp" title="pyxu.abc.operator.NormalOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">NormalOp</span></code></a></p>
-<p>Base class for <em>self-adjoint</em> operators.</p>
-<p>Self-adjoint operators satisfy the relation <span class="math notranslate nohighlight">\(\mathbf{A}^{\ast} = \mathbf{A}\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+<dl class="py property">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.datafile">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">datafile</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><span class="pre">str</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/pathlib.html#pathlib.Path" title="(in Python v3.11)"><span class="pre">Path</span></a></em><a class="headerlink" href="#pyxu.abc.Solver.datafile" title="Link to this definition">#</a></dt>
+<dd><dl class="field-list simple">
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>df</strong> – Absolute path to the file on disk where <code class="docutils literal notranslate"><span class="pre">log_var</span></code> (s) are stored during checkpointing or after solver has
+stopped.</p>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Path" title="pyxu.info.ptype.Path"><code class="xref py py-class docutils literal notranslate"><span class="pre">Path</span></code></a></p>
 </dd>
 </dl>
 </dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.UnitOp">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">UnitOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#UnitOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.UnitOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.NormalOp" title="pyxu.abc.operator.NormalOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">NormalOp</span></code></a></p>
-<p>Base class for <em>unitary</em> operators.</p>
-<p>Unitary operators satisfy the relation <span class="math notranslate nohighlight">\(\mathbf{A} \mathbf{A}^{\ast} = \mathbf{A}^{\ast} \mathbf{A} = I\)</span>.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.busy">
+<span class="sig-name descname"><span class="pre">busy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.busy"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.busy" title="Link to this definition">#</a></dt>
+<dd><p>Test if an async-running solver has stopped.</p>
+<p>This method is only usable after calling <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> with mode=ASYNC.  See
+<a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> for usage examples.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>b</strong> – True if solver has stopped, False otherwise.</p>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a></p>
 </dd>
 </dl>
 </dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.ProjOp">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ProjOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#ProjOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.ProjOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.SquareOp" title="pyxu.abc.operator.SquareOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareOp</span></code></a></p>
-<p>Base class for <em>projection</em> operators.</p>
-<p>Projection operators are <em>idempotent</em>, i.e. <span class="math notranslate nohighlight">\(\mathbf{A}^{2} = \mathbf{A}\)</span>.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.solution">
+<span class="sig-name descname"><span class="pre">solution</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.solution"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.solution" title="Link to this definition">#</a></dt>
+<dd><p>Output the “solution” of the optimization problem.</p>
+<p>This is a helper method intended for novice users.  The return type is sub-class dependent, so don’t write an
+API using this: use <a class="reference internal" href="#pyxu.abc.Solver.stats" title="pyxu.abc.Solver.stats"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stats()</span></code></a> instead.</p>
+</dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.stop">
+<span class="sig-name descname"><span class="pre">stop</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.stop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.stop" title="Link to this definition">#</a></dt>
+<dd><p>Stop an async-running solver.</p>
+<p>This method is only usable after calling <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> with mode=ASYNC.  See
+<a class="reference internal" href="#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> for usage examples.</p>
+<p>This method will block until the solver has stopped.</p>
+<p>There is no guarantee that a checkpoint on disk exists once halted.  (Reason: potential exceptions raised during
+solver’s progress.) Users should invoke <a class="reference internal" href="#pyxu.abc.Solver.writeback" title="pyxu.abc.Solver.writeback"><code class="xref py py-meth docutils literal notranslate"><span class="pre">writeback()</span></code></a> afterwards if needed.</p>
+<p>Users must call this method to terminate an async-solver, even if <a class="reference internal" href="#pyxu.abc.Solver.busy" title="pyxu.abc.Solver.busy"><code class="xref py py-meth docutils literal notranslate"><span class="pre">busy()</span></code></a> is False.</p>
+</dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.writeback">
+<span class="sig-name descname"><span class="pre">writeback</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.writeback"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.writeback" title="Link to this definition">#</a></dt>
+<dd><p>Checkpoint state to disk.</p>
+</dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.default_stop_crit">
+<span class="sig-name descname"><span class="pre">default_stop_crit</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.default_stop_crit"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.default_stop_crit" title="Link to this definition">#</a></dt>
+<dd><p>Default stopping criterion for solver if unspecified in <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> calls.</p>
+<p>Sub-classes are expected to overwrite this method.  If not overridden, then omitting the <code class="code docutils literal notranslate"><span class="pre">stop_crit</span></code> parameter
+in <a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> is forbidden.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><em>StoppingCriterion</em></a></p>
 </dd>
 </dl>
 </dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.OrthProjOp">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">OrthProjOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#OrthProjOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.OrthProjOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.ProjOp" title="pyxu.abc.operator.ProjOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProjOp</span></code></a>, <a class="reference internal" href="#pyxu.abc.SelfAdjointOp" title="pyxu.abc.operator.SelfAdjointOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SelfAdjointOp</span></code></a></p>
-<p>Base class for <em>orthogonal projection</em> operators.</p>
-<p>Orthogonal projection operators are <em>idempotent</em> and <em>self-adjoint</em>, i.e.  <span class="math notranslate nohighlight">\(\mathbf{A}^{2} = \mathbf{A}\)</span> and
-<span class="math notranslate nohighlight">\(\mathbf{A}^{\ast} = \mathbf{A}\)</span>.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.Solver.objective_func">
+<span class="sig-name descname"><span class="pre">objective_func</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#Solver.objective_func"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Solver.objective_func" title="Link to this definition">#</a></dt>
+<dd><p>Evaluate objective function given current math state.</p>
+<p>The output array must have shape:</p>
+<ul class="simple">
+<li><p>(1,) if evaluated at 1 point,</p></li>
+<li><p>(N, 1) if evaluated at N different points.</p></li>
+</ul>
+<p>Sub-classes are expected to overwrite this method.  If not overridden, then enabling <code class="code docutils literal notranslate"><span class="pre">track_objective</span></code> in
+<a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> is forbidden.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a></p>
 </dd>
 </dl>
 </dd></dl>
+</dd></dl>
 <dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.PosDefOp">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PosDefOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#PosDefOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.PosDefOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.SelfAdjointOp" title="pyxu.abc.operator.SelfAdjointOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SelfAdjointOp</span></code></a></p>
-<p>Base class for <em>positive-definite</em> operators.</p>
+<dt class="sig sig-object py" id="pyxu.abc.SolverMode">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SolverMode</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">names</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">module</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">qualname</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">boundary</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#SolverMode"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SolverMode" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/enum.html#enum.Enum" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Enum</span></code></a></p>
+<p>Solver execution mode.</p>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="pyxu.abc.SolverMode.BLOCK">
+<span class="sig-name descname"><span class="pre">BLOCK</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">1</span></em><a class="headerlink" href="#pyxu.abc.SolverMode.BLOCK" title="Link to this definition">#</a></dt>
+<dd></dd></dl>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="pyxu.abc.SolverMode.MANUAL">
+<span class="sig-name descname"><span class="pre">MANUAL</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">2</span></em><a class="headerlink" href="#pyxu.abc.SolverMode.MANUAL" title="Link to this definition">#</a></dt>
+<dd></dd></dl>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="pyxu.abc.SolverMode.ASYNC">
+<span class="sig-name descname"><span class="pre">ASYNC</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">3</span></em><a class="headerlink" href="#pyxu.abc.SolverMode.ASYNC" title="Link to this definition">#</a></dt>
+<dd></dd></dl>
+</dd></dl>
+<dl class="py class">
+<dt class="sig sig-object py" id="pyxu.abc.StoppingCriterion">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">StoppingCriterion</span></span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#StoppingCriterion"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.StoppingCriterion" title="Link to this definition">#</a></dt>
+<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
+<p>State machines (SM) which decide when to stop iterative solvers by examining their mathematical state.</p>
+<p>SM decisions are always accompanied by at least one numerical statistic. These stats may be queried by solvers via
+<a class="reference internal" href="#pyxu.abc.StoppingCriterion.info" title="pyxu.abc.StoppingCriterion.info"><code class="xref py py-meth docutils literal notranslate"><span class="pre">info()</span></code></a> to provide diagnostic information to users.</p>
+<p>Composite stopping criteria can be implemented via the overloaded (and[<code class="docutils literal notranslate"><span class="pre">&amp;</span></code>], or[<code class="docutils literal notranslate"><span class="pre">|</span></code>]) operators.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.StoppingCriterion.stop">
+<span class="sig-name descname"><span class="pre">stop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">state</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#StoppingCriterion.stop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.StoppingCriterion.stop" title="Link to this definition">#</a></dt>
+<dd><p>Compute a stop signal based on the current mathematical state.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+<dd class="field-odd"><p><strong>state</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – <p>Full mathematical state of solver at some iteration, i.e. <a class="reference internal" href="#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">_mstate</span></code></a>.</p>
+<p>Values from <code class="code docutils literal notranslate"><span class="pre">state</span></code> may be cached inside the instance to form complex stopping conditions.</p>
+</p>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>s</strong> – True if no further iterations should be performed, False otherwise.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a></p>
 </dd>
 </dl>
 </dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.abc.LinFunc">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">LinFunc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/operator.html#LinFunc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinFunc" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.abc.ProxDiffFunc" title="pyxu.abc.operator.ProxDiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxDiffFunc</span></code></a>, <a class="reference internal" href="#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
-<p>Base class for real-valued linear functionals <span class="math notranslate nohighlight">\(f: \mathbb{R}^{M} \to \mathbb{R}\)</span>.</p>
-<p>Instances of this class must implement <a class="reference internal" href="#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>, and <a class="reference internal" href="#pyxu.abc.LinOp.adjoint" title="pyxu.abc.LinOp.adjoint"><code class="xref py py-meth docutils literal notranslate"><span class="pre">adjoint()</span></code></a>.</p>
-<p>If known, the Lipschitz constant <span class="math notranslate nohighlight">\(L\)</span> should be stored in the <a class="reference internal" href="#pyxu.abc.Map.lipschitz" title="pyxu.abc.Map.lipschitz"><code class="xref py py-attr docutils literal notranslate"><span class="pre">lipschitz</span></code></a> property.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.StoppingCriterion.info">
+<span class="sig-name descname"><span class="pre">info</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#StoppingCriterion.info"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.StoppingCriterion.info" title="Link to this definition">#</a></dt>
+<dd><p>Get statistics associated with the last call to <a class="reference internal" href="#pyxu.abc.StoppingCriterion.stop" title="pyxu.abc.StoppingCriterion.stop"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stop()</span></code></a>.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
+<dt class="field-odd">Returns<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>data</strong></p>
+</dd>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a></p>
 </dd>
 </dl>
 </dd></dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pyxu.abc.StoppingCriterion.clear">
+<span class="sig-name descname"><span class="pre">clear</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/abc/solver.html#StoppingCriterion.clear"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.StoppingCriterion.clear" title="Link to this definition">#</a></dt>
+<dd><p>Clear SM state (if any).</p>
+<p>This method is useful when a <a class="reference internal" href="#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a> instance must be reused in another call to
+<a class="reference internal" href="#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>.</p>
+</dd></dl>
+</dd></dl>
+</section>
 </section>
 </article>
 <footer class="bd-footer-article">
@@ -2391,144 +2414,153 @@ <h1>pyxu.abc<a class="headerlink" href="#pyxu-abc" title="Link to this heading">
   </div>
 <nav class="bd-toc-nav page-toc">
 <ul class="visible nav section-nav flex-column">
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver"><code class="docutils literal notranslate"><span class="pre">Solver</span></code></a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver._mstate"><code class="docutils literal notranslate"><span class="pre">Solver._mstate</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver._astate"><code class="docutils literal notranslate"><span class="pre">Solver._astate</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.__init__"><code class="docutils literal notranslate"><span class="pre">Solver.__init__()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.fit"><code class="docutils literal notranslate"><span class="pre">Solver.fit()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.m_init"><code class="docutils literal notranslate"><span class="pre">Solver.m_init()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.m_step"><code class="docutils literal notranslate"><span class="pre">Solver.m_step()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.steps"><code class="docutils literal notranslate"><span class="pre">Solver.steps()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.stats"><code class="docutils literal notranslate"><span class="pre">Solver.stats()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.workdir"><code class="docutils literal notranslate"><span class="pre">Solver.workdir</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.logfile"><code class="docutils literal notranslate"><span class="pre">Solver.logfile</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.datafile"><code class="docutils literal notranslate"><span class="pre">Solver.datafile</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.busy"><code class="docutils literal notranslate"><span class="pre">Solver.busy()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.solution"><code class="docutils literal notranslate"><span class="pre">Solver.solution()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.stop"><code class="docutils literal notranslate"><span class="pre">Solver.stop()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.writeback"><code class="docutils literal notranslate"><span class="pre">Solver.writeback()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.default_stop_crit"><code class="docutils literal notranslate"><span class="pre">Solver.default_stop_crit()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.objective_func"><code class="docutils literal notranslate"><span class="pre">Solver.objective_func()</span></code></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu-abc-arithmetic">pyxu.abc.arithmetic</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.arithmetic.Rule"><code class="docutils literal notranslate"><span class="pre">Rule</span></code></a><ul class="nav section-nav flex-column">
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.arithmetic.Rule.op"><code class="docutils literal notranslate"><span class="pre">Rule.op()</span></code></a></li>
+</ul>
+</li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.arithmetic.ScaleRule"><code class="docutils literal notranslate"><span class="pre">ScaleRule</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.arithmetic.ArgScaleRule"><code class="docutils literal notranslate"><span class="pre">ArgScaleRule</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.arithmetic.ArgShiftRule"><code class="docutils literal notranslate"><span class="pre">ArgShiftRule</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.arithmetic.AddRule"><code class="docutils literal notranslate"><span class="pre">AddRule</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.arithmetic.ChainRule"><code class="docutils literal notranslate"><span class="pre">ChainRule</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.arithmetic.PowerRule"><code class="docutils literal notranslate"><span class="pre">PowerRule</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.arithmetic.TransposeRule"><code class="docutils literal notranslate"><span class="pre">TransposeRule</span></code></a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu-abc-operator">pyxu.abc.operator</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property"><code class="docutils literal notranslate"><span class="pre">Property</span></code></a><ul class="nav section-nav flex-column">
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.CAN_EVAL"><code class="docutils literal notranslate"><span class="pre">Property.CAN_EVAL</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.FUNCTIONAL"><code class="docutils literal notranslate"><span class="pre">Property.FUNCTIONAL</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.PROXIMABLE"><code class="docutils literal notranslate"><span class="pre">Property.PROXIMABLE</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.DIFFERENTIABLE"><code class="docutils literal notranslate"><span class="pre">Property.DIFFERENTIABLE</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.DIFFERENTIABLE_FUNCTION"><code class="docutils literal notranslate"><span class="pre">Property.DIFFERENTIABLE_FUNCTION</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.LINEAR"><code class="docutils literal notranslate"><span class="pre">Property.LINEAR</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.LINEAR_SQUARE"><code class="docutils literal notranslate"><span class="pre">Property.LINEAR_SQUARE</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.LINEAR_NORMAL"><code class="docutils literal notranslate"><span class="pre">Property.LINEAR_NORMAL</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.LINEAR_IDEMPOTENT"><code class="docutils literal notranslate"><span class="pre">Property.LINEAR_IDEMPOTENT</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.LINEAR_SELF_ADJOINT"><code class="docutils literal notranslate"><span class="pre">Property.LINEAR_SELF_ADJOINT</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.LINEAR_POSITIVE_DEFINITE"><code class="docutils literal notranslate"><span class="pre">Property.LINEAR_POSITIVE_DEFINITE</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.LINEAR_UNITARY"><code class="docutils literal notranslate"><span class="pre">Property.LINEAR_UNITARY</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.QUADRATIC"><code class="docutils literal notranslate"><span class="pre">Property.QUADRATIC</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.arithmetic_methods"><code class="docutils literal notranslate"><span class="pre">Property.arithmetic_methods()</span></code></a></li>
+</ul>
+</li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Operator"><code class="docutils literal notranslate"><span class="pre">Operator</span></code></a><ul class="nav section-nav flex-column">
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Operator.__init__"><code class="docutils literal notranslate"><span class="pre">Operator.__init__()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Operator.shape"><code class="docutils literal notranslate"><span class="pre">Operator.shape</span></code></a></li>
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 </li>
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-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.DiffFunc.grad"><code class="docutils literal notranslate"><span class="pre">DiffFunc.grad()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.NormalOp"><code class="docutils literal notranslate"><span class="pre">NormalOp</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.SelfAdjointOp"><code class="docutils literal notranslate"><span class="pre">SelfAdjointOp</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.UnitOp"><code class="docutils literal notranslate"><span class="pre">UnitOp</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.ProjOp"><code class="docutils literal notranslate"><span class="pre">ProjOp</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.OrthProjOp"><code class="docutils literal notranslate"><span class="pre">OrthProjOp</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.PosDefOp"><code class="docutils literal notranslate"><span class="pre">PosDefOp</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinFunc"><code class="docutils literal notranslate"><span class="pre">LinFunc</span></code></a></li>
 </ul>
 </li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.ProxFunc"><code class="docutils literal notranslate"><span class="pre">ProxFunc</span></code></a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.ProxFunc.prox"><code class="docutils literal notranslate"><span class="pre">ProxFunc.prox()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.ProxFunc.fenchel_prox"><code class="docutils literal notranslate"><span class="pre">ProxFunc.fenchel_prox()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.ProxFunc.moreau_envelope"><code class="docutils literal notranslate"><span class="pre">ProxFunc.moreau_envelope()</span></code></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu-abc-solver">pyxu.abc.solver</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver"><code class="docutils literal notranslate"><span class="pre">Solver</span></code></a><ul class="nav section-nav flex-column">
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver._mstate"><code class="docutils literal notranslate"><span class="pre">Solver._mstate</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver._astate"><code class="docutils literal notranslate"><span class="pre">Solver._astate</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.__init__"><code class="docutils literal notranslate"><span class="pre">Solver.__init__()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.fit"><code class="docutils literal notranslate"><span class="pre">Solver.fit()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.m_init"><code class="docutils literal notranslate"><span class="pre">Solver.m_init()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.m_step"><code class="docutils literal notranslate"><span class="pre">Solver.m_step()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.steps"><code class="docutils literal notranslate"><span class="pre">Solver.steps()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.stats"><code class="docutils literal notranslate"><span class="pre">Solver.stats()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.workdir"><code class="docutils literal notranslate"><span class="pre">Solver.workdir</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.logfile"><code class="docutils literal notranslate"><span class="pre">Solver.logfile</span></code></a></li>
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+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.busy"><code class="docutils literal notranslate"><span class="pre">Solver.busy()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.solution"><code class="docutils literal notranslate"><span class="pre">Solver.solution()</span></code></a></li>
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+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.writeback"><code class="docutils literal notranslate"><span class="pre">Solver.writeback()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.default_stop_crit"><code class="docutils literal notranslate"><span class="pre">Solver.default_stop_crit()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Solver.objective_func"><code class="docutils literal notranslate"><span class="pre">Solver.objective_func()</span></code></a></li>
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-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.QuadraticFunc.__init__"><code class="docutils literal notranslate"><span class="pre">QuadraticFunc.__init__()</span></code></a></li>
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.SolverMode"><code class="docutils literal notranslate"><span class="pre">SolverMode</span></code></a><ul class="nav section-nav flex-column">
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.SolverMode.BLOCK"><code class="docutils literal notranslate"><span class="pre">SolverMode.BLOCK</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.SolverMode.MANUAL"><code class="docutils literal notranslate"><span class="pre">SolverMode.MANUAL</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.SolverMode.ASYNC"><code class="docutils literal notranslate"><span class="pre">SolverMode.ASYNC</span></code></a></li>
 </ul>
 </li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp"><code class="docutils literal notranslate"><span class="pre">LinOp</span></code></a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.adjoint"><code class="docutils literal notranslate"><span class="pre">LinOp.adjoint()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.T"><code class="docutils literal notranslate"><span class="pre">LinOp.T</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.to_sciop"><code class="docutils literal notranslate"><span class="pre">LinOp.to_sciop()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.estimate_lipschitz"><code class="docutils literal notranslate"><span class="pre">LinOp.estimate_lipschitz()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.svdvals"><code class="docutils literal notranslate"><span class="pre">LinOp.svdvals()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.asarray"><code class="docutils literal notranslate"><span class="pre">LinOp.asarray()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.gram"><code class="docutils literal notranslate"><span class="pre">LinOp.gram()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.cogram"><code class="docutils literal notranslate"><span class="pre">LinOp.cogram()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.pinv"><code class="docutils literal notranslate"><span class="pre">LinOp.pinv()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinOp.dagger"><code class="docutils literal notranslate"><span class="pre">LinOp.dagger()</span></code></a></li>
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.StoppingCriterion"><code class="docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a><ul class="nav section-nav flex-column">
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.StoppingCriterion.stop"><code class="docutils literal notranslate"><span class="pre">StoppingCriterion.stop()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.StoppingCriterion.info"><code class="docutils literal notranslate"><span class="pre">StoppingCriterion.info()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.StoppingCriterion.clear"><code class="docutils literal notranslate"><span class="pre">StoppingCriterion.clear()</span></code></a></li>
 </ul>
 </li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.SquareOp"><code class="docutils literal notranslate"><span class="pre">SquareOp</span></code></a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.SquareOp.trace"><code class="docutils literal notranslate"><span class="pre">SquareOp.trace()</span></code></a></li>
 </ul>
 </li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.NormalOp"><code class="docutils literal notranslate"><span class="pre">NormalOp</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.SelfAdjointOp"><code class="docutils literal notranslate"><span class="pre">SelfAdjointOp</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.UnitOp"><code class="docutils literal notranslate"><span class="pre">UnitOp</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.ProjOp"><code class="docutils literal notranslate"><span class="pre">ProjOp</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.OrthProjOp"><code class="docutils literal notranslate"><span class="pre">OrthProjOp</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.PosDefOp"><code class="docutils literal notranslate"><span class="pre">PosDefOp</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinFunc"><code class="docutils literal notranslate"><span class="pre">LinFunc</span></code></a></li>
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@@ -127,28 +201,68 @@
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+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
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@@ -156,75 +270,144 @@
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+                      <a class="nav-link nav-internal" href="../index.html">
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+                
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+                      <a class="nav-link nav-internal" href="../../fair/index.html">
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+                
+  </ul>
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-</li>
+        
+      </div>
+    
+    
+    
+      <div class="sidebar-header-items__end">
+        
+          <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
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+    aria-label="Icon Links">
+        <li class="nav-item">
+          
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+            <label class="sr-only">GitHub</label></a>
+        </li>
+        <li class="nav-item">
+          
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+          
+          
+          
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+          
+          <a href="https://pypi.org/project/pyxu/" title="PyPI" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-python"></i></span>
+            <label class="sr-only">PyPI</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
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+          
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+          
+          
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+            <label class="sr-only">Contact</label></a>
+        </li>
+        <li class="nav-item">
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+          
+          
+          
+          
+          
+          <a href="https://imaging.epfl.ch/" title="EPFL Center for Imaging" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><img src="../../_static/imaging.png" class="icon-link-image" alt="EPFL Center for Imaging"/></a>
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 </ul></div>
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@@ -258,37 +441,64 @@
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+            <div class="bd-article-container">
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 <div class="header-article-items header-article__inner">
-<div class="header-article-items__start">
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+    <div class="header-article-items__start">
+      
+        <div class="header-article-item">
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 <nav aria-label="Breadcrumbs">
-<ul aria-label="Breadcrumb" class="bd-breadcrumbs" role="navigation">
-<li class="breadcrumb-item breadcrumb-home">
-<a aria-label="Home" class="nav-link" href="../../index.html">
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-<li class="breadcrumb-item"><a class="nav-link" href="../index.html">API Reference</a></li>
-<li class="breadcrumb-item"><a class="nav-link" href="index.html">pyxu.abc</a></li>
-<li aria-current="page" class="breadcrumb-item active">pyxu.abc.operator</li>
-</ul>
+  <ul class="bd-breadcrumbs" role="navigation" aria-label="Breadcrumb">
+    
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+      <a href="../../index.html" class="nav-link" aria-label="Home">
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+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">pyxu.abc</a></li>
+    
+    <li class="breadcrumb-item active" aria-current="page">pyxu.abc.operator</li>
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 <div id="searchbox"></div>
-<article class="bd-article" role="main">
-<section id="pyxu-abc-operator">
+                <article class="bd-article" role="main">
+                  
+  <section id="pyxu-abc-operator">
 <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link to this heading">#</a></h1>
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.Property">
@@ -303,54 +513,67 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <dt class="sig sig-object py" id="pyxu.abc.Property.CAN_EVAL">
 <span class="sig-name descname"><span class="pre">CAN_EVAL</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">1</span></em><a class="headerlink" href="#pyxu.abc.Property.CAN_EVAL" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.FUNCTIONAL">
 <span class="sig-name descname"><span class="pre">FUNCTIONAL</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">2</span></em><a class="headerlink" href="#pyxu.abc.Property.FUNCTIONAL" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.PROXIMABLE">
 <span class="sig-name descname"><span class="pre">PROXIMABLE</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">3</span></em><a class="headerlink" href="#pyxu.abc.Property.PROXIMABLE" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.DIFFERENTIABLE">
 <span class="sig-name descname"><span class="pre">DIFFERENTIABLE</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">4</span></em><a class="headerlink" href="#pyxu.abc.Property.DIFFERENTIABLE" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.DIFFERENTIABLE_FUNCTION">
 <span class="sig-name descname"><span class="pre">DIFFERENTIABLE_FUNCTION</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">5</span></em><a class="headerlink" href="#pyxu.abc.Property.DIFFERENTIABLE_FUNCTION" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.LINEAR">
 <span class="sig-name descname"><span class="pre">LINEAR</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">6</span></em><a class="headerlink" href="#pyxu.abc.Property.LINEAR" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.LINEAR_SQUARE">
 <span class="sig-name descname"><span class="pre">LINEAR_SQUARE</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">7</span></em><a class="headerlink" href="#pyxu.abc.Property.LINEAR_SQUARE" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.LINEAR_NORMAL">
 <span class="sig-name descname"><span class="pre">LINEAR_NORMAL</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">8</span></em><a class="headerlink" href="#pyxu.abc.Property.LINEAR_NORMAL" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.LINEAR_IDEMPOTENT">
 <span class="sig-name descname"><span class="pre">LINEAR_IDEMPOTENT</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">9</span></em><a class="headerlink" href="#pyxu.abc.Property.LINEAR_IDEMPOTENT" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.LINEAR_SELF_ADJOINT">
 <span class="sig-name descname"><span class="pre">LINEAR_SELF_ADJOINT</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">10</span></em><a class="headerlink" href="#pyxu.abc.Property.LINEAR_SELF_ADJOINT" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.LINEAR_POSITIVE_DEFINITE">
 <span class="sig-name descname"><span class="pre">LINEAR_POSITIVE_DEFINITE</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">11</span></em><a class="headerlink" href="#pyxu.abc.Property.LINEAR_POSITIVE_DEFINITE" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.LINEAR_UNITARY">
 <span class="sig-name descname"><span class="pre">LINEAR_UNITARY</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">12</span></em><a class="headerlink" href="#pyxu.abc.Property.LINEAR_UNITARY" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py attribute">
 <dt class="sig sig-object py" id="pyxu.abc.Property.QUADRATIC">
 <span class="sig-name descname"><span class="pre">QUADRATIC</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">13</span></em><a class="headerlink" href="#pyxu.abc.Property.QUADRATIC" title="Link to this definition">#</a></dt>
 <dd></dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Property.arithmetic_methods">
 <span class="sig-name descname"><span class="pre">arithmetic_methods</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Property.arithmetic_methods"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Property.arithmetic_methods" title="Link to this definition">#</a></dt>
@@ -361,7 +584,9 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.Operator">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Operator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator" title="Link to this definition">#</a></dt>
@@ -388,21 +613,25 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py property">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.shape">
 <em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">shape</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><span class="pre">tuple</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><span class="pre">Integral</span></a><span class="p"><span class="pre">,</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><span class="pre">Integral</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#pyxu.abc.Operator.shape" title="Link to this definition">#</a></dt>
 <dd><p>Return (N, M) operator shape.</p>
 </dd></dl>
+
 <dl class="py property">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.dim">
 <em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">dim</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><span class="pre">Integral</span></a></em><a class="headerlink" href="#pyxu.abc.Operator.dim" title="Link to this definition">#</a></dt>
 <dd><p>Return dimension of operator’s domain. (M)</p>
 </dd></dl>
+
 <dl class="py property">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.codim">
 <em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">codim</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><span class="pre">Integral</span></a></em><a class="headerlink" href="#pyxu.abc.Operator.codim" title="Link to this definition">#</a></dt>
 <dd><p>Return dimension of operator’s co-domain. (N)</p>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.properties">
 <em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">properties</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.properties"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.properties" title="Link to this definition">#</a></dt>
@@ -413,6 +642,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.has">
 <em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">has</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prop</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.has"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.has" title="Link to this definition">#</a></dt>
@@ -426,6 +656,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.asop">
 <span class="sig-name descname"><span class="pre">asop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cast_to</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.asop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.asop" title="Link to this definition">#</a></dt>
@@ -453,6 +684,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <a class="reference external" href="https://docs.python.org/3/library/exceptions.html#NotImplementedError" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">NotImplementedError</span></code></a> when called.</p></li>
 </ul>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.__add__">
 <span class="sig-name descname"><span class="pre">__add__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.__add__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.__add__" title="Link to this definition">#</a></dt>
@@ -484,6 +716,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <p><a class="reference internal" href="arithmetic.html#pyxu.abc.arithmetic.AddRule" title="pyxu.abc.arithmetic.AddRule"><code class="xref py py-class docutils literal notranslate"><span class="pre">AddRule</span></code></a></p>
 </div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.__sub__">
 <span class="sig-name descname"><span class="pre">__sub__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.__sub__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.__sub__" title="Link to this definition">#</a></dt>
@@ -503,6 +736,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.__neg__">
 <span class="sig-name descname"><span class="pre">__neg__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.__neg__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.__neg__" title="Link to this definition">#</a></dt>
@@ -516,6 +750,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.__mul__">
 <span class="sig-name descname"><span class="pre">__mul__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.__mul__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.__mul__" title="Link to this definition">#</a></dt>
@@ -543,6 +778,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <p><a class="reference internal" href="arithmetic.html#pyxu.abc.arithmetic.ScaleRule" title="pyxu.abc.arithmetic.ScaleRule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ScaleRule</span></code></a>, <a class="reference internal" href="arithmetic.html#pyxu.abc.arithmetic.ChainRule" title="pyxu.abc.arithmetic.ChainRule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ChainRule</span></code></a></p>
 </div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.__pow__">
 <span class="sig-name descname"><span class="pre">__pow__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">k</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.__pow__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.__pow__" title="Link to this definition">#</a></dt>
@@ -565,6 +801,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <p><a class="reference internal" href="arithmetic.html#pyxu.abc.arithmetic.PowerRule" title="pyxu.abc.arithmetic.PowerRule"><code class="xref py py-class docutils literal notranslate"><span class="pre">PowerRule</span></code></a></p>
 </div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.argscale">
 <span class="sig-name descname"><span class="pre">argscale</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">scalar</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.argscale"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.argscale" title="Link to this definition">#</a></dt>
@@ -585,6 +822,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <p><a class="reference internal" href="arithmetic.html#pyxu.abc.arithmetic.ArgScaleRule" title="pyxu.abc.arithmetic.ArgScaleRule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArgScaleRule</span></code></a></p>
 </div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.argshift">
 <span class="sig-name descname"><span class="pre">argshift</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shift</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.argshift"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.argshift" title="Link to this definition">#</a></dt>
@@ -605,6 +843,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <p><a class="reference internal" href="arithmetic.html#pyxu.abc.arithmetic.ArgShiftRule" title="pyxu.abc.arithmetic.ArgShiftRule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArgShiftRule</span></code></a></p>
 </div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.squeeze">
 <span class="sig-name descname"><span class="pre">squeeze</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.squeeze"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.squeeze" title="Link to this definition">#</a></dt>
@@ -615,6 +854,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Operator.expr">
 <span class="sig-name descname"><span class="pre">expr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">level</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">strip</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Operator.expr"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Operator.expr" title="Link to this definition">#</a></dt>
@@ -653,7 +893,9 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.Map">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Map</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Map"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Map" title="Link to this definition">#</a></dt>
@@ -677,6 +919,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Map.apply">
 <span class="sig-name descname"><span class="pre">apply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Map.apply"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Map.apply" title="Link to this definition">#</a></dt>
@@ -693,6 +936,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Map.__call__">
 <span class="sig-name descname"><span class="pre">__call__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Map.__call__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Map.__call__" title="Link to this definition">#</a></dt>
@@ -706,6 +950,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py property">
 <dt class="sig sig-object py" id="pyxu.abc.Map.lipschitz">
 <em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">lipschitz</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><span class="pre">Real</span></a></em><a class="headerlink" href="#pyxu.abc.Map.lipschitz" title="Link to this definition">#</a></dt>
@@ -743,6 +988,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </li>
 </ul>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.Map.estimate_lipschitz">
 <span class="sig-name descname"><span class="pre">estimate_lipschitz</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Map.estimate_lipschitz"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Map.estimate_lipschitz" title="Link to this definition">#</a></dt>
@@ -772,7 +1018,9 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </li>
 </ul>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.Func">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Func</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#Func"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.Func" title="Link to this definition">#</a></dt>
@@ -805,7 +1053,9 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.DiffMap">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DiffMap</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#DiffMap"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.DiffMap" title="Link to this definition">#</a></dt>
@@ -857,6 +1107,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 \qquad
 \forall (i,j) \in \{1,\ldots,N\} \times \{1,\ldots,M\}.\]</div>
 </dd></dl>
+
 <dl class="py property">
 <dt class="sig sig-object py" id="pyxu.abc.DiffMap.diff_lipschitz">
 <em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">diff_lipschitz</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><span class="pre">Real</span></a></em><a class="headerlink" href="#pyxu.abc.DiffMap.diff_lipschitz" title="Link to this definition">#</a></dt>
@@ -894,6 +1145,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </li>
 </ul>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.DiffMap.estimate_diff_lipschitz">
 <span class="sig-name descname"><span class="pre">estimate_diff_lipschitz</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#DiffMap.estimate_diff_lipschitz"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.DiffMap.estimate_diff_lipschitz" title="Link to this definition">#</a></dt>
@@ -923,7 +1175,9 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </li>
 </ul>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.DiffFunc">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DiffFunc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#DiffFunc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.DiffFunc" title="Link to this definition">#</a></dt>
@@ -965,7 +1219,9 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 \frac{\partial f}{\partial x_{M}}(\mathbf{x})
 \end{array}\right].\end{split}\]</div>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.ProxFunc">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ProxFunc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#ProxFunc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.ProxFunc" title="Link to this definition">#</a></dt>
@@ -1010,6 +1266,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 \quad
 \forall \mathbf{z} \in \mathbb{R}^{M}.\]</div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.ProxFunc.fenchel_prox">
 <span class="sig-name descname"><span class="pre">fenchel_prox</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#ProxFunc.fenchel_prox"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.ProxFunc.fenchel_prox" title="Link to this definition">#</a></dt>
@@ -1041,6 +1298,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 =
 \mathbf{z} - \sigma \mathbf{\text{prox}}_{f/\sigma}(\mathbf{z}/\sigma).\]</div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.ProxFunc.moreau_envelope">
 <span class="sig-name descname"><span class="pre">moreau_envelope</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mu</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#ProxFunc.moreau_envelope"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.ProxFunc.moreau_envelope" title="Link to this definition">#</a></dt>
@@ -1083,56 +1341,58 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 conjugate of <span class="math notranslate nohighlight">\(f^{\mu}\)</span> is strongly-convex.</p>
 <p class="rubric">Example</p>
 <p>Construct and plot the Moreau envelope of the <span class="math notranslate nohighlight">\(\ell_{1}\)</span>-norm:</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <span class="n">ProxFunc</span>
 
-<span class="k">class</span> <span class="nc">L1Norm</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../../api/abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a><span class="p">):</span>
-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">dim</span><span class="p">:</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#int" title="int"><span class="nb">int</span></a><span class="p">):</span>
-        <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#super" title="super"><span class="nb">super</span></a><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim</span><span class="p">))</span>
+<span class="k">class</span> <span class="nc">L1Norm</span><span class="p">(</span><span class="n">ProxFunc</span><span class="p">):</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">dim</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim</span><span class="p">))</span>
     <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span>
-        <span class="k">return</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html#numpy.linalg.norm" title="numpy.linalg.norm"><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span></a><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="nb">ord</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="nb">ord</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
     <span class="k">def</span> <span class="nf">prox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">,</span> <span class="n">tau</span><span class="p">):</span>
-        <span class="k">return</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.clip.html#numpy.clip" title="numpy.clip"><span class="n">np</span><span class="o">.</span><span class="n">clip</span></a><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span><span class="o">-</span><span class="n">tau</span><span class="p">,</span> <span class="n">a_min</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">a_max</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.sign.html#numpy.sign" title="numpy.sign"><span class="n">np</span><span class="o">.</span><span class="n">sign</span></a><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">clip</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span><span class="o">-</span><span class="n">tau</span><span class="p">,</span> <span class="n">a_min</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">a_max</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
 
 <span class="n">N</span> <span class="o">=</span> <span class="mi">512</span>
 <span class="n">l1_norm</span> <span class="o">=</span> <span class="n">L1Norm</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="n">N</span><span class="p">)</span>
 <span class="n">mus</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
 <span class="n">smooth_l1_norms</span> <span class="o">=</span> <span class="p">[</span><span class="n">l1_norm</span><span class="o">.</span><span class="n">moreau_envelope</span><span class="p">(</span><span class="n">mu</span><span class="p">)</span> <span class="k">for</span> <span class="n">mu</span> <span class="ow">in</span> <span class="n">mus</span><span class="p">]</span>
 
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">)[:,</span> <span class="kc">None</span><span class="p">]</span>
-<span class="n">labels</span><span class="o">=</span><span class="p">[</span><span class="s1">'mu=0'</span><span class="p">]</span>
-<span class="n">labels</span><span class="o">.</span><span class="n">extend</span><span class="p">([</span><span class="sa">f</span><span class="s1">'mu=</span><span class="si">{</span><span class="n">mu</span><span class="si">}</span><span class="s1">'</span> <span class="k">for</span> <span class="n">mu</span> <span class="ow">in</span> <span class="n">mus</span><span class="p">])</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">l1_norm</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">N</span><span class="p">)[:,</span> <span class="kc">None</span><span class="p">]</span>
+<span class="n">labels</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;mu=0&#39;</span><span class="p">]</span>
+<span class="n">labels</span><span class="o">.</span><span class="n">extend</span><span class="p">([</span><span class="sa">f</span><span class="s1">&#39;mu=</span><span class="si">{</span><span class="n">mu</span><span class="si">}</span><span class="s1">&#39;</span> <span class="k">for</span> <span class="n">mu</span> <span class="ow">in</span> <span class="n">mus</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">l1_norm</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
 <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">smooth_l1_norms</span><span class="p">:</span>
-    <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">labels</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Moreau Envelope'</span><span class="p">)</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">labels</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Moreau Envelope&#39;</span><span class="p">)</span>
 
-<span class="n">labels</span><span class="o">=</span><span class="p">[</span><span class="sa">f</span><span class="s1">'mu=</span><span class="si">{</span><span class="n">mu</span><span class="si">}</span><span class="s1">'</span> <span class="k">for</span> <span class="n">mu</span> <span class="ow">in</span> <span class="n">mus</span><span class="p">]</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
+<span class="n">labels</span><span class="o">=</span><span class="p">[</span><span class="sa">f</span><span class="s1">&#39;mu=</span><span class="si">{</span><span class="n">mu</span><span class="si">}</span><span class="s1">&#39;</span> <span class="k">for</span> <span class="n">mu</span> <span class="ow">in</span> <span class="n">mus</span><span class="p">]</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
 <span class="k">for</span> <span class="n">f</span> <span class="ow">in</span> <span class="n">smooth_l1_norms</span><span class="p">:</span>
-    <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">(</span><span class="n">labels</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Derivative of Moreau Envelope'</span><span class="p">)</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">f</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">labels</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Derivative of Moreau Envelope&#39;</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>(<a class="reference download internal" download="" href="../../_downloads/361d1b99c32bc7c73255c4c2931a831c/operator-1.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>)</p>
 <figure class="align-default" id="id1">
-<img alt="../../_images/operator-1_00.png" class="plot-directive" src="../../_images/operator-1_00.png"/>
+<img alt="../../_images/operator-1_00.png" class="plot-directive" src="../../_images/operator-1_00.png" />
 <figcaption>
 <p><span class="caption-text">(<a class="reference download internal" download="" href="../../_downloads/9349be48fdb330bb37c232589c22ff15/operator-1_00.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/974082c7d04ec660ca43a107ea8e53ba/operator-1_00.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/6d6eb2e18628afcd80afb9b1f46a86c9/operator-1_00.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id1" title="Link to this image">#</a></p>
 </figcaption>
 </figure>
 <figure class="align-default" id="id2">
-<img alt="../../_images/operator-1_01.png" class="plot-directive" src="../../_images/operator-1_01.png"/>
+<img alt="../../_images/operator-1_01.png" class="plot-directive" src="../../_images/operator-1_01.png" />
 <figcaption>
 <p><span class="caption-text">(<a class="reference download internal" download="" href="../../_downloads/de31929cc6f8f0bc6cc09c15e633691b/operator-1_01.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/f8ea786379495b526ad196ae9c2114a1/operator-1_01.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/468910fa079d504203df7361bc14fe4f/operator-1_01.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id2" title="Link to this image">#</a></p>
 </figcaption>
 </figure>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.ProxDiffFunc">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ProxDiffFunc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#ProxDiffFunc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.ProxDiffFunc" title="Link to this definition">#</a></dt>
@@ -1149,6 +1409,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.QuadraticFunc">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">QuadraticFunc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Q</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">t</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#QuadraticFunc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.QuadraticFunc" title="Link to this definition">#</a></dt>
@@ -1206,13 +1467,16 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.QuadraticFunc._quad_spec">
 <span class="sig-name descname"><span class="pre">_quad_spec</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#QuadraticFunc._quad_spec"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.QuadraticFunc._quad_spec" title="Link to this definition">#</a></dt>
 <dd><p>Canonical quadratic parameterization.</p>
 <p>Useful for some internal methods, and overloaded during operator arithmetic.</p>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">LinOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp" title="Link to this definition">#</a></dt>
@@ -1251,11 +1515,13 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 \qquad
 \forall (\mathbf{x},\mathbf{y})\in \mathbb{R}^{M} \times \mathbb{R}^{N}.\]</div>
 </dd></dl>
+
 <dl class="py property">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.T">
 <em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">T</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><span class="pre">OpT</span></a></em><a class="headerlink" href="#pyxu.abc.LinOp.T" title="Link to this definition">#</a></dt>
 <dd><p>Return the (M, N) adjoint of <span class="math notranslate nohighlight">\(\mathbf{A}\)</span>.</p>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.to_sciop">
 <span class="sig-name descname"><span class="pre">to_sciop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp.to_sciop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.to_sciop" title="Link to this definition">#</a></dt>
@@ -1276,6 +1542,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.estimate_lipschitz">
 <span class="sig-name descname"><span class="pre">estimate_lipschitz</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp.estimate_lipschitz"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.estimate_lipschitz" title="Link to this definition">#</a></dt>
@@ -1283,7 +1550,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>method</strong> (<code class="docutils literal notranslate"><span class="pre">"svd"</span></code> | <code class="docutils literal notranslate"><span class="pre">"trace"</span></code>) – <ul>
+<li><p><strong>method</strong> (<code class="docutils literal notranslate"><span class="pre">&quot;svd&quot;</span></code> | <code class="docutils literal notranslate"><span class="pre">&quot;trace&quot;</span></code>) – <ul>
 <li><p>If <code class="code docutils literal notranslate"><span class="pre">svd</span></code>, compute the optimal Lipschitz constant.</p></li>
 <li><p>If <code class="code docutils literal notranslate"><span class="pre">trace</span></code>, compute an upper bound. (Default)</p></li>
 </ul>
@@ -1313,6 +1580,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 where the equality is reached (worst-case scenario) when the eigenspectrum of the linear operator is flat.</p></li>
 </ul>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.svdvals">
 <span class="sig-name descname"><span class="pre">svdvals</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">k</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">which</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'LM'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp.svdvals"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.svdvals" title="Link to this definition">#</a></dt>
@@ -1321,7 +1589,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>k</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Number of singular values to compute.</p></li>
-<li><p><strong>which</strong> (<code class="docutils literal notranslate"><span class="pre">"LM"</span></code> | <code class="docutils literal notranslate"><span class="pre">"SM"</span></code>) – <p>Which <code class="code docutils literal notranslate"><span class="pre">k</span></code> singular values to find:</p>
+<li><p><strong>which</strong> (<code class="docutils literal notranslate"><span class="pre">&quot;LM&quot;</span></code> | <code class="docutils literal notranslate"><span class="pre">&quot;SM&quot;</span></code>) – <p>Which <code class="code docutils literal notranslate"><span class="pre">k</span></code> singular values to find:</p>
 <blockquote>
 <div><ul>
 <li><p><code class="code docutils literal notranslate"><span class="pre">LM</span></code>: largest magnitude</p></li>
@@ -1341,6 +1609,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.asarray">
 <span class="sig-name descname"><span class="pre">asarray</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">xp</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp.asarray"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.asarray" title="Link to this definition">#</a></dt>
@@ -1365,6 +1634,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 backend-specific operator, <a class="reference internal" href="#pyxu.abc.LinOp.asarray" title="pyxu.abc.LinOp.asarray"><code class="xref py py-meth docutils literal notranslate"><span class="pre">asarray()</span></code></a> may need to be overriden.</p>
 </div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.gram">
 <span class="sig-name descname"><span class="pre">gram</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp.gram"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.gram" title="Link to this definition">#</a></dt>
@@ -1384,6 +1654,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 should re-define this method.</p>
 </div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.cogram">
 <span class="sig-name descname"><span class="pre">cogram</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp.cogram"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.cogram" title="Link to this definition">#</a></dt>
@@ -1403,6 +1674,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 user should re-define this method.</p>
 </div>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.pinv">
 <span class="sig-name descname"><span class="pre">pinv</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">damp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_fit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp.pinv"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.pinv" title="Link to this definition">#</a></dt>
@@ -1450,6 +1722,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 \[(\mathbf{A}^{\ast} \mathbf{A} + \tau I) \mathbf{x} = \mathbf{A}^{\ast} \mathbf{y},\]</div>
 <p>where <span class="math notranslate nohighlight">\(\tau &gt; 0\)</span> corresponds to the <code class="code docutils literal notranslate"><span class="pre">damp</span></code> parameter.</p>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.dagger">
 <span class="sig-name descname"><span class="pre">dagger</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">damp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_init</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kwargs_fit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp.dagger"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.dagger" title="Link to this definition">#</a></dt>
@@ -1470,6 +1743,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.abc.LinOp.from_array">
 <em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_array</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinOp.from_array"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinOp.from_array" title="Link to this definition">#</a></dt>
@@ -1489,7 +1763,9 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.SquareOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SquareOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#SquareOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SquareOp" title="Link to this definition">#</a></dt>
@@ -1508,7 +1784,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>method</strong> (<code class="docutils literal notranslate"><span class="pre">"explicit"</span></code> | <code class="docutils literal notranslate"><span class="pre">"hutchpp"</span></code>) – <ul>
+<li><p><strong>method</strong> (<code class="docutils literal notranslate"><span class="pre">&quot;explicit&quot;</span></code> | <code class="docutils literal notranslate"><span class="pre">&quot;hutchpp&quot;</span></code>) – <ul>
 <li><p>If <code class="code docutils literal notranslate"><span class="pre">explicit</span></code>, compute the exact trace.</p></li>
 <li><p>If <code class="code docutils literal notranslate"><span class="pre">hutchpp</span></code>, compute an approximation.</p></li>
 </ul>
@@ -1529,7 +1805,9 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.NormalOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NormalOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#NormalOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.NormalOp" title="Link to this definition">#</a></dt>
@@ -1544,6 +1822,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.SelfAdjointOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SelfAdjointOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#SelfAdjointOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.SelfAdjointOp" title="Link to this definition">#</a></dt>
@@ -1556,6 +1835,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.UnitOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">UnitOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#UnitOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.UnitOp" title="Link to this definition">#</a></dt>
@@ -1568,6 +1848,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.ProjOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ProjOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#ProjOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.ProjOp" title="Link to this definition">#</a></dt>
@@ -1580,6 +1861,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.OrthProjOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">OrthProjOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#OrthProjOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.OrthProjOp" title="Link to this definition">#</a></dt>
@@ -1593,6 +1875,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.PosDefOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PosDefOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#PosDefOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.PosDefOp" title="Link to this definition">#</a></dt>
@@ -1604,6 +1887,7 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.abc.LinFunc">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">LinFunc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/abc/operator.html#LinFunc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.abc.LinFunc" title="Link to this definition">#</a></dt>
@@ -1617,37 +1901,56 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 </dd>
 </dl>
 </dd></dl>
+
 </section>
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 <div class="prev-next-area">
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+    <a class="left-prev"
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+        <p class="prev-next-subtitle">next</p>
+        <p class="prev-next-title">pyxu.abc.solver</p>
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+  
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-<i class="fa-solid fa-list"></i> On this page
+
+                </footer>
+              
+            </div>
+            
+            
+              
+                <div class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
+
+  <div class="sidebar-secondary-item">
+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> On this page
   </div>
-<nav class="bd-toc-nav page-toc">
-<ul class="visible nav section-nav flex-column">
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property"><code class="docutils literal notranslate"><span class="pre">Property</span></code></a><ul class="visible nav section-nav flex-column">
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.CAN_EVAL"><code class="docutils literal notranslate"><span class="pre">Property.CAN_EVAL</span></code></a></li>
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.Property.FUNCTIONAL"><code class="docutils literal notranslate"><span class="pre">Property.FUNCTIONAL</span></code></a></li>
@@ -1744,13 +2047,16 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.PosDefOp"><code class="docutils literal notranslate"><span class="pre">PosDefOp</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.abc.LinFunc"><code class="docutils literal notranslate"><span class="pre">LinFunc</span></code></a></li>
 </ul>
-</nav></div>
-<div class="sidebar-secondary-item">
+  </nav></div>
+
+  <div class="sidebar-secondary-item">
 <div id="searchbox"></div></div>
-<div class="sidebar-secondary-item">
-<div class="tocsection editthispage">
-<a href="https://github.com/matthieumeo/pyxu/edit/main/doc/api/abc/operator.rst">
-<i class="fa-solid fa-pencil"></i>
+
+  <div class="sidebar-secondary-item">
+  
+  <div class="tocsection editthispage">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/api/abc/operator.rst">
+      <i class="fa-solid fa-pencil"></i>
       
       
         
@@ -1758,48 +2064,67 @@ <h1>pyxu.abc.operator<a class="headerlink" href="#pyxu-abc-operator" title="Link
         
       
     </a>
+  </div>
 </div>
-</div>
-<div class="sidebar-secondary-item">
-<div class="tocsection sourcelink">
-<a href="../../_sources/api/abc/operator.rst">
-<i class="fa-solid fa-file-lines"></i> Show Source
+
+  <div class="sidebar-secondary-item">
+  <div class="tocsection sourcelink">
+    <a href="../../_sources/api/abc/operator.rst">
+      <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
+  </div>
 </div>
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+        <div class="footer-item">
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 </html>
\ No newline at end of file
diff --git a/api/abc/solver.html b/api/abc/solver.html
index b0f06abd..33e08e26 100644
--- a/api/abc/solver.html
+++ b/api/abc/solver.html
@@ -28,7 +28,7 @@
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-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
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-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
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-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
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diff --git a/api/experimental.html b/api/experimental.html
deleted file mode 100644
index a5596cca..00000000
--- a/api/experimental.html
+++ /dev/null
@@ -1,765 +0,0 @@
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-<meta charset="utf-8"/>
-<meta content="width=device-width, initial-scale=1.0" name="viewport"/><meta content="width=device-width, initial-scale=1" name="viewport"/>
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-<section id="module-pyxu.experimental.sampler">
-<span id="pyxu-experimental"></span><h1>pyxu.experimental<a class="headerlink" href="#module-pyxu.experimental.sampler" title="Link to this heading">#</a></h1>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.MYULA">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MYULA</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gamma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lamb</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/_sampler.html#MYULA"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.MYULA" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.experimental.sampler.ULA" title="pyxu.experimental.sampler._sampler.ULA"><code class="xref py py-class docutils literal notranslate"><span class="pre">ULA</span></code></a></p>
-<p>Moreau-Yosida unajusted Langevin algorithm (MYULA).</p>
-<p>Generates samples from the distribution</p>
-<div class="math notranslate nohighlight">
-\[p(\mathbf{x}) = \frac{\exp(-\mathcal{F}(\mathbf{x}) - \mathcal{G}(\mathbf{x}))}{\int_{\mathbb{R}^N}
-\exp(-\mathcal{F}(\tilde{\mathbf{x}}) - \mathcal{G}(\tilde{\mathbf{x}})) \mathrm{d} \tilde{\mathbf{x}} },\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathcal{F}: \mathbb{R}^N \to \mathbb{R}\)</span> is <em>convex</em> and <em>differentiable</em> with <span class="math notranslate nohighlight">\(\beta\)</span>-
-<em>Lipschitz continuous</em> gradient, and <span class="math notranslate nohighlight">\(\mathcal{G}: \mathbb{R}^N \to \mathbb{R}\)</span> is <em>proper</em>, <em>lower semi-
-continuous</em> and <em>convex</em> with <em>simple proximal operator</em>.</p>
-<p class="rubric">Notes</p>
-<p>MYULA is an extension of <a class="reference internal" href="#pyxu.experimental.sampler.ULA" title="pyxu.experimental.sampler._sampler.ULA"><code class="xref py py-class docutils literal notranslate"><span class="pre">ULA</span></code></a> to sample from distributions whose
-logarithm is nonsmooth.
-It consists in applying ULA to the differentiable functional <span class="math notranslate nohighlight">\(\mathcal{U}^\lambda = \mathcal{F} + \mathcal{G}^\lambda\)</span>
-for some <span class="math notranslate nohighlight">\(\lambda &gt; 0\)</span>, where</p>
-<blockquote>
-<div><div class="math notranslate nohighlight">
-\[\mathcal{G}^\lambda (\mathbf{x}) = \inf_{\tilde{\mathbf{x}} \in \mathbb{R}^N} \frac{1}{2 \lambda} \Vert
-\tilde{\mathbf{x}} - \mathbf{x} \Vert_2^2 + \mathcal{G}(\tilde{\mathbf{x}})\]</div>
-</div></blockquote>
-<p>is the Moreau-Yosida envelope of <span class="math notranslate nohighlight">\(\mathcal{G}\)</span> with parameter <span class="math notranslate nohighlight">\(\lambda\)</span>.
-We then have</p>
-<div class="math notranslate nohighlight">
-\[\nabla \mathcal{U}^\lambda (\mathbf{x}) = \nabla \mathcal{F}(\mathbf{x}) + \frac{1}{\lambda} (\mathbf{x} -
-\mathrm{prox}_{\lambda \mathcal{G}}(\mathbf{x})),\]</div>
-<p>hence <span class="math notranslate nohighlight">\(\nabla \mathcal{U}^\lambda\)</span> is <span class="math notranslate nohighlight">\((\beta + \frac{1}{\lambda})\)</span>-Lipschitz continuous, where
-<span class="math notranslate nohighlight">\(\beta\)</span> is the Lipschitz constant of <span class="math notranslate nohighlight">\(\nabla \mathcal{F}\)</span>.
-Note that the target distribution of the underlying ULA Markov chain is not exactly <span class="math notranslate nohighlight">\(p(\mathbf{x})\)</span>, but the distribution</p>
-<div class="math notranslate nohighlight">
-\[p^\lambda(\mathbf{x}) \propto \exp(-\mathcal{F}(\mathbf{x})-\mathcal{G}^\lambda(\mathbf{x})),\]</div>
-<p>which introduces some additional bias on top of the bias of ULA related to the step size <span class="math notranslate nohighlight">\(\gamma\)</span> (see <code class="code docutils literal notranslate"><span class="pre">Notes</span></code>
-of <a class="reference internal" href="#pyxu.experimental.sampler.ULA" title="pyxu.experimental.sampler._sampler.ULA"><code class="xref py py-class docutils literal notranslate"><span class="pre">ULA</span></code></a> documentation).
-MYULA is guaranteed to converges when <span class="math notranslate nohighlight">\(\gamma \leq \frac{1}{\beta + \frac{1}{\lambda}}\)</span>, in which case it converges
-toward the stationary distribution <span class="math notranslate nohighlight">\(p^\lambda_\gamma(\mathbf{x})\)</span> that satisfies</p>
-<div class="math notranslate nohighlight">
-\[\lim_{\gamma, \lambda \to 0} \Vert p^\lambda_\gamma - p \Vert_{\mathrm{TV}} = 0\]</div>
-<p>(see <a class="reference internal" href="../references.html#myula" id="id1"><span>[MYULA]</span></a>).
-The parameter <span class="math notranslate nohighlight">\(\lambda\)</span> parameter is subject to a similar bias-variance tradeoff as <span class="math notranslate nohighlight">\(\gamma\)</span>.
-It is recommended to set it in the order of <span class="math notranslate nohighlight">\(\frac{1}{\beta}\)</span>, so that the contributions of <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>
-and <span class="math notranslate nohighlight">\(\mathcal{G}^\lambda\)</span> to the Lipschitz constant of <span class="math notranslate nohighlight">\(\nabla \mathcal{U}^\lambda\)</span> is well balanced.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a>) – </p></li>
-<li><p><strong>gamma</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-<li><p><strong>lamb</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.MYULA.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gamma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lamb</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/_sampler.html#MYULA.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.MYULA.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a> | None) – Differentiable functional.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a> | None) – Proximable functional.</p></li>
-<li><p><strong>gamma</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Euler-Maruyama discretization step of the Langevin equation (see <code class="code docutils literal notranslate"><span class="pre">Notes</span></code> of
-<a class="reference internal" href="#pyxu.experimental.sampler.ULA" title="pyxu.experimental.sampler._sampler.ULA"><code class="xref py py-class docutils literal notranslate"><span class="pre">ULA</span></code></a> documentation).</p></li>
-<li><p><strong>lamb</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Moreau-Yosida envelope parameter for <code class="code docutils literal notranslate"><span class="pre">g</span></code>.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.OnlineCenteredMoment">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">OnlineCenteredMoment</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/statistics.html#OnlineCenteredMoment"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.OnlineCenteredMoment" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_OnlineStat</span></code></p>
-<p>Pointwise online centered moment.</p>
-<p>For <span class="math notranslate nohighlight">\(d \geq 2\)</span>, the <span class="math notranslate nohighlight">\(d\)</span>-th order centered moment of the <span class="math notranslate nohighlight">\(K\)</span> samples <span class="math notranslate nohighlight">\((\mathbf{x}_k)_{1 \leq
-k \leq K}\)</span> is given by <span class="math notranslate nohighlight">\(\boldsymbol{\mu}_d=\frac{1}{K} \sum_{k=1}^K (\mathbf{x}_k-\boldsymbol{\mu})^d\)</span>, where
-<span class="math notranslate nohighlight">\(\boldsymbol{\mu}\)</span> is the sample mean.</p>
-<p class="rubric">Notes</p>
-<p>This class implements the <em>Welford algorithm</em> described in <a class="reference internal" href="../references.html#welfordalg" id="id2"><span>[WelfordAlg]</span></a>, which is a numerically stable algorithm
-for computing online centered moments. In particular, it avoids <a class="reference external" href="https://en.wikipedia.org/wiki/Catastrophic_cancellation">catastrophic cancellation</a> issues that may arise when naively computing online
-centered moments, which would lead to a loss of numerical precision.</p>
-<p>Note that this class internally stores the values of all online centered moments of order <span class="math notranslate nohighlight">\(d'\)</span> for
-<span class="math notranslate nohighlight">\(2 \leq d' \leq d\)</span> in the attribute <code class="docutils literal notranslate"><span class="pre">_corrected_sums</span></code> as well as the online mean (<code class="docutils literal notranslate"><span class="pre">_mean</span></code> attribute). More
-precisely, the array <code class="docutils literal notranslate"><span class="pre">_corrected_sums[i,</span> <span class="pre">:]</span></code> corresponds to the online sum <span class="math notranslate nohighlight">\(\boldsymbol{\mu}_{i+2}=
-\sum_{k=1}^K (\mathbf{x}_k-\boldsymbol{\mu})^{i+2}\)</span> for <span class="math notranslate nohighlight">\(0 \leq i \leq d-2\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>order</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.OnlineCenteredMoment.update">
-<span class="sig-name descname"><span class="pre">update</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/statistics.html#OnlineCenteredMoment.update"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.OnlineCenteredMoment.update" title="Link to this definition">#</a></dt>
-<dd><p>Update the online statistic based on a new sample. Should update <code class="code docutils literal notranslate"><span class="pre">_num_samples</span></code> and <code class="code docutils literal notranslate"><span class="pre">_stat</span></code> attributes.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – New sample.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>stat</strong> – Updated statistic.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.OnlineKurtosis">
-<span class="sig-name descname"><span class="pre">OnlineKurtosis</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/statistics.html#OnlineKurtosis"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.OnlineKurtosis" title="Link to this definition">#</a></dt>
-<dd><p>Pointwise online kurtosis.</p>
-<p>The pointwise online variance of the <span class="math notranslate nohighlight">\(K\)</span> samples <span class="math notranslate nohighlight">\((\mathbf{x}_k)_{1 \leq k \leq K}\)</span> is given by
-<span class="math notranslate nohighlight">\(\frac{1}{K}\sum_{k=1}^K \left( \frac{\mathbf{x}_k-\boldsymbol{\mu}}{\boldsymbol{\sigma}}\right)^4\)</span>, where
-<span class="math notranslate nohighlight">\(\boldsymbol{\mu}\)</span> is the sample mean and <span class="math notranslate nohighlight">\(\boldsymbol{\sigma}\)</span> its standard deviation.</p>
-<p><a class="reference external" href="https://en.wikipedia.org/wiki/Kurtosis">Kurtosis</a> is a measure of the heavy-tailedness of a distribution. In
-particular, the kurtosis of a Gaussian distribution is always 3.</p>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.OnlineMoment">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">OnlineMoment</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/statistics.html#OnlineMoment"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.OnlineMoment" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_OnlineStat</span></code></p>
-<p>Pointwise online moment.</p>
-<p>For <span class="math notranslate nohighlight">\(d \geq 1\)</span>, the <span class="math notranslate nohighlight">\(d\)</span>-th order centered moment of the <span class="math notranslate nohighlight">\(K\)</span> samples <span class="math notranslate nohighlight">\((\mathbf{x}_k)_{1 \leq
-k \leq K}\)</span> is given by <span class="math notranslate nohighlight">\(\frac{1}{K}\sum_{k=1}^K \mathbf{x}_k^d\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>order</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.OnlineMoment.update">
-<span class="sig-name descname"><span class="pre">update</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/statistics.html#OnlineMoment.update"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.OnlineMoment.update" title="Link to this definition">#</a></dt>
-<dd><p>Update the online statistic based on a new sample. Should update <code class="code docutils literal notranslate"><span class="pre">_num_samples</span></code> and <code class="code docutils literal notranslate"><span class="pre">_stat</span></code> attributes.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – New sample.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>stat</strong> – Updated statistic.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.OnlineSkewness">
-<span class="sig-name descname"><span class="pre">OnlineSkewness</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/statistics.html#OnlineSkewness"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.OnlineSkewness" title="Link to this definition">#</a></dt>
-<dd><p>Pointwise online skewness.</p>
-<p>The pointwise online skewness of the <span class="math notranslate nohighlight">\(K\)</span> samples <span class="math notranslate nohighlight">\((\mathbf{x}_k)_{1 \leq k \leq K}\)</span> is given by
-<span class="math notranslate nohighlight">\(\frac{1}{K}\sum_{k=1}^K \left( \frac{\mathbf{x}_k-\boldsymbol{\mu}}{\boldsymbol{\sigma}}\right)^3\)</span>, where
-<span class="math notranslate nohighlight">\(\boldsymbol{\mu}\)</span> is the sample mean and <span class="math notranslate nohighlight">\(\boldsymbol{\sigma}\)</span> its standard deviation.</p>
-<p><a class="reference external" href="https://en.wikipedia.org/wiki/Skewness">Skewness</a> is a measure of asymmetry of a distribution around its mean.
-Negative skewness indicates that the distribution has a heavier tail on the left side than on the right side,
-positive skewness indicates the opposite, and values close to zero indicate a symmetric distribution.</p>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.OnlineStd">
-<span class="sig-name descname"><span class="pre">OnlineStd</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/statistics.html#OnlineStd"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.OnlineStd" title="Link to this definition">#</a></dt>
-<dd><p>Pointwise online standard deviation.</p>
-<p>The pointwise online standard deviation of the <span class="math notranslate nohighlight">\(K\)</span> samples <span class="math notranslate nohighlight">\((\mathbf{x}_k)_{1 \leq k \leq K}\)</span> is given
-by <span class="math notranslate nohighlight">\(\boldsymbol{\sigma}=\sqrt{\frac{1}{K}\sum_{k=1}^K (\mathbf{x}_k - \boldsymbol{\mu})^2}\)</span>, where
-<span class="math notranslate nohighlight">\(\boldsymbol{\mu}\)</span> is the sample mean.</p>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.OnlineVariance">
-<span class="sig-name descname"><span class="pre">OnlineVariance</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/statistics.html#OnlineVariance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.OnlineVariance" title="Link to this definition">#</a></dt>
-<dd><p>Pointwise online variance.</p>
-<p>The pointwise online variance of the <span class="math notranslate nohighlight">\(K\)</span> samples <span class="math notranslate nohighlight">\((\mathbf{x}_k)_{1 \leq k \leq K}\)</span> is given by
-<span class="math notranslate nohighlight">\(\boldsymbol{\sigma}^2 = \frac{1}{K}\sum_{k=1}^K (\mathbf{x}_k-\boldsymbol{\mu})^2\)</span>, where
-<span class="math notranslate nohighlight">\(\boldsymbol{\mu}\)</span> is the sample mean.</p>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.ULA">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ULA</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gamma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/_sampler.html#ULA"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.ULA" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_Sampler</span></code></p>
-<p>Unajusted Langevin algorithm (ULA).</p>
-<p>Generates samples from the distribution</p>
-<div class="math notranslate nohighlight">
-\[p(\mathbf{x})
-=
-\frac{\exp(-\mathcal{F}(\mathbf{x}))}{\int_{\mathbb{R}^N} \exp(-\mathcal{F}(\tilde{\mathbf{x}}))
-\mathrm{d} \tilde{\mathbf{x}} },\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathcal{F}: \mathbb{R}^N \to \mathbb{R}\)</span> is <em>differentiable</em> with <span class="math notranslate nohighlight">\(\beta\)</span>-<em>Lipschitz continuous</em>
-gradient.</p>
-<p class="rubric">Notes</p>
-<p>ULA is a Monte-Carlo Markov chain (MCMC) method that derives from the discretization of overdamped Langevin diffusions.
-More specifically, it relies on the Langevin stochastic differential equation (SDE):</p>
-<div class="math notranslate nohighlight">
-\[\mathrm{d} \mathbf{X}_t
-=
-- \nabla \mathcal{F}(\mathbf{X}_t) \mathrm{d}t + \sqrt{2} \mathrm{d} \mathbf{B}_t,\]</div>
-<p>where <span class="math notranslate nohighlight">\((\mathbf{B}_t)_{t \geq 0}\)</span> is a <span class="math notranslate nohighlight">\(N\)</span>-dimensional Brownian motion.
-It is well known that under mild technical assumptions, this SDE has a unique strong solution whose invariant distribution
-is <span class="math notranslate nohighlight">\(p(\mathbf{x}) \propto \exp(-\mathcal{F}(\mathbf{x}))\)</span>.
-The discrete-time Euler-Maruyama discretization of this SDE then yields the ULA Markov chain</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{X}_{k+1} = \mathbf{X}_{k} - \gamma \nabla \mathcal{F}(\mathbf{X}_k) + \sqrt{2 \gamma} \mathbf{Z}_{k+1}\]</div>
-<p>for all <span class="math notranslate nohighlight">\(k \in \mathbb{Z}\)</span>, where <span class="math notranslate nohighlight">\(\gamma\)</span> is the discretization step size and <span class="math notranslate nohighlight">\((\mathbf{Z}_k)_{k
-\in \mathbb{Z}}\)</span> is a sequence of independant and identically distributed <span class="math notranslate nohighlight">\(N\)</span>-dimensional standard Gaussian
-distributions.
-When <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is differentiable with <span class="math notranslate nohighlight">\(\beta\)</span>-Lipschitz continuous gradient and <span class="math notranslate nohighlight">\(\gamma \leq \frac{1}{\beta}\)</span>,
-the ULA Markov chain converges (see <a class="reference internal" href="../references.html#ula" id="id3"><span>[ULA]</span></a>) to a unique stationary distribution <span class="math notranslate nohighlight">\(p_\gamma\)</span> such that</p>
-<div class="math notranslate nohighlight">
-\[\lim_{\gamma \to 0} \Vert p_\gamma - p \Vert_{\mathrm{TV}} = 0.\]</div>
-<p>The discretization step <span class="math notranslate nohighlight">\(\gamma\)</span> is subject to the bias-variance tradeoff:
-a larger step will lead to faster convergence of the Markov chain at the expense of a larger bias in the
-approximation of the distribution <span class="math notranslate nohighlight">\(p\)</span>.
-Setting <span class="math notranslate nohighlight">\(\gamma\)</span> as large as possible (default behavior) is recommended for large-scale problems, since
-convergence speed (rather than approximation bias) is then typically the main bottelneck.
-See <code class="code docutils literal notranslate"><span class="pre">Example</span></code> section below for a concrete illustration of this tradeoff.</p>
-<section id="remarks">
-<h2>Remarks<a class="headerlink" href="#remarks" title="Link to this heading">#</a></h2>
-<p>Like all MCMC sampling methods, ULA comes with the following challenges:</p>
-<ul class="simple">
-<li><p>The first few samples of the chain may not be adequate for computing statistics, as they might be located in low
-probability regions.
-This challenge can either be alleviated by selecting a representative starting point to the chain, or by having a
-<code class="code docutils literal notranslate"><span class="pre">burn-in</span></code> phase where the first few samples are discarded.</p></li>
-<li><p>Consecutive samples are typically correlated, which can deteriorate the Monte-Carlo estimation of quantities of
-interest.
-This issue can be alleviated by <code class="code docutils literal notranslate"><span class="pre">thinning</span></code> the chain, i.e., selecting only every <span class="math notranslate nohighlight">\(k\)</span> samples, at the expense
-of an increased computational cost.
-Useful diagnostic tools to quantify this correlation between samples include the pixel-wise autocorrelation function
-and the <a class="reference external" href="https://mc-stan.org/docs/reference-manual/effective-sample-size.html">effective sample size</a>.</p></li>
-</ul>
-<p class="rubric">Example</p>
-<p>We illustrate ULA on a 1D example (<span class="math notranslate nohighlight">\(N = 1\)</span>) where <span class="math notranslate nohighlight">\(\mathcal{F}(x) = \frac{x^2}{2}\)</span>; the target
-distribution <span class="math notranslate nohighlight">\(p(x)\)</span> is thus the 1D standard Gaussian.
-In this toy example, the biased distribution <span class="math notranslate nohighlight">\(p_\gamma(x)\)</span> can be computed in closed form.
-The ULA Markov chain is given by</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{X}_{k+1} &amp;= \mathbf{X}_{k} - \gamma \nabla\mathcal{F}(\mathbf{X}_k) + \sqrt{2\gamma}\mathbf{Z}_{k+1} \\
-&amp;= \mathbf{X}_{k} (1 - \gamma) + \sqrt{2 \gamma} \mathbf{Z}_{k+1}.\end{split}\]</div>
-<p>Assuming for simplicity that <span class="math notranslate nohighlight">\(\mathbf{X}_0\)</span> is Gaussian with mean <span class="math notranslate nohighlight">\(\mu_0\)</span> and variance
-<span class="math notranslate nohighlight">\(\sigma_0^2\)</span>, <span class="math notranslate nohighlight">\(\mathbf{X}_k\)</span> is Gaussian for any <span class="math notranslate nohighlight">\(k \in \mathbb{Z}\)</span> as a linear combination of
-Gaussians.
-Taking the expected value of the recurrence relation yields</p>
-<div class="math notranslate nohighlight">
-\[\mu_k := \mathbb{E}(\mathbf{X}_{k}) = \mathbb{E}(\mathbf{X}_{k-1}) (1 - \gamma) = \mu_0 (1 - \gamma)^k\]</div>
-<p>(geometric sequence).
-Taking the expected value of the square of the recurrence relation yields</p>
-<div class="math notranslate nohighlight">
-\[\mu^{(2)}_k := \mathbb{E}(\mathbf{X}_{k}^2) = \mathbb{E}(\mathbf{X}_{k-1}^2) (1 - \gamma)^2 + 2 \gamma =
-(1 - \gamma)^{2k} (\sigma_0^2 - b) + b\]</div>
-<p>with <span class="math notranslate nohighlight">\(b = \frac{2 \gamma}{1 - (1 - \gamma)^{2}} = \frac{1}{1-\frac{\gamma}{2}}\)</span> (arithmetico-geometric
-sequence) due to the independence of <span class="math notranslate nohighlight">\(\mathbf{X}_{k-1}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{Z}_{k}\)</span>.
-Hence, <span class="math notranslate nohighlight">\(p_\gamma(x)\)</span> is a Gaussian with mean <span class="math notranslate nohighlight">\(\mu_\gamma= \lim_{k \to \infty} \mu_k = 0\)</span> and
-variance <span class="math notranslate nohighlight">\(\sigma_\gamma^2 = \lim_{k \to \infty} \mu^{(2)}_k - \mu_k^2 = \frac{1}{1-\frac{\gamma}{2}}\)</span>.
-As expected, we have <span class="math notranslate nohighlight">\(\lim_{\gamma \to 0} \sigma_\gamma^2 = 1\)</span>, which is the variance of the target
-distribution <span class="math notranslate nohighlight">\(p(x)\)</span>.</p>
-<p>We plot the distribution of the samples of ULA for one large (<span class="math notranslate nohighlight">\(\gamma_1 \approx 1\)</span>, i.e.
-<span class="math notranslate nohighlight">\(\sigma_{\gamma_1}^2 \approx 2\)</span>) and one small (<span class="math notranslate nohighlight">\(\gamma_2 = 0.1\)</span>, i.e. <span class="math notranslate nohighlight">\(\sigma_{\gamma_2}^2
-\approx 1.05\)</span>) step size.
-As expected, the larger step size <span class="math notranslate nohighlight">\(\gamma_1\)</span> leads to a larger bias in the approximation of <span class="math notranslate nohighlight">\(p(x)\)</span>.
-To quantify the speed of convergence of the Markov chains, we compute the <a class="reference external" href="https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93von_Mises_criterion">Cramér-von Mises</a> tests of goodness of fit of the
-empirical distributions to the stationary distributions of ULA <span class="math notranslate nohighlight">\(p_{\gamma_1}(x)\)</span> and <span class="math notranslate nohighlight">\(p_{\gamma_2}(x)\)</span>.
-We observe that the larger step <span class="math notranslate nohighlight">\(\gamma_1\)</span> leads to a better fit (lower Cramér-von Mises criterion), which
-illustrates the aforementioned bias-variance tradeoff for the choice of the step size.</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/experimental.html#module-pyxu.experimental.sampler" title="pyxu.experimental.sampler"><span class="nn">pyxu.experimental.sampler</span></a> <span class="k">as</span> <span class="nn">pxe_sampler</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/index.html#module-scipy" title="scipy"><span class="nn">scipy</span></a> <span class="k">as</span> <span class="nn">sp</span>
-
-<span class="n">f</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.func.norm.SquaredL2Norm" title="pyxu.operator.func.norm.SquaredL2Norm"><span class="n">pxo</span><span class="o">.</span><span class="n">SquaredL2Norm</span></a><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>  <span class="c1"># To sample 1D normal distribution (mean 0, variance 1)</span>
-<a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.ULA" title="pyxu.experimental.sampler._sampler.ULA"><span class="n">ula</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.ULA" title="pyxu.experimental.sampler._sampler.ULA"><span class="n">pxe_sampler</span><span class="o">.</span><span class="n">ULA</span></a><span class="p">(</span><span class="n">f</span><span class="o">=</span><span class="n">f</span><span class="p">)</span>  <span class="c1"># Sampler with maximum step size</span>
-<a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.ULA" title="pyxu.experimental.sampler._sampler.ULA"><span class="n">ula_lb</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.ULA" title="pyxu.experimental.sampler._sampler.ULA"><span class="n">pxe_sampler</span><span class="o">.</span><span class="n">ULA</span></a><span class="p">(</span><span class="n">f</span><span class="o">=</span><span class="n">f</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">1e-1</span><span class="p">)</span>  <span class="c1"># Sampler with small step size</span>
-
-<a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Generator" title="collections.abc.Generator"><span class="n">gen_ula</span></a> <span class="o">=</span> <span class="n">ula</span><span class="o">.</span><span class="n">samples</span><span class="p">(</span><span class="n">x0</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="mi">1</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Generator" title="collections.abc.Generator"><span class="n">gen_ula_lb</span></a> <span class="o">=</span> <span class="n">ula_lb</span><span class="o">.</span><span class="n">samples</span><span class="p">(</span><span class="n">x0</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="mi">1</span><span class="p">))</span>
-<span class="n">n_burn_in</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#int" title="int"><span class="nb">int</span></a><span class="p">(</span><span class="mf">1e3</span><span class="p">)</span>  <span class="c1"># Number of burn-in iterations</span>
-<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#range" title="range"><span class="nb">range</span></a><span class="p">(</span><span class="n">n_burn_in</span><span class="p">):</span>
-    <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#next" title="next"><span class="nb">next</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Generator" title="collections.abc.Generator"><span class="n">gen_ula</span></a><span class="p">)</span>
-    <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#next" title="next"><span class="nb">next</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Generator" title="collections.abc.Generator"><span class="n">gen_ula_lb</span></a><span class="p">)</span>
-
-<span class="c1"># Online statistics objects</span>
-<a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.OnlineMoment" title="pyxu.experimental.sampler.statistics.OnlineMoment"><span class="n">mean_ula</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.OnlineMoment" title="pyxu.experimental.sampler.statistics.OnlineMoment"><span class="n">pxe_sampler</span><span class="o">.</span><span class="n">OnlineMoment</span></a><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.OnlineMoment" title="pyxu.experimental.sampler.statistics.OnlineMoment"><span class="n">mean_ula_lb</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.OnlineMoment" title="pyxu.experimental.sampler.statistics.OnlineMoment"><span class="n">pxe_sampler</span><span class="o">.</span><span class="n">OnlineMoment</span></a><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
-<span class="n">var_ula</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.OnlineVariance" title="pyxu.experimental.sampler.OnlineVariance"><span class="n">pxe_sampler</span><span class="o">.</span><span class="n">OnlineVariance</span></a><span class="p">()</span>
-<span class="n">var_ula_lb</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/experimental.html#pyxu.experimental.sampler.OnlineVariance" title="pyxu.experimental.sampler.OnlineVariance"><span class="n">pxe_sampler</span><span class="o">.</span><span class="n">OnlineVariance</span></a><span class="p">()</span>
-
-<span class="n">n</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#int" title="int"><span class="nb">int</span></a><span class="p">(</span><span class="mf">1e4</span><span class="p">)</span>  <span class="c1"># Number of samples</span>
-<span class="n">samples_ula</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">n</span><span class="p">)</span>
-<span class="n">samples_ula_lb</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">n</span><span class="p">)</span>
-<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#range" title="range"><span class="nb">range</span></a><span class="p">(</span><span class="n">n</span><span class="p">):</span>
-    <span class="n">sample</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#next" title="next"><span class="nb">next</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Generator" title="collections.abc.Generator"><span class="n">gen_ula</span></a><span class="p">)</span>
-    <span class="n">sample_lb</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#next" title="next"><span class="nb">next</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Generator" title="collections.abc.Generator"><span class="n">gen_ula_lb</span></a><span class="p">)</span>
-    <span class="n">samples_ula</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">sample</span>
-    <span class="n">samples_ula_lb</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">sample_lb</span>
-    <span class="n">mean</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#float" title="float"><span class="nb">float</span></a><span class="p">(</span><span class="n">mean_ula</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">sample</span><span class="p">))</span>
-    <span class="n">var</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#float" title="float"><span class="nb">float</span></a><span class="p">(</span><span class="n">var_ula</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">sample</span><span class="p">))</span>
-    <span class="n">mean_lb</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#float" title="float"><span class="nb">float</span></a><span class="p">(</span><span class="n">mean_ula_lb</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">sample_lb</span><span class="p">))</span>
-    <span class="n">var_lb</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#float" title="float"><span class="nb">float</span></a><span class="p">(</span><span class="n">var_ula_lb</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">sample_lb</span><span class="p">))</span>
-
-<span class="c1"># Theoretical variances of biased stationary distributions of ULA</span>
-<span class="n">biased_var</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">ula</span><span class="o">.</span><span class="n">_gamma</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
-<span class="n">biased_var_lb</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">ula_lb</span><span class="o">.</span><span class="n">_gamma</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
-
-<span class="c1"># Quantify goodness of fit of empirical distribution with theoretical distribution (Cramér-von Mises test)</span>
-<span class="n">cvm</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.cramervonmises.html#scipy.stats.cramervonmises" title="scipy.stats.cramervonmises"><span class="n">sp</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">cramervonmises</span></a><span class="p">(</span><span class="n">samples_ula</span><span class="p">,</span> <span class="s2">"norm"</span><span class="p">,</span> <span class="n">args</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><span class="n">biased_var</span><span class="p">)))</span>
-<span class="n">cvm_lb</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.cramervonmises.html#scipy.stats.cramervonmises" title="scipy.stats.cramervonmises"><span class="n">sp</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">cramervonmises</span></a><span class="p">(</span><span class="n">samples_ula_lb</span><span class="p">,</span> <span class="s2">"norm"</span><span class="p">,</span> <span class="n">args</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><span class="n">biased_var_lb</span><span class="p">)))</span>
-
-<span class="c1"># Plots</span>
-<span class="n">grid</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
-
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span>
-    <span class="sa">f</span><span class="s2">"ULA samples (large step size) </span><span class="se">\n</span><span class="s2"> Empirical mean: </span><span class="si">{</span><span class="n">mean</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2"> (theoretical: 0) </span><span class="se">\n</span><span class="s2"> "</span>
-    <span class="sa">f</span><span class="s2">"Empirical variance: </span><span class="si">{</span><span class="n">var</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2"> (theoretical: </span><span class="si">{</span><span class="n">biased_var</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">) </span><span class="se">\n</span><span class="s2">"</span>
-    <span class="sa">f</span><span class="s2">"Cramér-von Mises goodness of fit: </span><span class="si">{</span><span class="n">cvm</span><span class="o">.</span><span class="n">statistic</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span>
-<span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.hist.html#matplotlib.pyplot.hist" title="matplotlib.pyplot.hist"><span class="n">plt</span><span class="o">.</span><span class="n">hist</span></a><span class="p">(</span><span class="n">samples_ula</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#min" title="min"><span class="nb">min</span></a><span class="p">(</span><span class="n">grid</span><span class="p">),</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#max" title="max"><span class="nb">max</span></a><span class="p">(</span><span class="n">grid</span><span class="p">)),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">sp</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">grid</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$p(x)$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">sp</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><span class="n">biased_var</span><span class="p">)),</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$p_{\gamma_1}(x)$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/5e5b9b1c67e25e4482d76496b68f3b68/experimental-1.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/e8d0761a439aeaea00dcf73a4a90445e/experimental-1_00_00.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/070f6a163480e1040e23b47cc06445ff/experimental-1_00_00.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ad2f7e24bddbd17a6cfa96e6423ca673/experimental-1_00_00.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/experimental-1_00_00.png" class="plot-directive" src="../_images/experimental-1_00_00.png"/>
-</figure>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span>
-    <span class="sa">f</span><span class="s2">"ULA samples (small step size) </span><span class="se">\n</span><span class="s2"> Empirical mean: </span><span class="si">{</span><span class="n">mean_lb</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2"> (theoretical: 0) </span><span class="se">\n</span><span class="s2"> "</span>
-    <span class="sa">f</span><span class="s2">"Empirical variance: </span><span class="si">{</span><span class="n">var_lb</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2"> (theoretical: </span><span class="si">{</span><span class="n">biased_var_lb</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">) </span><span class="se">\n</span><span class="s2">"</span>
-    <span class="sa">f</span><span class="s2">"Cramér-von Mises goodness of fit: </span><span class="si">{</span><span class="n">cvm_lb</span><span class="o">.</span><span class="n">statistic</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span>
-<span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.hist.html#matplotlib.pyplot.hist" title="matplotlib.pyplot.hist"><span class="n">plt</span><span class="o">.</span><span class="n">hist</span></a><span class="p">(</span><span class="n">samples_ula_lb</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#min" title="min"><span class="nb">min</span></a><span class="p">(</span><span class="n">grid</span><span class="p">),</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#max" title="max"><span class="nb">max</span></a><span class="p">(</span><span class="n">grid</span><span class="p">)),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">sp</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">grid</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$p(x)$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">sp</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><span class="n">biased_var_lb</span><span class="p">)),</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">"$p_{\gamma_2}(x)$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/b36aa4a64f4a3c14b29c9ba6aa0773dd/experimental-1_01_00.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/4835132393171dc4fee6fa57fd1d6c6a/experimental-1_01_00.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/8860ae0fe6ee3c63137f67234c7ff9a8/experimental-1_01_00.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/experimental-1_01_00.png" class="plot-directive" src="../_images/experimental-1_01_00.png"/>
-</figure>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.ULA.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gamma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/_sampler.html#ULA.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.ULA.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>) – Differentiable functional.</p></li>
-<li><p><strong>gamma</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Euler-Maruyama discretization step of the Langevin equation (see <code class="code docutils literal notranslate"><span class="pre">Notes</span></code>).</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.experimental.sampler.ULA.objective_func">
-<span class="sig-name descname"><span class="pre">objective_func</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/experimental/sampler/_sampler.html#ULA.objective_func"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.experimental.sampler.ULA.objective_func" title="Link to this definition">#</a></dt>
-<dd><p>Negative logarithm of the target ditribution (up to the a constant) evaluated at the current state of the
-Markov chain.</p>
-<p>Useful for diagnostics purposes to monitor whether the Markov chain is sufficiently warm-started.
-If so, the samples should accumulate around the modes of the target distribution, i.e., toward the minimum of
-<span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p></li>
-<li><p><strong>gamma</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-</ul>
-</dd>
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-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.experimental.sampler.MYULA.__init__"><code class="docutils literal notranslate"><span class="pre">MYULA.__init__()</span></code></a></li>
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-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.experimental.sampler.OnlineMoment"><code class="docutils literal notranslate"><span class="pre">OnlineMoment</span></code></a><ul class="visible nav section-nav flex-column">
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-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.experimental.sampler.OnlineStd"><code class="docutils literal notranslate"><span class="pre">OnlineStd()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.experimental.sampler.OnlineVariance"><code class="docutils literal notranslate"><span class="pre">OnlineVariance()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.experimental.sampler.ULA"><code class="docutils literal notranslate"><span class="pre">ULA</span></code></a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.experimental.sampler.ULA.__init__"><code class="docutils literal notranslate"><span class="pre">ULA.__init__()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.experimental.sampler.ULA.objective_func"><code class="docutils literal notranslate"><span class="pre">ULA.objective_func()</span></code></a></li>
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diff --git a/api/experimental.sampler.html b/api/experimental.sampler.html
index 9297d309..79b2c7e1 100644
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 <link href="../references.html" rel="next" title="References"/>
-<link href="util/operator.html" rel="prev" title="pyxu.util.operator"/>
+<link href="util.html" rel="prev" title="pyxu.util"/>
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@@ -225,16 +225,11 @@
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-<li class="toctree-l2"><a class="reference internal" href="abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="abc.html">pyxu.abc</a></li>
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 <li class="toctree-l1"><a class="reference internal" href="info.warning.html">pyxu.info.warning</a></li>
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+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
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 <li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
@@ -246,13 +241,7 @@
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 <li class="toctree-l1"><a class="reference internal" href="runtime.html">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="math.html">pyxu.math</a></li>
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-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
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@@ -332,10 +321,10 @@
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
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-<li><p><strong>lamb</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a>) – </p></li>
+<li><p><strong>gamma</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
+<li><p><strong>lamb</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 </ul>
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@@ -345,8 +334,8 @@
 <dd><dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
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-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Differentiable functional.</p></li>
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@@ -373,7 +362,7 @@
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@@ -412,7 +401,7 @@
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-<dd class="field-odd"><p><strong>order</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p>
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@@ -625,7 +614,7 @@ <h2>Remarks<a class="headerlink" href="#remarks" title="Link to this heading">#<
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@@ -641,7 +630,7 @@ <h2>Remarks<a class="headerlink" href="#remarks" title="Link to this heading">#<
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@@ -649,8 +638,8 @@ <h2>Remarks<a class="headerlink" href="#remarks" title="Link to this heading">#<
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-<li><p><strong>gamma</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p></li>
+<li><p><strong>gamma</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -661,11 +650,11 @@ <h2>Remarks<a class="headerlink" href="#remarks" title="Link to this heading">#<
 <div class="footer-article-items footer-article__inner">
 <div class="footer-article-item"><!-- Previous / next buttons -->
 <div class="prev-next-area">
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 <p class="prev-next-subtitle">previous</p>
-<p class="prev-next-title">pyxu.util.operator</p>
+<p class="prev-next-title">pyxu.util</p>
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diff --git a/api/index.html b/api/index.html
index 62da3389..ebe4ddcb 100644
--- a/api/index.html
+++ b/api/index.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
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     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
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 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -63,8 +63,8 @@
     <link rel="icon" href="../_static/favicon.png"/>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
-    <link rel="next" title="pyxu.abc" href="abc/index.html" />
-    <link rel="prev" title="Differential operators in Pyxu" href="../examples/DifferentialOperators.html" />
+    <link rel="next" title="pyxu.abc" href="abc.html" />
+    <link rel="prev" title="Convolution with Pyxu" href="../examples/stencils.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
   <meta name="docsearch:language" content="en"/>
   </head>
@@ -408,16 +408,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="operator/blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
@@ -429,13 +424,7 @@
 <li class="toctree-l1"><a class="reference internal" href="opt.stop.html">pyxu.opt.stop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="runtime.html">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="util/array_module.html">pyxu.util.array_module</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../references.html"><strong>References</strong></a></li>
 </ul>
@@ -577,58 +566,58 @@ <h2><a class="toc-backref" href="#id4" role="doc-backlink">pyxu.abc</a><a class=
 <h3><a class="toc-backref" href="#id5" role="doc-backlink">Operator-related</a><a class="headerlink" href="#operator-related" title="Link to this heading">#</a></h3>
 <table class="autosummary longtable table autosummary">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>(shape)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>(shape)</p></td>
 <td><p>Base class for real-valued differentiable functionals <span class="math notranslate nohighlight">\(f: \mathbb{R}^{M} \to \mathbb{R}\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiffMap</span></code></a>(shape)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DiffMap</span></code></a>(shape)</p></td>
 <td><p>Base class for real-valued differentiable maps <span class="math notranslate nohighlight">\(\mathbf{f}: \mathbb{R}^{M} \to \mathbb{R}^{N}\)</span>.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.Func" title="pyxu.abc.Func"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Func</span></code></a>(shape)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.Func" title="pyxu.abc.Func"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Func</span></code></a>(shape)</p></td>
 <td><p>Base class for real-valued functionals <span class="math notranslate nohighlight">\(f: \mathbb{R}^{M} \to \mathbb{R}\cup\{+\infty\}\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.LinFunc" title="pyxu.abc.LinFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LinFunc</span></code></a>(shape)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.LinFunc" title="pyxu.abc.LinFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LinFunc</span></code></a>(shape)</p></td>
 <td><p>Base class for real-valued linear functionals <span class="math notranslate nohighlight">\(f: \mathbb{R}^{M} \to \mathbb{R}\)</span>.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LinOp</span></code></a>(shape)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LinOp</span></code></a>(shape)</p></td>
 <td><p>Base class for real-valued linear operators <span class="math notranslate nohighlight">\(\mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{N}\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.Map" title="pyxu.abc.Map"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Map</span></code></a>(shape)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.Map" title="pyxu.abc.Map"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Map</span></code></a>(shape)</p></td>
 <td><p>Base class for real-valued maps <span class="math notranslate nohighlight">\(\mathbf{f}: \mathbb{R}^{M} \to \mathbb{R}^{N}\)</span>.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.NormalOp" title="pyxu.abc.NormalOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NormalOp</span></code></a>(shape)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.NormalOp" title="pyxu.abc.NormalOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NormalOp</span></code></a>(shape)</p></td>
 <td><p>Base class for <em>normal</em> operators.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Operator</span></code></a>(shape)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Operator</span></code></a>(shape)</p></td>
 <td><p>Abstract Base Class for Pyxu operators.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.OrthProjOp" title="pyxu.abc.OrthProjOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OrthProjOp</span></code></a>(shape)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.OrthProjOp" title="pyxu.abc.OrthProjOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OrthProjOp</span></code></a>(shape)</p></td>
 <td><p>Base class for <em>orthogonal projection</em> operators.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.PosDefOp" title="pyxu.abc.PosDefOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PosDefOp</span></code></a>(shape)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.PosDefOp" title="pyxu.abc.PosDefOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PosDefOp</span></code></a>(shape)</p></td>
 <td><p>Base class for <em>positive-definite</em> operators.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.ProjOp" title="pyxu.abc.ProjOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ProjOp</span></code></a>(shape)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.ProjOp" title="pyxu.abc.ProjOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ProjOp</span></code></a>(shape)</p></td>
 <td><p>Base class for <em>projection</em> operators.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.Property" title="pyxu.abc.Property"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Property</span></code></a>(value[, names, module, qualname, ...])</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.Property" title="pyxu.abc.Property"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Property</span></code></a>(value[, names, module, qualname, ...])</p></td>
 <td><p>Mathematical property.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.ProxDiffFunc" title="pyxu.abc.ProxDiffFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ProxDiffFunc</span></code></a>(shape)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.ProxDiffFunc" title="pyxu.abc.ProxDiffFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ProxDiffFunc</span></code></a>(shape)</p></td>
 <td><p>Base class for real-valued differentiable <em>and</em> proximable functionals <span class="math notranslate nohighlight">\(f:\mathbb{R}^{M} \to \mathbb{R}\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>(shape)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>(shape)</p></td>
 <td><p>Base class for real-valued proximable functionals <span class="math notranslate nohighlight">\(f: \mathbb{R}^{M} \to \mathbb{R} \cup \{+\infty\}\)</span>.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.QuadraticFunc" title="pyxu.abc.QuadraticFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">QuadraticFunc</span></code></a>(shape[, Q, c, t])</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.QuadraticFunc" title="pyxu.abc.QuadraticFunc"><code class="xref py py-obj docutils literal notranslate"><span class="pre">QuadraticFunc</span></code></a>(shape[, Q, c, t])</p></td>
 <td><p>Base class for quadratic functionals <span class="math notranslate nohighlight">\(f: \mathbb{R}^{M} \to \mathbb{R} \cup \{+\infty\}\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.SelfAdjointOp" title="pyxu.abc.SelfAdjointOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SelfAdjointOp</span></code></a>(shape)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.SelfAdjointOp" title="pyxu.abc.SelfAdjointOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SelfAdjointOp</span></code></a>(shape)</p></td>
 <td><p>Base class for <em>self-adjoint</em> operators.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.SquareOp" title="pyxu.abc.SquareOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SquareOp</span></code></a>(shape)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.SquareOp" title="pyxu.abc.SquareOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SquareOp</span></code></a>(shape)</p></td>
 <td><p>Base class for <em>square</em> linear operators, i.e. <span class="math notranslate nohighlight">\(\mathbf{A}: \mathbb{R}^{M} \to \mathbb{R}^{M}\)</span> (endomorphsisms).</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.UnitOp" title="pyxu.abc.UnitOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">UnitOp</span></code></a>(shape)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.UnitOp" title="pyxu.abc.UnitOp"><code class="xref py py-obj docutils literal notranslate"><span class="pre">UnitOp</span></code></a>(shape)</p></td>
 <td><p>Base class for <em>unitary</em> operators.</p></td>
 </tr>
 </tbody>
@@ -638,13 +627,13 @@ <h3><a class="toc-backref" href="#id5" role="doc-backlink">Operator-related</a><
 <h3><a class="toc-backref" href="#id6" role="doc-backlink">Solver-related</a><a class="headerlink" href="#solver-related" title="Link to this heading">#</a></h3>
 <table class="autosummary longtable table autosummary">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Solver</span></code></a>(*[, folder, exist_ok, stop_rate, ...])</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Solver</span></code></a>(*[, folder, exist_ok, stop_rate, ...])</p></td>
 <td><p>Iterative solver for minimization problems of the form <span class="math notranslate nohighlight">\(\hat{x} = \arg\min_{x \in \mathbb{R}^{N}} \mathcal{F}(x)\)</span>, where the form of <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is solver-dependent.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/solver.html#pyxu.abc.SolverMode" title="pyxu.abc.SolverMode"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SolverMode</span></code></a>(value[, names, module, qualname, ...])</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.SolverMode" title="pyxu.abc.SolverMode"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SolverMode</span></code></a>(value[, names, module, qualname, ...])</p></td>
 <td><p>Solver execution mode.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/solver.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-obj docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a>()</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-obj docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a>()</p></td>
 <td><p>State machines (SM) which decide when to stop iterative solvers by examining their mathematical state.</p></td>
 </tr>
 </tbody>
@@ -654,29 +643,29 @@ <h3><a class="toc-backref" href="#id6" role="doc-backlink">Solver-related</a><a
 <h3><a class="toc-backref" href="#id7" role="doc-backlink">Arithmetic Rules (low-level)</a><a class="headerlink" href="#arithmetic-rules-low-level" title="Link to this heading">#</a></h3>
 <table class="autosummary longtable table autosummary">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/arithmetic.html#pyxu.abc.arithmetic.AddRule" title="pyxu.abc.arithmetic.AddRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.AddRule</span></code></a>(lhs, rhs)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.arithmetic.AddRule" title="pyxu.abc.arithmetic.AddRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.AddRule</span></code></a>(lhs, rhs)</p></td>
 <td><p>Arithmetic rules for operator addition: <span class="math notranslate nohighlight">\(C(x) = A(x) + B(x)\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/arithmetic.html#pyxu.abc.arithmetic.ArgScaleRule" title="pyxu.abc.arithmetic.ArgScaleRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.ArgScaleRule</span></code></a>(op, cst)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.arithmetic.ArgScaleRule" title="pyxu.abc.arithmetic.ArgScaleRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.ArgScaleRule</span></code></a>(op, cst)</p></td>
 <td><p>Arithmetic rules for element-wise parameter scaling: <span class="math notranslate nohighlight">\(B(x) = A(\alpha x)\)</span>.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/arithmetic.html#pyxu.abc.arithmetic.ArgShiftRule" title="pyxu.abc.arithmetic.ArgShiftRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.ArgShiftRule</span></code></a>(op, cst)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.arithmetic.ArgShiftRule" title="pyxu.abc.arithmetic.ArgShiftRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.ArgShiftRule</span></code></a>(op, cst)</p></td>
 <td><p>Arithmetic rules for parameter shifting: <span class="math notranslate nohighlight">\(B(x) = A(x - c)\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/arithmetic.html#pyxu.abc.arithmetic.ChainRule" title="pyxu.abc.arithmetic.ChainRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.ChainRule</span></code></a>(lhs, rhs)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.arithmetic.ChainRule" title="pyxu.abc.arithmetic.ChainRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.ChainRule</span></code></a>(lhs, rhs)</p></td>
 <td><p>Arithmetic rules for operator composition: <span class="math notranslate nohighlight">\(C(x) = (A \circ B)(x)\)</span>.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/arithmetic.html#pyxu.abc.arithmetic.PowerRule" title="pyxu.abc.arithmetic.PowerRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.PowerRule</span></code></a>(op, k)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.arithmetic.PowerRule" title="pyxu.abc.arithmetic.PowerRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.PowerRule</span></code></a>(op, k)</p></td>
 <td><p>Arithmetic rules for operator exponentiation: <span class="math notranslate nohighlight">\(B(x) = A^{k}(x)\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/arithmetic.html#pyxu.abc.arithmetic.Rule" title="pyxu.abc.arithmetic.Rule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.Rule</span></code></a>()</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.arithmetic.Rule" title="pyxu.abc.arithmetic.Rule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.Rule</span></code></a>()</p></td>
 <td><p>General arithmetic rule.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="abc/arithmetic.html#pyxu.abc.arithmetic.ScaleRule" title="pyxu.abc.arithmetic.ScaleRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.ScaleRule</span></code></a>(op, cst)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="abc.html#pyxu.abc.arithmetic.ScaleRule" title="pyxu.abc.arithmetic.ScaleRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.ScaleRule</span></code></a>(op, cst)</p></td>
 <td><p>Arithmetic rules for element-wise scaling: <span class="math notranslate nohighlight">\(B(x) = \alpha A(x)\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="abc/arithmetic.html#pyxu.abc.arithmetic.TransposeRule" title="pyxu.abc.arithmetic.TransposeRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.TransposeRule</span></code></a>(op)</p></td>
-<td><p>Arithmetic rules for <a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> transposition: <span class="math notranslate nohighlight">\(B(x) = A^{T}(x)\)</span>.</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="abc.html#pyxu.abc.arithmetic.TransposeRule" title="pyxu.abc.arithmetic.TransposeRule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic.TransposeRule</span></code></a>(op)</p></td>
+<td><p>Arithmetic rules for <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> transposition: <span class="math notranslate nohighlight">\(B(x) = A^{T}(x)\)</span>.</p></td>
 </tr>
 </tbody>
 </table>
@@ -764,31 +753,31 @@ <h2><a class="toc-backref" href="#id10" role="doc-backlink">pyxu.info.ptype</a><
 <td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a> shape specifier.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpC" title="pyxu.info.ptype.OpC"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OpC</span></code></a></p></td>
-<td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> hierarchy class type.</p></td>
+<td><p><a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> hierarchy class type.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpShape" title="pyxu.info.ptype.OpShape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OpShape</span></code></a></p></td>
-<td><p><a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> shape specifier.</p></td>
+<td><p><a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> shape specifier.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OpT</span></code></a></p></td>
-<td><p>Top-level abstract <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> interface exposed to users.</p></td>
+<td><p>Top-level abstract <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> interface exposed to users.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Path" title="pyxu.info.ptype.Path"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Path</span></code></a></p></td>
 <td><p>Path-like object.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Property" title="pyxu.info.ptype.Property"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Property</span></code></a></p></td>
-<td><p>Mathematical properties attached to <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> objects.</p></td>
+<td><p>Mathematical properties attached to <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> objects.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Real</span></code></a>()</p></td>
 <td><p>To Complex, Real adds the operations that work on real numbers.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.SolverC" title="pyxu.info.ptype.SolverC"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SolverC</span></code></a></p></td>
-<td><p><a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> hierarchy class type.</p></td>
+<td><p><a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> hierarchy class type.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.SolverM" title="pyxu.info.ptype.SolverM"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SolverM</span></code></a></p></td>
 <td><p>Solver run-modes.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.SolverT" title="pyxu.info.ptype.SolverT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SolverT</span></code></a></p></td>
-<td><p>Top-level abstract <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> interface exposed to users.</p></td>
+<td><p>Top-level abstract <a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> interface exposed to users.</p></td>
 </tr>
 <tr class="row-even"><td><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.SparseArray" title="pyxu.info.ptype.SparseArray"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SparseArray</span></code></a></p></td>
 <td><p>Supported sparse array types.</p></td>
@@ -859,7 +848,7 @@ <h3><a class="toc-backref" href="#id14" role="doc-backlink">General</a><a class=
 <table class="autosummary longtable table autosummary">
 <tbody>
 <tr class="row-odd"><td><p><a class="reference internal" href="operator.interop.html#pyxu.operator.interop.from_source" title="pyxu.operator.interop.from_source"><code class="xref py py-obj docutils literal notranslate"><span class="pre">from_source</span></code></a>(cls, shape[, embed, vectorize, ...])</p></td>
-<td><p>Define an <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from low-level constructs.</p></td>
+<td><p>Define an <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from low-level constructs.</p></td>
 </tr>
 </tbody>
 </table>
@@ -869,7 +858,7 @@ <h3><a class="toc-backref" href="#id15" role="doc-backlink">SciPy</a><a class="h
 <table class="autosummary longtable table autosummary">
 <tbody>
 <tr class="row-odd"><td><p><a class="reference internal" href="operator.interop.html#pyxu.operator.interop.from_sciop" title="pyxu.operator.interop.from_sciop"><code class="xref py py-obj docutils literal notranslate"><span class="pre">from_sciop</span></code></a>(cls, sp_op)</p></td>
-<td><p>Wrap a <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html#scipy.sparse.linalg.LinearOperator" title="(in SciPy v1.11.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinearOperator</span></code></a> as a <a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> (or sub-class thereof).</p></td>
+<td><p>Wrap a <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html#scipy.sparse.linalg.LinearOperator" title="(in SciPy v1.11.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinearOperator</span></code></a> as a <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> (or sub-class thereof).</p></td>
 </tr>
 </tbody>
 </table>
@@ -885,7 +874,7 @@ <h3><a class="toc-backref" href="#id16" role="doc-backlink">JAX</a><a class="hea
 <td><p>NumPy/CuPy -&gt; JAX conversion.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="operator.interop.html#pyxu.operator.interop.from_jax" title="pyxu.operator.interop.from_jax"><code class="xref py py-obj docutils literal notranslate"><span class="pre">from_jax</span></code></a>(cls, shape[, vectorize, jit, ...])</p></td>
-<td><p>Define an <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from JAX functions.</p></td>
+<td><p>Define an <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from JAX functions.</p></td>
 </tr>
 </tbody>
 </table>
@@ -901,7 +890,7 @@ <h3><a class="toc-backref" href="#id17" role="doc-backlink">PyTorch</a><a class=
 <td><p>NumPy/CuPy -&gt; PyTorch conversion.</p></td>
 </tr>
 <tr class="row-odd"><td><p><a class="reference internal" href="operator.interop.html#pyxu.operator.interop.from_torch" title="pyxu.operator.interop.from_torch"><code class="xref py py-obj docutils literal notranslate"><span class="pre">from_torch</span></code></a>(apply, shape[, cls, vectorize, ...])</p></td>
-<td><p>Define an <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from PyTorch functions.</p></td>
+<td><p>Define an <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from PyTorch functions.</p></td>
 </tr>
 </tbody>
 </table>
@@ -1386,12 +1375,18 @@ <h2><a class="toc-backref" href="#id27" role="doc-backlink">pyxu.util</a><a clas
 <h3><a class="toc-backref" href="#id28" role="doc-backlink">Array Backend-Related</a><a class="headerlink" href="#array-backend-related" title="Link to this heading">#</a></h3>
 <table class="autosummary longtable table autosummary">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/array_module.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_array_module</span></code></a>(x[, fallback])</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.compute" title="pyxu.util.compute"><code class="xref py py-obj docutils literal notranslate"><span class="pre">compute</span></code></a>(*args[, mode])</p></td>
+<td><p>Force computation of Dask collections.</p></td>
+</tr>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_array_module</span></code></a>(x[, fallback])</p></td>
 <td><p>Get the array namespace corresponding to a given object.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/array_module.html#pyxu.util.redirect" title="pyxu.util.redirect"><code class="xref py py-obj docutils literal notranslate"><span class="pre">redirect</span></code></a>(i, **kwargs)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.redirect" title="pyxu.util.redirect"><code class="xref py py-obj docutils literal notranslate"><span class="pre">redirect</span></code></a>(i, **kwargs)</p></td>
 <td><p>Change codepath for supplied array backends.</p></td>
 </tr>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.to_NUMPY" title="pyxu.util.to_NUMPY"><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_NUMPY</span></code></a>(x)</p></td>
+<td><p>Convert an array from a specific backend to NUMPY.</p></td>
+</tr>
 </tbody>
 </table>
 </section>
@@ -1399,16 +1394,16 @@ <h3><a class="toc-backref" href="#id28" role="doc-backlink">Array Backend-Relate
 <h3><a class="toc-backref" href="#id29" role="doc-backlink">Complex Number Handling</a><a class="headerlink" href="#complex-number-handling" title="Link to this heading">#</a></h3>
 <table class="autosummary longtable table autosummary">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/complex.html#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-obj docutils literal notranslate"><span class="pre">view_as_complex_mat</span></code></a>(rmat[, real_input, ...])</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-obj docutils literal notranslate"><span class="pre">view_as_complex_mat</span></code></a>(rmat[, real_input, ...])</p></td>
 <td><p>View real-valued matrix as its complex-valued equivalent.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/complex.html#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-obj docutils literal notranslate"><span class="pre">view_as_complex</span></code></a>(x)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-obj docutils literal notranslate"><span class="pre">view_as_complex</span></code></a>(x)</p></td>
 <td><p>View real-valued array as its complex-valued bijection.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/complex.html#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-obj docutils literal notranslate"><span class="pre">view_as_real_mat</span></code></a>(cmat[, real_input, real_output])</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-obj docutils literal notranslate"><span class="pre">view_as_real_mat</span></code></a>(cmat[, real_input, real_output])</p></td>
 <td><p>View complex-valued matrix as its real-valued equivalent.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-obj docutils literal notranslate"><span class="pre">view_as_real</span></code></a>(x)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-obj docutils literal notranslate"><span class="pre">view_as_real</span></code></a>(x)</p></td>
 <td><p>View complex-valued array as its real-valued bijection.</p></td>
 </tr>
 </tbody>
@@ -1418,11 +1413,11 @@ <h3><a class="toc-backref" href="#id29" role="doc-backlink">Complex Number Handl
 <h3><a class="toc-backref" href="#id30" role="doc-backlink">Operator-Related</a><a class="headerlink" href="#id2" title="Link to this heading">#</a></h3>
 <table class="autosummary longtable table autosummary">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/operator.html#pyxu.util.as_canonical_shape" title="pyxu.util.as_canonical_shape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">as_canonical_shape</span></code></a>(x)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.as_canonical_shape" title="pyxu.util.as_canonical_shape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">as_canonical_shape</span></code></a>(x)</p></td>
 <td><p>Transform a lone integer into a valid tuple-based shape specifier.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/operator.html#pyxu.util.vectorize" title="pyxu.util.vectorize"><code class="xref py py-obj docutils literal notranslate"><span class="pre">vectorize</span></code></a>(i[, method, codim])</p></td>
-<td><p>Decorator to auto-vectorize an array function to abide by <a class="reference internal" href="abc/operator.html#pyxu.abc.Property" title="pyxu.abc.Property"><code class="xref py py-class docutils literal notranslate"><span class="pre">Property</span></code></a> API rules.</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.vectorize" title="pyxu.util.vectorize"><code class="xref py py-obj docutils literal notranslate"><span class="pre">vectorize</span></code></a>(i[, method, codim])</p></td>
+<td><p>Decorator to auto-vectorize an array function to abide by <a class="reference internal" href="abc.html#pyxu.abc.Property" title="pyxu.abc.Property"><code class="xref py py-class docutils literal notranslate"><span class="pre">Property</span></code></a> API rules.</p></td>
 </tr>
 </tbody>
 </table>
@@ -1431,48 +1426,42 @@ <h3><a class="toc-backref" href="#id30" role="doc-backlink">Operator-Related</a>
 <h3><a class="toc-backref" href="#id31" role="doc-backlink">Misc</a><a class="headerlink" href="#id3" title="Link to this heading">#</a></h3>
 <table class="autosummary longtable table autosummary">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.compute" title="pyxu.util.compute"><code class="xref py py-obj docutils literal notranslate"><span class="pre">compute</span></code></a>(*args[, mode])</p></td>
-<td><p>Force computation of Dask collections.</p></td>
-</tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.copy_if_unsafe" title="pyxu.util.copy_if_unsafe"><code class="xref py py-obj docutils literal notranslate"><span class="pre">copy_if_unsafe</span></code></a>(x)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.copy_if_unsafe" title="pyxu.util.copy_if_unsafe"><code class="xref py py-obj docutils literal notranslate"><span class="pre">copy_if_unsafe</span></code></a>(x)</p></td>
 <td><p>Copy array if it is unsafe to do in-place updates on it.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.import_module" title="pyxu.util.import_module"><code class="xref py py-obj docutils literal notranslate"><span class="pre">import_module</span></code></a>(name[, fail_on_error])</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.import_module" title="pyxu.util.import_module"><code class="xref py py-obj docutils literal notranslate"><span class="pre">import_module</span></code></a>(name[, fail_on_error])</p></td>
 <td><p>Load a Python module dynamically.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.infer_composition_shape" title="pyxu.util.infer_composition_shape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">infer_composition_shape</span></code></a>(sh1, sh2)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.infer_composition_shape" title="pyxu.util.infer_composition_shape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">infer_composition_shape</span></code></a>(sh1, sh2)</p></td>
 <td><p>Infer shape of arithmetic operation <span class="math notranslate nohighlight">\(A \circ B\)</span>.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.infer_sum_shape" title="pyxu.util.infer_sum_shape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">infer_sum_shape</span></code></a>(sh1, sh2)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.infer_sum_shape" title="pyxu.util.infer_sum_shape"><code class="xref py py-obj docutils literal notranslate"><span class="pre">infer_sum_shape</span></code></a>(sh1, sh2)</p></td>
 <td><p>Infer shape of arithmetic operation <span class="math notranslate nohighlight">\(A + B\)</span>.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.next_fast_len" title="pyxu.util.next_fast_len"><code class="xref py py-obj docutils literal notranslate"><span class="pre">next_fast_len</span></code></a>(N[, even])</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.next_fast_len" title="pyxu.util.next_fast_len"><code class="xref py py-obj docutils literal notranslate"><span class="pre">next_fast_len</span></code></a>(N[, even])</p></td>
 <td><p>Compute the next <a class="reference external" href="https://en.wikipedia.org/wiki/Smooth_number">5-smooth number</a> greater-or-equal to <code class="code docutils literal notranslate"><span class="pre">N</span></code>.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.parse_params" title="pyxu.util.parse_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">parse_params</span></code></a>(func, *args, **kwargs)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.parse_params" title="pyxu.util.parse_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">parse_params</span></code></a>(func, *args, **kwargs)</p></td>
 <td><p>Get function parameterization.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.read_only" title="pyxu.util.read_only"><code class="xref py py-obj docutils literal notranslate"><span class="pre">read_only</span></code></a>(x)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.read_only" title="pyxu.util.read_only"><code class="xref py py-obj docutils literal notranslate"><span class="pre">read_only</span></code></a>(x)</p></td>
 <td><p>Make an array read-only.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.to_NUMPY" title="pyxu.util.to_NUMPY"><code class="xref py py-obj docutils literal notranslate"><span class="pre">to_NUMPY</span></code></a>(x)</p></td>
-<td><p>Convert an array from a specific backend to NUMPY.</p></td>
-</tr>
 </tbody>
 </table>
 <p class="rubric">Low-lever Helpers</p>
 <table class="autosummary longtable table autosummary">
 <tbody>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.util.misc.peaks</span></code></a>(x, y)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.util.misc.peaks</span></code></a>(x, y)</p></td>
 <td><p>Matlab 2D peaks function.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/misc.html#pyxu.util.misc.star_like_sample" title="pyxu.util.misc.star_like_sample"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.util.misc.star_like_sample</span></code></a>(N, w, s, po, x0)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.misc.star_like_sample" title="pyxu.util.misc.star_like_sample"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.util.misc.star_like_sample</span></code></a>(N, w, s, po, x0)</p></td>
 <td><p>Star-like test image.</p></td>
 </tr>
-<tr class="row-odd"><td><p><a class="reference internal" href="util/operator.html#pyxu.util.operator._array_ize" title="pyxu.util.operator._array_ize"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.util.operator._array_ize</span></code></a>(data, shape, dtype)</p></td>
+<tr class="row-odd"><td><p><a class="reference internal" href="util.html#pyxu.util.operator._array_ize" title="pyxu.util.operator._array_ize"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.util.operator._array_ize</span></code></a>(data, shape, dtype)</p></td>
 <td><p>Transform a Dask-delayed object into its Dask-array counterpart.</p></td>
 </tr>
-<tr class="row-even"><td><p><a class="reference internal" href="util/operator.html#pyxu.util.operator._dask_zip" title="pyxu.util.operator._dask_zip"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.util.operator._dask_zip</span></code></a>(func, data, ...)</p></td>
+<tr class="row-even"><td><p><a class="reference internal" href="util.html#pyxu.util.operator._dask_zip" title="pyxu.util.operator._dask_zip"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pyxu.util.operator._dask_zip</span></code></a>(func, data, ...)</p></td>
 <td><p>Map functions in parallel via Dask.</p></td>
 </tr>
 </tbody>
@@ -1495,16 +1484,16 @@ <h3><a class="toc-backref" href="#id31" role="doc-backlink">Misc</a><a class="he
     <div class="footer-article-item"><!-- Previous / next buttons -->
 <div class="prev-next-area">
     <a class="left-prev"
-       href="../examples/DifferentialOperators.html"
+       href="../examples/stencils.html"
        title="previous page">
       <i class="fa-solid fa-angle-left"></i>
       <div class="prev-next-info">
         <p class="prev-next-subtitle">previous</p>
-        <p class="prev-next-title">Differential operators in Pyxu</p>
+        <p class="prev-next-title">Convolution with Pyxu</p>
       </div>
     </a>
     <a class="right-next"
-       href="abc/index.html"
+       href="abc.html"
        title="next page">
       <div class="prev-next-info">
         <p class="prev-next-subtitle">next</p>
diff --git a/api/info.deps.html b/api/info.deps.html
index 7f493f22..e789b5d8 100644
--- a/api/info.deps.html
+++ b/api/info.deps.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
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@@ -38,13 +38,13 @@
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     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
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 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
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     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -62,7 +62,7 @@
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
     <link rel="next" title="pyxu.info.ptype" href="info.ptype.html" />
-    <link rel="prev" title="pyxu.abc.solver" href="abc/solver.html" />
+    <link rel="prev" title="pyxu.abc" href="abc.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
   <meta name="docsearch:language" content="en"/>
   </head>
@@ -406,16 +406,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="abc.html">pyxu.abc</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="operator/blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
@@ -427,13 +422,7 @@
 <li class="toctree-l1"><a class="reference internal" href="opt.stop.html">pyxu.opt.stop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="runtime.html">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="util/array_module.html">pyxu.util.array_module</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../references.html"><strong>References</strong></a></li>
 </ul>
@@ -497,7 +486,7 @@
 <span id="pyxu-info-deps"></span><h1>pyxu.info.deps<a class="headerlink" href="#module-pyxu.info.deps" title="Link to this heading">#</a></h1>
 <dl class="py data">
 <dt class="sig sig-object py" id="pyxu.info.deps.CUPY_ENABLED">
-<span class="sig-name descname"><span class="pre">CUPY_ENABLED</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><span class="pre">bool</span></a></em><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">False</span></em><a class="headerlink" href="#pyxu.info.deps.CUPY_ENABLED" title="Link to this definition">#</a></dt>
+<span class="sig-name descname"><span class="pre">CUPY_ENABLED</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><span class="pre">bool</span></a></em><a class="headerlink" href="#pyxu.info.deps.CUPY_ENABLED" title="Link to this definition">#</a></dt>
 <dd><p>Show if CuPy-based backends are available.</p>
 </dd></dl>
 
@@ -711,12 +700,12 @@
     <div class="footer-article-item"><!-- Previous / next buttons -->
 <div class="prev-next-area">
     <a class="left-prev"
-       href="abc/solver.html"
+       href="abc.html"
        title="previous page">
       <i class="fa-solid fa-angle-left"></i>
       <div class="prev-next-info">
         <p class="prev-next-subtitle">previous</p>
-        <p class="prev-next-title">pyxu.abc.solver</p>
+        <p class="prev-next-title">pyxu.abc</p>
       </div>
     </a>
     <a class="right-next"
diff --git a/api/info.html b/api/info.html
deleted file mode 100644
index 8936e896..00000000
--- a/api/info.html
+++ /dev/null
@@ -1,1102 +0,0 @@
-
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-
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-<html lang="en" data-theme="light">
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-    <meta charset="utf-8" />
-    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
-
-    <title>pyxu.info &#8212; Pyxu Documentation</title>
-  
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-  
-  <script data-cfasync="false">
-    document.documentElement.dataset.mode = localStorage.getItem("mode") || "light";
-    document.documentElement.dataset.theme = localStorage.getItem("theme") || "light";
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-  <section id="pyxu-info">
-<h1>pyxu.info<a class="headerlink" href="#pyxu-info" title="Link to this heading">#</a></h1>
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-<p class="topic-title">Table of Contents</p>
-<ul class="simple">
-<li><p><a class="reference internal" href="#module-pyxu.info.ptype" id="id1">pyxu.info.ptype</a></p></li>
-<li><p><a class="reference internal" href="#module-pyxu.info.deps" id="id2">pyxu.info.deps</a></p></li>
-<li><p><a class="reference internal" href="#module-pyxu.info.warning" id="id3">pyxu.info.warning</a></p></li>
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-<section id="module-pyxu.info.ptype">
-<span id="pyxu-info-ptype"></span><h2><a class="toc-backref" href="#id1" role="doc-backlink">pyxu.info.ptype</a><a class="headerlink" href="#module-pyxu.info.ptype" title="Link to this heading">#</a></h2>
-<p>The purpose of this module is to group all abstract types and helpers useful to Python’s static type-checker.</p>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.ptype.NDArray">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NDArray</span></span><a class="headerlink" href="#pyxu.info.ptype.NDArray" title="Link to this definition">#</a></dt>
-<dd><p>Supported dense array types.</p>
-<p>alias of TypeVar(‘NDArray’, ~dask.array.core.Array, ~numpy.ndarray)</p>
-</dd></dl>
-
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.ptype.ArrayModule">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ArrayModule</span></span><a class="headerlink" href="#pyxu.info.ptype.ArrayModule" title="Link to this definition">#</a></dt>
-<dd><p>Supported dense array modules.</p>
-<p>alias of TypeVar(‘ArrayModule’, ~typing.Literal[&lt;module ‘dask.array’ from ‘/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/dask/array/__init__.py’&gt;], ~typing.Literal[&lt;module ‘numpy’ from ‘/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/numpy/__init__.py’&gt;])</p>
-</dd></dl>
-
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.ptype.SparseArray">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SparseArray</span></span><a class="headerlink" href="#pyxu.info.ptype.SparseArray" title="Link to this definition">#</a></dt>
-<dd><p>Supported sparse array types.</p>
-<p>alias of TypeVar(‘SparseArray’, ~sparse._sparse_array.SparseArray, ~scipy.sparse._matrix.spmatrix)</p>
-</dd></dl>
-
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.ptype.SparseModule">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SparseModule</span></span><a class="headerlink" href="#pyxu.info.ptype.SparseModule" title="Link to this definition">#</a></dt>
-<dd><p>Supported sparse array modules.</p>
-<p>alias of TypeVar(‘SparseModule’, ~typing.Literal[&lt;module ‘scipy.sparse’ from ‘/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/scipy/sparse/__init__.py’&gt;], ~typing.Literal[&lt;module ‘sparse’ from ‘/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/sparse/__init__.py’&gt;])</p>
-</dd></dl>
-
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.ptype.OpT">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">OpT</span></span><a class="headerlink" href="#pyxu.info.ptype.OpT" title="Link to this definition">#</a></dt>
-<dd><p>Top-level abstract <a class="reference internal" href="abc.html#pyxu.abc.operator.Operator" title="pyxu.abc.operator.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> interface exposed to users.</p>
-<p>alias of TypeVar(‘OpT’, pxo.Operator, pxo.DiffFunc, pxo.ProxDiffFunc, pxo.NormalOp, pxo.ProxFunc, pxo.SquareOp, pxo.QuadraticFunc, pxo.ProjOp, pxo.LinFunc, pxo.PosDefOp, pxo.Map, pxo.Func, pxo.OrthProjOp, pxo.DiffMap, pxo.UnitOp, pxo.SelfAdjointOp, pxo.LinOp)</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.OpC">
-<span class="sig-name descname"><span class="pre">OpC</span></span><a class="headerlink" href="#pyxu.info.ptype.OpC" title="Link to this definition">#</a></dt>
-<dd><p><a class="reference internal" href="abc.html#pyxu.abc.operator.Operator" title="pyxu.abc.operator.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> hierarchy class type.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Type</span></code></a>[<a class="reference internal" href="#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OpT</span></code></a>]</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Property">
-<span class="sig-name descname"><span class="pre">Property</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">'pxo.Property'</span></em><a class="headerlink" href="#pyxu.info.ptype.Property" title="Link to this definition">#</a></dt>
-<dd><p>Mathematical properties attached to <a class="reference internal" href="abc.html#pyxu.abc.operator.Operator" title="pyxu.abc.operator.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> objects.</p>
-</dd></dl>
-
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.ptype.SolverT">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SolverT</span></span><a class="headerlink" href="#pyxu.info.ptype.SolverT" title="Link to this definition">#</a></dt>
-<dd><p>Top-level abstract <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> interface exposed to users.</p>
-<p>alias of TypeVar(‘SolverT’, bound=<code class="xref py py-class docutils literal notranslate"><span class="pre">pxs.Solver</span></code>)</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.SolverC">
-<span class="sig-name descname"><span class="pre">SolverC</span></span><a class="headerlink" href="#pyxu.info.ptype.SolverC" title="Link to this definition">#</a></dt>
-<dd><p><a class="reference internal" href="abc.html#pyxu.abc.solver.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> hierarchy class type.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Type</span></code></a>[<a class="reference internal" href="#pyxu.info.ptype.SolverT" title="pyxu.info.ptype.SolverT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SolverT</span></code></a>]</p>
-</dd></dl>
-
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.ptype.SolverM">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SolverM</span></span><a class="headerlink" href="#pyxu.info.ptype.SolverM" title="Link to this definition">#</a></dt>
-<dd><p>Solver run-modes.</p>
-<p>alias of TypeVar(‘SolverM’, bound=<code class="xref py py-class docutils literal notranslate"><span class="pre">pxs.Mode</span></code>)</p>
-</dd></dl>
-
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Integer">
-<span class="sig-name descname"><span class="pre">Integer</span></span><a class="headerlink" href="#pyxu.info.ptype.Integer" title="Link to this definition">#</a></dt>
-<dd><p>alias of <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a></p>
-</dd></dl>
-
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Real">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Real</span></span><a class="reference internal" href="../_modules/numbers.html#Real"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.ptype.Real" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Complex" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Complex</span></code></a></p>
-<p>To Complex, Real adds the operations that work on real numbers.</p>
-<p>In short, those are: a conversion to float, trunc(), divmod,
-%, &lt;, &lt;=, &gt;, and &gt;=.</p>
-<p>Real also provides defaults for the derived operations.</p>
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Real.real">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">real</span></span><a class="headerlink" href="#pyxu.info.ptype.Real.real" title="Link to this definition">#</a></dt>
-<dd><p>Real numbers are their real component.</p>
-</dd></dl>
-
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Real.imag">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">imag</span></span><a class="headerlink" href="#pyxu.info.ptype.Real.imag" title="Link to this definition">#</a></dt>
-<dd><p>Real numbers have no imaginary component.</p>
-</dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Real.conjugate">
-<span class="sig-name descname"><span class="pre">conjugate</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/numbers.html#Real.conjugate"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.ptype.Real.conjugate" title="Link to this definition">#</a></dt>
-<dd><p>Conjugate is a no-op for Reals.</p>
-</dd></dl>
-
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.DType">
-<span class="sig-name descname"><span class="pre">DType</span></span><a class="headerlink" href="#pyxu.info.ptype.DType" title="Link to this definition">#</a></dt>
-<dd><p>NDArray dtype specifier.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dtype</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>], <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Type</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>], <code class="xref py py-class docutils literal notranslate"><span class="pre">_SupportsDType</span></code>[<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dtype</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>]], <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">Tuple</span></code>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>], <code class="xref py py-class docutils literal notranslate"><span class="pre">Tuple</span></code>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">SupportsIndex</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">SupportsIndex</span></code></a>]]], <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">List</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>], <code class="xref py py-class docutils literal notranslate"><span class="pre">_DTypeDict</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">Tuple</span></code>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>]]</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.OpShape">
-<span class="sig-name descname"><span class="pre">OpShape</span></span><a class="headerlink" href="#pyxu.info.ptype.OpShape" title="Link to this definition">#</a></dt>
-<dd><p>Operator shape specifier.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>]</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.NDArrayAxis">
-<span class="sig-name descname"><span class="pre">NDArrayAxis</span></span><a class="headerlink" href="#pyxu.info.ptype.NDArrayAxis" title="Link to this definition">#</a></dt>
-<dd><p>Axis/Axes specifier.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, …]]</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.NDArrayShape">
-<span class="sig-name descname"><span class="pre">NDArrayShape</span></span><a class="headerlink" href="#pyxu.info.ptype.NDArrayShape" title="Link to this definition">#</a></dt>
-<dd><p>NDArray shape specifier.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, …]]</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Path">
-<span class="sig-name descname"><span class="pre">Path</span></span><a class="headerlink" href="#pyxu.info.ptype.Path" title="Link to this definition">#</a></dt>
-<dd><p>Path-like object.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/pathlib.html#pathlib.Path" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Path</span></code></a>]</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.VarName">
-<span class="sig-name descname"><span class="pre">VarName</span></span><a class="headerlink" href="#pyxu.info.ptype.VarName" title="Link to this definition">#</a></dt>
-<dd><p>Variable name(s).</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Collection</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>]]</p>
-</dd></dl>
-
-</section>
-<section id="module-pyxu.info.deps">
-<span id="pyxu-info-deps"></span><h2><a class="toc-backref" href="#id2" role="doc-backlink">pyxu.info.deps</a><a class="headerlink" href="#module-pyxu.info.deps" title="Link to this heading">#</a></h2>
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.deps.CUPY_ENABLED">
-<span class="sig-name descname"><span class="pre">CUPY_ENABLED</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><span class="pre">bool</span></a></em><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">False</span></em><a class="headerlink" href="#pyxu.info.deps.CUPY_ENABLED" title="Link to this definition">#</a></dt>
-<dd><p>Show if CuPy-based backends are available.</p>
-</dd></dl>
-
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.deps.NDArrayInfo">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NDArrayInfo</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">names</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">module</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">qualname</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">boundary</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#NDArrayInfo"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.NDArrayInfo" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/enum.html#enum.Enum" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Enum</span></code></a></p>
-<p>Supported dense array backends.</p>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.info.deps.NDArrayInfo.NUMPY">
-<span class="sig-name descname"><span class="pre">NUMPY</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">1</span></em><a class="headerlink" href="#pyxu.info.deps.NDArrayInfo.NUMPY" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.info.deps.NDArrayInfo.DASK">
-<span class="sig-name descname"><span class="pre">DASK</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">2</span></em><a class="headerlink" href="#pyxu.info.deps.NDArrayInfo.DASK" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.info.deps.NDArrayInfo.CUPY">
-<span class="sig-name descname"><span class="pre">CUPY</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">3</span></em><a class="headerlink" href="#pyxu.info.deps.NDArrayInfo.CUPY" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.deps.NDArrayInfo.default">
-<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">default</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#NDArrayInfo.default"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.NDArrayInfo.default" title="Link to this definition">#</a></dt>
-<dd><p>Default array backend to use.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="#pyxu.info.deps.NDArrayInfo" title="pyxu.info.deps.NDArrayInfo"><em>NDArrayInfo</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.deps.NDArrayInfo.type">
-<span class="sig-name descname"><span class="pre">type</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#NDArrayInfo.type"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.NDArrayInfo.type" title="Link to this definition">#</a></dt>
-<dd><p>Array type associated to a backend.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#type" title="(in Python v3.11)">type</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.deps.NDArrayInfo.from_obj">
-<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_obj</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">obj</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#NDArrayInfo.from_obj"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.NDArrayInfo.from_obj" title="Link to this definition">#</a></dt>
-<dd><p>Find array backend associated to <code class="code docutils literal notranslate"><span class="pre">obj</span></code>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="#pyxu.info.deps.NDArrayInfo" title="pyxu.info.deps.NDArrayInfo"><em>NDArrayInfo</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.deps.NDArrayInfo.from_flag">
-<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_flag</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">gpu</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#NDArrayInfo.from_flag"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.NDArrayInfo.from_flag" title="Link to this definition">#</a></dt>
-<dd><p>Find array backend suitable for in-memory CPU/GPU computing.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="#pyxu.info.deps.NDArrayInfo" title="pyxu.info.deps.NDArrayInfo"><em>NDArrayInfo</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.deps.NDArrayInfo.module">
-<span class="sig-name descname"><span class="pre">module</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">linalg</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#NDArrayInfo.module"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.NDArrayInfo.module" title="Link to this definition">#</a></dt>
-<dd><p>Python module associated to an array backend.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>linalg</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Return the linear-algebra submodule with identical API to <a class="reference external" href="https://numpy.org/doc/stable/reference/routines.linalg.html#module-numpy.linalg" title="(in NumPy v1.25)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.linalg</span></code></a>.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p>module</p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.info.deps.SparseArrayInfo">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SparseArrayInfo</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">names</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">module</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">qualname</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">boundary</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#SparseArrayInfo"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.SparseArrayInfo" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/enum.html#enum.Enum" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Enum</span></code></a></p>
-<p>Supported sparse array backends.</p>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.info.deps.SparseArrayInfo.SCIPY_SPARSE">
-<span class="sig-name descname"><span class="pre">SCIPY_SPARSE</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">1</span></em><a class="headerlink" href="#pyxu.info.deps.SparseArrayInfo.SCIPY_SPARSE" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.info.deps.SparseArrayInfo.PYDATA_SPARSE">
-<span class="sig-name descname"><span class="pre">PYDATA_SPARSE</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">2</span></em><a class="headerlink" href="#pyxu.info.deps.SparseArrayInfo.PYDATA_SPARSE" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.info.deps.SparseArrayInfo.CUPY_SPARSE">
-<span class="sig-name descname"><span class="pre">CUPY_SPARSE</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">3</span></em><a class="headerlink" href="#pyxu.info.deps.SparseArrayInfo.CUPY_SPARSE" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.deps.SparseArrayInfo.default">
-<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">default</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#SparseArrayInfo.default"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.SparseArrayInfo.default" title="Link to this definition">#</a></dt>
-<dd><p>Default array backend to use.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="#pyxu.info.deps.SparseArrayInfo" title="pyxu.info.deps.SparseArrayInfo"><em>SparseArrayInfo</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.deps.SparseArrayInfo.type">
-<span class="sig-name descname"><span class="pre">type</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#SparseArrayInfo.type"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.SparseArrayInfo.type" title="Link to this definition">#</a></dt>
-<dd><p>Array type associated to a backend.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#type" title="(in Python v3.11)">type</a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.deps.SparseArrayInfo.from_obj">
-<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">from_obj</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">obj</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#SparseArrayInfo.from_obj"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.SparseArrayInfo.from_obj" title="Link to this definition">#</a></dt>
-<dd><p>Find array backend associated to <code class="code docutils literal notranslate"><span class="pre">obj</span></code>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="#pyxu.info.deps.SparseArrayInfo" title="pyxu.info.deps.SparseArrayInfo"><em>SparseArrayInfo</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.deps.SparseArrayInfo.module">
-<span class="sig-name descname"><span class="pre">module</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">linalg</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#SparseArrayInfo.module"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.SparseArrayInfo.module" title="Link to this definition">#</a></dt>
-<dd><p>Python module associated to an array backend.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>linalg</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Return the linear-algebra submodule with identical API to <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/sparse.linalg.html#module-scipy.sparse.linalg" title="(in SciPy v1.11.2)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy.sparse.linalg</span></code></a>.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p>module</p>
-</dd>
-</dl>
-</dd></dl>
-
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.info.deps.supported_array_types">
-<span class="sig-name descname"><span class="pre">supported_array_types</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#supported_array_types"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.supported_array_types" title="Link to this definition">#</a></dt>
-<dd><p>List of all supported dense array types in current Pyxu install.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a>[<a class="reference external" href="https://docs.python.org/3/library/functions.html#type" title="(in Python v3.11)">type</a>]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.info.deps.supported_array_modules">
-<span class="sig-name descname"><span class="pre">supported_array_modules</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#supported_array_modules"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.supported_array_modules" title="Link to this definition">#</a></dt>
-<dd><p>List of all supported dense array modules in current Pyxu install.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a>[module]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.info.deps.supported_sparse_types">
-<span class="sig-name descname"><span class="pre">supported_sparse_types</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#supported_sparse_types"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.supported_sparse_types" title="Link to this definition">#</a></dt>
-<dd><p>List of all supported sparse array types in current Pyxu install.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a>[<a class="reference external" href="https://docs.python.org/3/library/functions.html#type" title="(in Python v3.11)">type</a>]</p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.info.deps.supported_sparse_modules">
-<span class="sig-name descname"><span class="pre">supported_sparse_modules</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/info/deps.html#supported_sparse_modules"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.deps.supported_sparse_modules" title="Link to this definition">#</a></dt>
-<dd><p>List of all supported sparse array modules in current Pyxu install.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a>[module]</p>
-</dd>
-</dl>
-</dd></dl>
-
-</section>
-<section id="module-pyxu.info.warning">
-<span id="pyxu-info-warning"></span><h2><a class="toc-backref" href="#id3" role="doc-backlink">pyxu.info.warning</a><a class="headerlink" href="#module-pyxu.info.warning" title="Link to this heading">#</a></h2>
-<p>Custom warnings used inside Pyxu.</p>
-<dl class="py exception">
-<dt class="sig sig-object py" id="pyxu.info.warning.PyxuWarning">
-<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PyxuWarning</span></span><a class="reference internal" href="../_modules/pyxu/info/warning.html#PyxuWarning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.warning.PyxuWarning" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/exceptions.html#UserWarning" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">UserWarning</span></code></a></p>
-<p>Parent class of all warnings raised in Pyxu.</p>
-</dd></dl>
-
-<dl class="py exception">
-<dt class="sig sig-object py" id="pyxu.info.warning.AutoInferenceWarning">
-<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">AutoInferenceWarning</span></span><a class="reference internal" href="../_modules/pyxu/info/warning.html#AutoInferenceWarning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.warning.AutoInferenceWarning" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.info.warning.PyxuWarning" title="pyxu.info.warning.PyxuWarning"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyxuWarning</span></code></a></p>
-<p>Use when a quantity was auto-inferenced with possible caveats.</p>
-</dd></dl>
-
-<dl class="py exception">
-<dt class="sig sig-object py" id="pyxu.info.warning.PerformanceWarning">
-<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PerformanceWarning</span></span><a class="reference internal" href="../_modules/pyxu/info/warning.html#PerformanceWarning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.warning.PerformanceWarning" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.info.warning.PyxuWarning" title="pyxu.info.warning.PyxuWarning"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyxuWarning</span></code></a></p>
-<p>Use for performance-related warnings.</p>
-</dd></dl>
-
-<dl class="py exception">
-<dt class="sig sig-object py" id="pyxu.info.warning.PrecisionWarning">
-<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PrecisionWarning</span></span><a class="reference internal" href="../_modules/pyxu/info/warning.html#PrecisionWarning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.warning.PrecisionWarning" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.info.warning.PyxuWarning" title="pyxu.info.warning.PyxuWarning"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyxuWarning</span></code></a></p>
-<p>Use for precision-related warnings.</p>
-</dd></dl>
-
-<dl class="py exception">
-<dt class="sig sig-object py" id="pyxu.info.warning.DenseWarning">
-<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DenseWarning</span></span><a class="reference internal" href="../_modules/pyxu/info/warning.html#DenseWarning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.warning.DenseWarning" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.info.warning.PyxuWarning" title="pyxu.info.warning.PyxuWarning"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyxuWarning</span></code></a></p>
-<p>Use for sparse-based algos which revert to dense arrays.</p>
-</dd></dl>
-
-<dl class="py exception">
-<dt class="sig sig-object py" id="pyxu.info.warning.NonTransparentWarning">
-<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NonTransparentWarning</span></span><a class="reference internal" href="../_modules/pyxu/info/warning.html#NonTransparentWarning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.warning.NonTransparentWarning" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.info.warning.PyxuWarning" title="pyxu.info.warning.PyxuWarning"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyxuWarning</span></code></a></p>
-<p>Inform test suite runner of (safe) non-transparent function call.</p>
-</dd></dl>
-
-<dl class="py exception">
-<dt class="sig sig-object py" id="pyxu.info.warning.BackendWarning">
-<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">BackendWarning</span></span><a class="reference internal" href="../_modules/pyxu/info/warning.html#BackendWarning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.warning.BackendWarning" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.info.warning.PyxuWarning" title="pyxu.info.warning.PyxuWarning"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyxuWarning</span></code></a></p>
-<p>Inform user of a backend-specific problem to be aware of.</p>
-</dd></dl>
-
-<dl class="py exception">
-<dt class="sig sig-object py" id="pyxu.info.warning.ContributionWarning">
-<em class="property"><span class="pre">exception</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ContributionWarning</span></span><a class="reference internal" href="../_modules/pyxu/info/warning.html#ContributionWarning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.warning.ContributionWarning" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.info.warning.PyxuWarning" title="pyxu.info.warning.PyxuWarning"><code class="xref py py-class docutils literal notranslate"><span class="pre">PyxuWarning</span></code></a></p>
-<p>Use for warnings related to Pyxu plugins.</p>
-</dd></dl>
-
-</section>
-</section>
-
-
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-    <ul class="visible nav section-nav flex-column">
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#module-pyxu.info.ptype">pyxu.info.ptype</a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.NDArray"><code class="docutils literal notranslate"><span class="pre">NDArray</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.ArrayModule"><code class="docutils literal notranslate"><span class="pre">ArrayModule</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SparseArray"><code class="docutils literal notranslate"><span class="pre">SparseArray</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SparseModule"><code class="docutils literal notranslate"><span class="pre">SparseModule</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.OpT"><code class="docutils literal notranslate"><span class="pre">OpT</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.OpC"><code class="docutils literal notranslate"><span class="pre">OpC</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Property"><code class="docutils literal notranslate"><span class="pre">Property</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SolverT"><code class="docutils literal notranslate"><span class="pre">SolverT</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SolverC"><code class="docutils literal notranslate"><span class="pre">SolverC</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SolverM"><code class="docutils literal notranslate"><span class="pre">SolverM</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Integer"><code class="docutils literal notranslate"><span class="pre">Integer</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Real"><code class="docutils literal notranslate"><span class="pre">Real</span></code></a><ul class="nav section-nav flex-column">
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Real.real"><code class="docutils literal notranslate"><span class="pre">Real.real</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Real.imag"><code class="docutils literal notranslate"><span class="pre">Real.imag</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Real.conjugate"><code class="docutils literal notranslate"><span class="pre">Real.conjugate()</span></code></a></li>
-</ul>
-</li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.DType"><code class="docutils literal notranslate"><span class="pre">DType</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.OpShape"><code class="docutils literal notranslate"><span class="pre">OpShape</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.NDArrayAxis"><code class="docutils literal notranslate"><span class="pre">NDArrayAxis</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.NDArrayShape"><code class="docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Path"><code class="docutils literal notranslate"><span class="pre">Path</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.VarName"><code class="docutils literal notranslate"><span class="pre">VarName</span></code></a></li>
-</ul>
-</li>
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-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.NDArrayInfo.NUMPY"><code class="docutils literal notranslate"><span class="pre">NDArrayInfo.NUMPY</span></code></a></li>
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-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.NDArrayInfo.CUPY"><code class="docutils literal notranslate"><span class="pre">NDArrayInfo.CUPY</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.NDArrayInfo.default"><code class="docutils literal notranslate"><span class="pre">NDArrayInfo.default()</span></code></a></li>
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-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.NDArrayInfo.from_obj"><code class="docutils literal notranslate"><span class="pre">NDArrayInfo.from_obj()</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.NDArrayInfo.from_flag"><code class="docutils literal notranslate"><span class="pre">NDArrayInfo.from_flag()</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.NDArrayInfo.module"><code class="docutils literal notranslate"><span class="pre">NDArrayInfo.module()</span></code></a></li>
-</ul>
-</li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.SparseArrayInfo"><code class="docutils literal notranslate"><span class="pre">SparseArrayInfo</span></code></a><ul class="nav section-nav flex-column">
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.SparseArrayInfo.SCIPY_SPARSE"><code class="docutils literal notranslate"><span class="pre">SparseArrayInfo.SCIPY_SPARSE</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.SparseArrayInfo.PYDATA_SPARSE"><code class="docutils literal notranslate"><span class="pre">SparseArrayInfo.PYDATA_SPARSE</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.SparseArrayInfo.CUPY_SPARSE"><code class="docutils literal notranslate"><span class="pre">SparseArrayInfo.CUPY_SPARSE</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.SparseArrayInfo.default"><code class="docutils literal notranslate"><span class="pre">SparseArrayInfo.default()</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.SparseArrayInfo.type"><code class="docutils literal notranslate"><span class="pre">SparseArrayInfo.type()</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.SparseArrayInfo.from_obj"><code class="docutils literal notranslate"><span class="pre">SparseArrayInfo.from_obj()</span></code></a></li>
-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.SparseArrayInfo.module"><code class="docutils literal notranslate"><span class="pre">SparseArrayInfo.module()</span></code></a></li>
-</ul>
-</li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.supported_array_types"><code class="docutils literal notranslate"><span class="pre">supported_array_types()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.supported_array_modules"><code class="docutils literal notranslate"><span class="pre">supported_array_modules()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.supported_sparse_types"><code class="docutils literal notranslate"><span class="pre">supported_sparse_types()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.deps.supported_sparse_modules"><code class="docutils literal notranslate"><span class="pre">supported_sparse_modules()</span></code></a></li>
-</ul>
-</li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#module-pyxu.info.warning">pyxu.info.warning</a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.warning.PyxuWarning"><code class="docutils literal notranslate"><span class="pre">PyxuWarning</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.warning.AutoInferenceWarning"><code class="docutils literal notranslate"><span class="pre">AutoInferenceWarning</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.warning.PerformanceWarning"><code class="docutils literal notranslate"><span class="pre">PerformanceWarning</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.warning.PrecisionWarning"><code class="docutils literal notranslate"><span class="pre">PrecisionWarning</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.warning.DenseWarning"><code class="docutils literal notranslate"><span class="pre">DenseWarning</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.warning.NonTransparentWarning"><code class="docutils literal notranslate"><span class="pre">NonTransparentWarning</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.warning.BackendWarning"><code class="docutils literal notranslate"><span class="pre">BackendWarning</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.warning.ContributionWarning"><code class="docutils literal notranslate"><span class="pre">ContributionWarning</span></code></a></li>
-</ul>
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diff --git a/api/info.ptype.html b/api/info.ptype.html
index e04403b9..abddc8c1 100644
--- a/api/info.ptype.html
+++ b/api/info.ptype.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
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     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -406,16 +406,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="operator/blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
@@ -427,13 +422,7 @@
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 <li class="toctree-l1"><a class="reference internal" href="runtime.html">pyxu.runtime</a></li>
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-<li class="toctree-l2"><a class="reference internal" href="util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../references.html"><strong>References</strong></a></li>
 </ul>
@@ -493,122 +482,92 @@
 <div id="searchbox"></div>
                 <article class="bd-article" role="main">
                   
-  <section id="module-pyxu.info.ptype">
-<span id="pyxu-info-ptype"></span><h1>pyxu.info.ptype<a class="headerlink" href="#module-pyxu.info.ptype" title="Link to this heading">#</a></h1>
-<dl class="py class">
+  <section id="pyxu-info-ptype">
+<h1>pyxu.info.ptype<a class="headerlink" href="#pyxu-info-ptype" title="Link to this heading">#</a></h1>
+<dl class="py class" id="module-pyxu.info.ptype">
 <dt class="sig sig-object py" id="pyxu.info.ptype.NDArray">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NDArray</span></span><a class="headerlink" href="#pyxu.info.ptype.NDArray" title="Link to this definition">#</a></dt>
 <dd><p>Supported dense array types.</p>
-<p>alias of TypeVar(‘NDArray’, ~dask.array.core.Array, ~numpy.ndarray)</p>
 </dd></dl>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.info.ptype.ArrayModule">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ArrayModule</span></span><a class="headerlink" href="#pyxu.info.ptype.ArrayModule" title="Link to this definition">#</a></dt>
 <dd><p>Supported dense array modules.</p>
-<p>alias of TypeVar(‘ArrayModule’, ~typing.Literal[&lt;module ‘numpy’ from ‘/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/numpy/__init__.py’&gt;], ~typing.Literal[&lt;module ‘dask.array’ from ‘/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/dask/array/__init__.py’&gt;])</p>
 </dd></dl>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.info.ptype.SparseArray">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SparseArray</span></span><a class="headerlink" href="#pyxu.info.ptype.SparseArray" title="Link to this definition">#</a></dt>
 <dd><p>Supported sparse array types.</p>
-<p>alias of TypeVar(‘SparseArray’, ~sparse._sparse_array.SparseArray, ~scipy.sparse._matrix.spmatrix)</p>
 </dd></dl>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.info.ptype.SparseModule">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SparseModule</span></span><a class="headerlink" href="#pyxu.info.ptype.SparseModule" title="Link to this definition">#</a></dt>
 <dd><p>Supported sparse array modules.</p>
-<p>alias of TypeVar(‘SparseModule’, ~typing.Literal[&lt;module ‘scipy.sparse’ from ‘/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/scipy/sparse/__init__.py’&gt;], ~typing.Literal[&lt;module ‘sparse’ from ‘/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/sparse/__init__.py’&gt;])</p>
 </dd></dl>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.info.ptype.OpT">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">OpT</span></span><a class="headerlink" href="#pyxu.info.ptype.OpT" title="Link to this definition">#</a></dt>
-<dd><p>Top-level abstract <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> interface exposed to users.</p>
-<p>alias of TypeVar(‘OpT’, pxo.Operator, pxo.DiffFunc, pxo.ProxDiffFunc, pxo.NormalOp, pxo.ProxFunc, pxo.SquareOp, pxo.QuadraticFunc, pxo.ProjOp, pxo.LinFunc, pxo.PosDefOp, pxo.Map, pxo.Func, pxo.OrthProjOp, pxo.DiffMap, pxo.UnitOp, pxo.SelfAdjointOp, pxo.LinOp)</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.OpC">
-<span class="sig-name descname"><span class="pre">OpC</span></span><a class="headerlink" href="#pyxu.info.ptype.OpC" title="Link to this definition">#</a></dt>
-<dd><p><a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> hierarchy class type.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Type</span></code></a>[<a class="reference internal" href="#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OpT</span></code></a>]</p>
+<dd><p>Top-level abstract <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> interface exposed to users.</p>
 </dd></dl>
 
 <dl class="py data">
 <dt class="sig sig-object py" id="pyxu.info.ptype.Property">
-<span class="sig-name descname"><span class="pre">Property</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">'pxo.Property'</span></em><a class="headerlink" href="#pyxu.info.ptype.Property" title="Link to this definition">#</a></dt>
-<dd><p>Mathematical properties attached to <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> objects.</p>
+<span class="sig-name descname"><span class="pre">Property</span></span><a class="headerlink" href="#pyxu.info.ptype.Property" title="Link to this definition">#</a></dt>
+<dd><p>Mathematical properties attached to <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> objects.</p>
 </dd></dl>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.info.ptype.SolverT">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SolverT</span></span><a class="headerlink" href="#pyxu.info.ptype.SolverT" title="Link to this definition">#</a></dt>
-<dd><p>Top-level abstract <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> interface exposed to users.</p>
-<p>alias of TypeVar(‘SolverT’, bound=<code class="xref py py-class docutils literal notranslate"><span class="pre">pxs.Solver</span></code>)</p>
-</dd></dl>
-
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.SolverC">
-<span class="sig-name descname"><span class="pre">SolverC</span></span><a class="headerlink" href="#pyxu.info.ptype.SolverC" title="Link to this definition">#</a></dt>
-<dd><p><a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> hierarchy class type.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Type</span></code></a>[<a class="reference internal" href="#pyxu.info.ptype.SolverT" title="pyxu.info.ptype.SolverT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SolverT</span></code></a>]</p>
+<dd><p>Top-level abstract <a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> interface exposed to users.</p>
 </dd></dl>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.info.ptype.SolverM">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SolverM</span></span><a class="headerlink" href="#pyxu.info.ptype.SolverM" title="Link to this definition">#</a></dt>
-<dd><p>Solver run-modes.</p>
-<p>alias of TypeVar(‘SolverM’, bound=<code class="xref py py-class docutils literal notranslate"><span class="pre">pxs.SolverMode</span></code>)</p>
-</dd></dl>
-
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Integer">
-<span class="sig-name descname"><span class="pre">Integer</span></span><a class="headerlink" href="#pyxu.info.ptype.Integer" title="Link to this definition">#</a></dt>
-<dd><p>alias of <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a></p>
+<dd><p>Solver run-mode(s).</p>
 </dd></dl>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.info.ptype.Real">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Real</span></span><a class="reference internal" href="../_modules/numbers.html#Real"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.ptype.Real" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Complex" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Complex</span></code></a></p>
-<p>To Complex, Real adds the operations that work on real numbers.</p>
-<p>In short, those are: a conversion to float, trunc(), divmod,
-%, &lt;, &lt;=, &gt;, and &gt;=.</p>
-<p>Real also provides defaults for the derived operations.</p>
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Real.real">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">real</span></span><a class="headerlink" href="#pyxu.info.ptype.Real.real" title="Link to this definition">#</a></dt>
-<dd><p>Real numbers are their real component.</p>
+<dd><p>Alias of <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">numbers.Real</span></code></a>.</p>
 </dd></dl>
 
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Real.imag">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">imag</span></span><a class="headerlink" href="#pyxu.info.ptype.Real.imag" title="Link to this definition">#</a></dt>
-<dd><p>Real numbers have no imaginary component.</p>
+<dl class="py data">
+<dt class="sig sig-object py" id="pyxu.info.ptype.DType">
+<span class="sig-name descname"><span class="pre">DType</span></span><a class="headerlink" href="#pyxu.info.ptype.DType" title="Link to this definition">#</a></dt>
+<dd><p><a class="reference internal" href="#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a> dtype specifier.</p>
 </dd></dl>
 
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.info.ptype.Real.conjugate">
-<span class="sig-name descname"><span class="pre">conjugate</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/numbers.html#Real.conjugate"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.info.ptype.Real.conjugate" title="Link to this definition">#</a></dt>
-<dd><p>Conjugate is a no-op for Reals.</p>
+<dl class="py data">
+<dt class="sig sig-object py" id="pyxu.info.ptype.OpC">
+<span class="sig-name descname"><span class="pre">OpC</span></span><a class="headerlink" href="#pyxu.info.ptype.OpC" title="Link to this definition">#</a></dt>
+<dd><p><a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> hierarchy class type.</p>
+<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Type</span></code></a>[<a class="reference internal" href="#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OpT</span></code></a>]</p>
 </dd></dl>
 
+<dl class="py data">
+<dt class="sig sig-object py" id="pyxu.info.ptype.SolverC">
+<span class="sig-name descname"><span class="pre">SolverC</span></span><a class="headerlink" href="#pyxu.info.ptype.SolverC" title="Link to this definition">#</a></dt>
+<dd><p><a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a> hierarchy class type.</p>
+<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Type</span></code></a>[<a class="reference internal" href="#pyxu.info.ptype.SolverT" title="pyxu.info.ptype.SolverT"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SolverT</span></code></a>]</p>
 </dd></dl>
 
-<dl class="py data">
-<dt class="sig sig-object py" id="pyxu.info.ptype.DType">
-<span class="sig-name descname"><span class="pre">DType</span></span><a class="headerlink" href="#pyxu.info.ptype.DType" title="Link to this definition">#</a></dt>
-<dd><p><a class="reference internal" href="#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a> dtype specifier.</p>
-<p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dtype</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>], <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Type</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>], <code class="xref py py-class docutils literal notranslate"><span class="pre">_SupportsDType</span></code>[<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dtype</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>]], <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">Tuple</span></code>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>], <code class="xref py py-class docutils literal notranslate"><span class="pre">Tuple</span></code>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">SupportsIndex</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">SupportsIndex</span></code></a>]]], <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">List</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>], <code class="xref py py-class docutils literal notranslate"><span class="pre">_DTypeDict</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">Tuple</span></code>[<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Any</span></code></a>]]</p>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="pyxu.info.ptype.Integer">
+<span class="sig-name descname"><span class="pre">Integer</span></span><a class="headerlink" href="#pyxu.info.ptype.Integer" title="Link to this definition">#</a></dt>
+<dd><p>alias of <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a></p>
 </dd></dl>
 
 <dl class="py data">
 <dt class="sig sig-object py" id="pyxu.info.ptype.OpShape">
 <span class="sig-name descname"><span class="pre">OpShape</span></span><a class="headerlink" href="#pyxu.info.ptype.OpShape" title="Link to this definition">#</a></dt>
-<dd><p><a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> shape specifier.</p>
+<dd><p><a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> shape specifier.</p>
 <p>alias of <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>]</p>
 </dd></dl>
 
@@ -694,19 +653,14 @@
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SparseArray"><code class="docutils literal notranslate"><span class="pre">SparseArray</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SparseModule"><code class="docutils literal notranslate"><span class="pre">SparseModule</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.OpT"><code class="docutils literal notranslate"><span class="pre">OpT</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.OpC"><code class="docutils literal notranslate"><span class="pre">OpC</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Property"><code class="docutils literal notranslate"><span class="pre">Property</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SolverT"><code class="docutils literal notranslate"><span class="pre">SolverT</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SolverC"><code class="docutils literal notranslate"><span class="pre">SolverC</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SolverM"><code class="docutils literal notranslate"><span class="pre">SolverM</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Integer"><code class="docutils literal notranslate"><span class="pre">Integer</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Real"><code class="docutils literal notranslate"><span class="pre">Real</span></code></a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Real.real"><code class="docutils literal notranslate"><span class="pre">Real.real</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Real.imag"><code class="docutils literal notranslate"><span class="pre">Real.imag</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Real.conjugate"><code class="docutils literal notranslate"><span class="pre">Real.conjugate()</span></code></a></li>
-</ul>
-</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Real"><code class="docutils literal notranslate"><span class="pre">Real</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.DType"><code class="docutils literal notranslate"><span class="pre">DType</span></code></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.OpC"><code class="docutils literal notranslate"><span class="pre">OpC</span></code></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.SolverC"><code class="docutils literal notranslate"><span class="pre">SolverC</span></code></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.Integer"><code class="docutils literal notranslate"><span class="pre">Integer</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.OpShape"><code class="docutils literal notranslate"><span class="pre">OpShape</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.NDArrayAxis"><code class="docutils literal notranslate"><span class="pre">NDArrayAxis</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.info.ptype.NDArrayShape"><code class="docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a></li>
diff --git a/api/info.warning.html b/api/info.warning.html
index 6cd6d233..917a9fcc 100644
--- a/api/info.warning.html
+++ b/api/info.warning.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -406,16 +406,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">pyxu.info.warning</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="operator/blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
@@ -427,13 +422,7 @@
 <li class="toctree-l1"><a class="reference internal" href="opt.stop.html">pyxu.opt.stop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="runtime.html">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
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-<li class="toctree-l2"><a class="reference internal" href="util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../references.html"><strong>References</strong></a></li>
 </ul>
diff --git a/api/math.html b/api/math.html
index 6a85c36e..407f052f 100644
--- a/api/math.html
+++ b/api/math.html
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-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
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-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
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-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
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@@ -63,7 +63,7 @@
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     <link rel="search" title="Search" href="../search.html" />
-    <link rel="next" title="pyxu.util" href="util/index.html" />
+    <link rel="next" title="pyxu.util" href="util.html" />
     <link rel="prev" title="pyxu.runtime" href="runtime.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
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@@ -408,16 +408,11 @@
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   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
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-<li class="toctree-l2"><a class="reference internal" href="abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
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+<li class="toctree-l1"><a class="reference internal" href="abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.deps.html">pyxu.info.deps</a></li>
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-<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="operator/blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
@@ -429,13 +424,7 @@
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 <li class="toctree-l1"><a class="reference internal" href="runtime.html">pyxu.runtime</a></li>
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-<li class="toctree-l1 has-children"><a class="reference internal" href="util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
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-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../references.html"><strong>References</strong></a></li>
 </ul>
@@ -504,12 +493,12 @@
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
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+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>) – Differentiable functional.</p></li>
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 <p>Specifying <code class="code docutils literal notranslate"><span class="pre">gradient</span></code> when known is an optimization: it will be autocomputed via
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+<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc.grad" title="pyxu.abc.DiffFunc.grad"><code class="xref py py-meth docutils literal notranslate"><span class="pre">grad()</span></code></a> if unspecified.</p>
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@@ -536,7 +525,7 @@
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
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+<li><p><strong>op</strong> (<a class="reference internal" href="abc.html#pyxu.abc.SquareOp" title="pyxu.abc.operator.SquareOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareOp</span></code></a>) – </p></li>
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 corresponds to having an estimation error smaller than 0.01 with probability 0.9.</p>
@@ -573,7 +562,7 @@
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
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@@ -610,7 +599,7 @@
       </div>
     </a>
     <a class="right-next"
-       href="util/index.html"
+       href="util.html"
        title="next page">
       <div class="prev-next-info">
         <p class="prev-next-subtitle">next</p>
diff --git a/api/operator.html b/api/operator.html
deleted file mode 100644
index 78e8f12b..00000000
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+++ /dev/null
@@ -1,6572 +0,0 @@
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-<section id="pyxu-operator">
-<h1>pyxu.operator<a class="headerlink" href="#pyxu-operator" title="Link to this heading">#</a></h1>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.ConstantValued">
-<span class="sig-name descname"><span class="pre">ConstantValued</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cst</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/base.html#ConstantValued"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.ConstantValued" title="Link to this definition">#</a></dt>
-<dd><p>Constant-valued operator <span class="math notranslate nohighlight">\(C: \mathbb{R}^{M} \to \mathbb{R}^{N}\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p></li>
-<li><p><strong>cst</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.L1Norm">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">L1Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#L1Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.L1Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
-<p><span class="math notranslate nohighlight">\(\ell_{1}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert_{1} := \sum_{i=1}^{N} |x_{i}|\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.L2Norm">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">L2Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#L2Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.L2Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
-<p><span class="math notranslate nohighlight">\(\ell_{2}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert_{2} := \sqrt{\sum_{i=1}^{N} |x_{i}|^{2}}\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.SquaredL2Norm">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SquaredL2Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#SquaredL2Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SquaredL2Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.QuadraticFunc" title="pyxu.abc.operator.QuadraticFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">QuadraticFunc</span></code></a></p>
-<p><span class="math notranslate nohighlight">\(\ell^{2}_{2}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert^{2}_{2} := \sum_{i=1}^{N} |x_{i}|^{2}\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.SquaredL1Norm">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SquaredL1Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prox_algo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sort'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#SquaredL1Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SquaredL1Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
-<p><span class="math notranslate nohighlight">\(\ell^{2}_{1}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert^{2}_{1} := (\sum_{i=1}^{N} |x_{i}|)^{2}\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p></li>
-<li><p><strong>prox_algo</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.SquaredL1Norm.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prox_algo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sort'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#SquaredL1Norm.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SquaredL1Norm.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>dim</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – </p></li>
-<li><p><strong>prox_algo</strong> (<code class="docutils literal notranslate"><span class="pre">"root"</span></code>, <code class="docutils literal notranslate"><span class="pre">"sort"</span></code>) – <p>Algorithm used for computing the proximal operator:</p>
-<ul>
-<li><p>’root’ uses <a class="reference internal" href="../references.html#firstord" id="id1"><span>[FirstOrd]</span></a> Lemma 6.70,</p></li>
-<li><p>’sort’ uses <a class="reference internal" href="../references.html#onkerlearn" id="id2"><span>[OnKerLearn]</span></a> Algorithm 2 (faster).</p></li>
-</ul>
-</p></li>
-</ul>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>Calling <a class="reference internal" href="#pyxu.operator.SquaredL1Norm.prox" title="pyxu.operator.SquaredL1Norm.prox"><code class="xref py py-meth docutils literal notranslate"><span class="pre">prox()</span></code></a> with DASK inputs when <code class="code docutils literal notranslate"><span class="pre">algo="sort"</span></code> is inefficient at
-scale.  Prefer <code class="code docutils literal notranslate"><span class="pre">algo="root"</span></code> in this case.</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.SquaredL1Norm.prox">
-<span class="sig-name descname"><span class="pre">prox</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tau</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#SquaredL1Norm.prox"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SquaredL1Norm.prox" title="Link to this definition">#</a></dt>
-<dd><p>Evaluate proximity operator of <span class="math notranslate nohighlight">\(\tau f\)</span> at specified point(s).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, M) input points.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive scale factor.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>out</strong> – (…, M) proximal evaluations.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>For <span class="math notranslate nohighlight">\(\tau &gt;0\)</span>, the <em>proximity operator</em> of a scaled functional <span class="math notranslate nohighlight">\(f: \mathbb{R}^{M} \to \mathbb{R}\)</span> is
-defined as:</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{\text{prox}}_{\tau f}(\mathbf{z})
-:=
-\arg\min_{\mathbf{x}\in\mathbb{R}^{M}} f(x)+\frac{1}{2\tau} \|\mathbf{x}-\mathbf{z}\|_{2}^{2},
-\quad
-\forall \mathbf{z} \in \mathbb{R}^{M}.\]</div>
-</dd></dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.shift_loss">
-<span class="sig-name descname"><span class="pre">shift_loss</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">data</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/loss.html#shift_loss"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.shift_loss" title="Link to this definition">#</a></dt>
-<dd><p>Shift a functional <span class="math notranslate nohighlight">\(f(x)\)</span> to a loss functional.</p>
-<div class="math notranslate nohighlight">
-\[g(x; c) = f(x - c)\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>data</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (M,) input data.</p></li>
-<li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (1, M) Loss functionial.  If <code class="code docutils literal notranslate"><span class="pre">data</span></code> is omitted, then this function is a no-op.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.KLDivergence">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">KLDivergence</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">data</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/loss.html#KLDivergence"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.KLDivergence" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
-<p>Generalised Kullback-Leibler divergence <span class="math notranslate nohighlight">\(D_{KL}(\mathbf{y}||\mathbf{x}):=\sum_{i=1}^N y_i\log(y_i/x_i) -y_i
-+x_i\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p></li>
-<li><p><strong>data</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.KLDivergence.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">data</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/loss.html#KLDivergence.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.KLDivergence.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>dim</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – </p></li>
-<li><p><strong>data</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (M,) strictly positive input data.</p></li>
-</ul>
-</dd>
-</dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">KLDivergence</span>
-
-<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
-<span class="n">loss</span> <span class="o">=</span> <span class="n">KLDivergence</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="n">y</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="n">data</span><span class="o">=</span><span class="n">y</span><span class="p">)</span>
-<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
-<span class="n">loss</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="c1"># 13.80837687480246</span>
-<span class="n">np</span><span class="o">.</span><span class="n">round</span><span class="p">(</span><span class="n">loss</span><span class="o">.</span><span class="n">prox</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">tau</span><span class="o">=</span><span class="mi">1</span><span class="p">))</span>
-<span class="c1"># array([ 0.,  2.,  4.,  6.,  8., 10., 12., 14., 16., 18.])</span>
-</pre></div>
-</div>
-<p class="rubric">Notes</p>
-<p>In information theory, and in the case where <span class="math notranslate nohighlight">\(\mathbf{y}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{x}\)</span>  sum to one  –and hence
-can be interpreted as discrete probability distributions, the KL-divergence can be interpreted as the relative
-entropy of <span class="math notranslate nohighlight">\(\mathbf{y}\)</span> w.r.t. <span class="math notranslate nohighlight">\(\mathbf{x}\)</span>, i.e. the amount of information lost when using
-<span class="math notranslate nohighlight">\(\mathbf{x}\)</span> to approximate <span class="math notranslate nohighlight">\(\mathbf{y}\)</span>. It is particularly useful in the context of count data
-with Poisson distribution. Indeed, the KL-divergence corresponds –up to an additive constant– to the likelihood
-of the data <span class="math notranslate nohighlight">\(\mathbf{y}\)</span> where each component is independent with Poisson distribution and respective
-intensities given by the entries of <span class="math notranslate nohighlight">\(\mathbf{x}\)</span>. See <a class="reference internal" href="../references.html#funcsphere" id="id3"><span>[FuncSphere]</span></a> Section 5 of Chapter 7 for the
-computation of its proximal operator.</p>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.LInfinityNorm">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">LInfinityNorm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#LInfinityNorm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.LInfinityNorm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
-<p><span class="math notranslate nohighlight">\(\ell_{\infty}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert_{\infty} := \max_{i=1,\ldots,N} |x_{i}|\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.L21Norm">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">L21Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">l2_axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(0,)</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#L21Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.L21Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
-<p>Mixed <span class="math notranslate nohighlight">\(\ell_{2}-\ell_{1}\)</span> norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert_{2, 1} := \sum_{i=1}^{N} \sqrt{\sum_{j=1}^{M}
-x_{i, j}^{2}}\)</span>.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>The input array need not be 2-dimensional: the <span class="math notranslate nohighlight">\(\ell_{2}\)</span> norm is applied along a predefined subset of
-dimensions, and the <span class="math notranslate nohighlight">\(\ell_{1}\)</span> norm on the remaining ones.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>l2_axis</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.L21Norm.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">l2_axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(0,)</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#L21Norm.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.L21Norm.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>l2_axis</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayAxis" title="pyxu.info.ptype.NDArrayAxis"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayAxis</span></code></a>) – Axis (or axes) along which the <span class="math notranslate nohighlight">\(\ell_{2}\)</span> norm is applied.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.PositiveL1Norm">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PositiveL1Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/norm.html#PositiveL1Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.PositiveL1Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
-<p><span class="math notranslate nohighlight">\(\ell_{1}\)</span>-norm, with a positivity constraint.</p>
-<div class="math notranslate nohighlight">
-\[f(\mathbf{x})
-:=
-\lVert\mathbf{x}\rVert_{1} + \iota_{+}(\mathbf{x}),\]</div>
-<div class="math notranslate nohighlight">
-\[\textbf{prox}_{\tau f}(\mathbf{z})
-:=
-\max(\mathrm{soft}_\tau(\mathbf{z}), \mathbf{0})\]</div>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.PositiveOrthant" title="pyxu.operator.PositiveOrthant"><code class="xref py py-class docutils literal notranslate"><span class="pre">PositiveOrthant</span></code></a></p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.L1Ball">
-<span class="sig-name descname"><span class="pre">L1Ball</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#L1Ball"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.L1Ball" title="Link to this definition">#</a></dt>
-<dd><p>Indicator function of the <span class="math notranslate nohighlight">\(\ell_{1}\)</span>-ball.</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\iota_{1}^{r}(\mathbf{x})
-:=
-\begin{cases}
-    0 &amp; \|\mathbf{x}\|_{1} \le r \\
-    \infty &amp; \text{otherwise}.
-\end{cases}\end{split}\]</div>
-<div class="math notranslate nohighlight">
-\[\text{prox}_{\tau\, \iota_{1}^{r}}(\mathbf{x})
-:=
-\mathbf{x} - \text{prox}_{r\, \ell_{\infty}}(\mathbf{x})\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>dim</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – </p></li>
-<li><p><strong>radius</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Ball radius. (Default: unit ball.)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong></p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.L2Ball">
-<span class="sig-name descname"><span class="pre">L2Ball</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#L2Ball"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.L2Ball" title="Link to this definition">#</a></dt>
-<dd><p>Indicator function of the <span class="math notranslate nohighlight">\(\ell_{2}\)</span>-ball.</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\iota_{2}^{r}(\mathbf{x})
-:=
-\begin{cases}
-    0 &amp; \|\mathbf{x}\|_{2} \le r \\
-    \infty &amp; \text{otherwise}.
-\end{cases}\end{split}\]</div>
-<div class="math notranslate nohighlight">
-\[\text{prox}_{\tau\, \iota_{2}^{r}}(\mathbf{x})
-:=
-\mathbf{x} - \text{prox}_{r\, \ell_{2}}(\mathbf{x})\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>dim</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – </p></li>
-<li><p><strong>radius</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Ball radius. (Default: unit ball.)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong></p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.LInfinityBall">
-<span class="sig-name descname"><span class="pre">LInfinityBall</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#LInfinityBall"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.LInfinityBall" title="Link to this definition">#</a></dt>
-<dd><p>Indicator function of the <span class="math notranslate nohighlight">\(\ell_{\infty}\)</span>-ball.</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\iota_{\infty}^{r}(\mathbf{x})
-:=
-\begin{cases}
-    0 &amp; \|\mathbf{x}\|_{\infty} \le r \\
-    \infty &amp; \text{otherwise}.
-\end{cases}\end{split}\]</div>
-<div class="math notranslate nohighlight">
-\[\text{prox}_{\tau\, \iota_{\infty}^{r}}(\mathbf{x})
-:=
-\mathbf{x} - \text{prox}_{r\, \ell_{1}}(\mathbf{x})\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>dim</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – </p></li>
-<li><p><strong>radius</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Ball radius. (Default: unit ball.)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong></p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.PositiveOrthant">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PositiveOrthant</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#PositiveOrthant"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.PositiveOrthant" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_IndicatorFunction</span></code></p>
-<p>Indicator function of the positive orthant.</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\iota_{+}(\mathbf{x})
-:=
-\begin{cases}
-    0 &amp; \min{\mathbf{x}} \ge 0,\\
-    \infty &amp; \text{otherwise}.
-\end{cases}\end{split}\]</div>
-<div class="math notranslate nohighlight">
-\[\text{prox}_{\tau\, \iota_{+}}(\mathbf{x})
-:=
-\max(\mathbf{x}, \mathbf{0})\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.HyperSlab">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">HyperSlab</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lb</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ub</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#HyperSlab"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.HyperSlab" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_IndicatorFunction</span></code></p>
-<p>Indicator function of a hyperslab.</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\iota_{\mathbf{a}}^{l,u}(\mathbf{x})
-:=
-\begin{cases}
-    0 &amp; l \le \langle \mathbf{a}, \mathbf{x} \rangle \le u \\
-    \infty &amp; \text{otherwise}.
-\end{cases}\end{split}\]</div>
-<div class="math notranslate nohighlight">
-\[\begin{split}\text{prox}_{\tau\, \iota_{\mathbf{a}}^{l,u}}(\mathbf{x})
-:=
-\begin{cases}
-    \mathbf{x} + \frac{l - \langle \mathbf{a}, \mathbf{x} \rangle}{\|\mathbf{a}\|^{2}} \mathbf{a} &amp; \langle \mathbf{a}, \mathbf{x} \rangle &lt; l, \\
-    \mathbf{x} + \frac{u - \langle \mathbf{a}, \mathbf{x} \rangle}{\|\mathbf{a}\|^{2}} \mathbf{a} &amp; \langle \mathbf{a}, \mathbf{x} \rangle &gt; u, \\
-    \mathbf{x} &amp; \text{otherwise}.
-\end{cases}\end{split}\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<a class="reference internal" href="abc.html#pyxu.abc.LinFunc" title="pyxu.abc.operator.LinFunc"><em>LinFunc</em></a>) – </p></li>
-<li><p><strong>lb</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-<li><p><strong>ub</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.HyperSlab.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lb</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ub</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#HyperSlab.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.HyperSlab.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="abc.html#pyxu.abc.LinFunc" title="pyxu.abc.operator.LinFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinFunc</span></code></a>) – (N,) operator</p></li>
-<li><p><strong>lb</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Lower bound</p></li>
-<li><p><strong>ub</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Upper bound</p></li>
-<li><p><strong>a</strong> (<a class="reference internal" href="abc.html#pyxu.abc.LinFunc" title="pyxu.abc.operator.LinFunc"><em>LinFunc</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.RangeSet">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">RangeSet</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#RangeSet"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.RangeSet" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_IndicatorFunction</span></code></p>
-<p>Indicator function of a range set.</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\iota_{\mathbf{A}}^{R}(\mathbf{x})
-:=
-\begin{cases}
-    0 &amp; \mathbf{x} \in \text{span}(\mathbf{A}) \\
-    \infty &amp; \text{otherwise}.
-\end{cases}\end{split}\]</div>
-<div class="math notranslate nohighlight">
-\[\text{prox}_{\tau\, \iota_{\mathbf{A}}^{R}}(\mathbf{x})
-:=
-\mathbf{A} (\mathbf{A}^{T} \mathbf{A})^{-1} \mathbf{A}^{T} \mathbf{x}.\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>A</strong> (<a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><em>LinOp</em></a>) – </p>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.RangeSet.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#RangeSet.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.RangeSet.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>A</strong> (<a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>) – (M, N) operator</p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.AffineSet">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">AffineSet</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#AffineSet"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.AffineSet" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_IndicatorFunction</span></code></p>
-<p>Indicator function of an affine set.</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\iota_{\mathbf{A}}^{\mathbf{b}}(\mathbf{x})
-:=
-\begin{cases}
-    0 &amp; \mathbf{A} \mathbf{x} = \mathbf{b} \\
-    \infty &amp; \text{otherwise}.
-\end{cases}\end{split}\]</div>
-<div class="math notranslate nohighlight">
-\[\text{prox}_{\tau\, \iota_{\mathbf{A}}^{\mathbf{b}}}(\mathbf{x})
-:=
-\mathbf{x} - \mathbf{A}^{T} (\mathbf{A}\mathbf{A}^{T})^{-1} (\mathbf{Ax - b})\]</div>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p>Assumptions on <span class="math notranslate nohighlight">\(\mathbf{A}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{b}\)</span>:</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(\mathbf{b} \in \text{span}(\mathbf{A})\)</span>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathbf{A}\)</span> has full row-rank, i.e. <span class="math notranslate nohighlight">\(\mathbf{A}\)</span> is square or fat.</p></li>
-</ul>
-</li>
-<li><p><a class="reference internal" href="#pyxu.operator.AffineSet" title="pyxu.operator.AffineSet"><code class="xref py py-class docutils literal notranslate"><span class="pre">AffineSet</span></code></a> instances are <strong>not arraymodule-agnostic</strong>:
-they will only work with NDArrays belonging to the same array module as <code class="code docutils literal notranslate"><span class="pre">A</span></code> and <code class="code docutils literal notranslate"><span class="pre">b</span></code>.</p></li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><em>LinOp</em></a>) – </p></li>
-<li><p><strong>b</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.AffineSet.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#AffineSet.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.AffineSet.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>) – (M, N) operator</p></li>
-<li><p><strong>b</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (M,)</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.ConvexSetIntersection">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ConvexSetIntersection</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#ConvexSetIntersection"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.ConvexSetIntersection" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_IndicatorFunction</span></code></p>
-<p>Indicator function of an intersection of convex domains <span class="math notranslate nohighlight">\(\mathcal{C}_{1} \cap \cdots \cap \mathcal{C}_{K}\)</span>.</p>
-<div class="math notranslate nohighlight">
-\[\iota(\mathbf{x})
-:=
-\iota_{1}(\mathbf{x}) + \cdots + \iota_{K}(\mathbf{x}).\]</div>
-<p><span class="math notranslate nohighlight">\(\text{prox}_{\tau\, \iota}(\mathbf{x})\)</span> is computed using the PoCS algorithm.  (Dykstra’s variant
-<a class="reference internal" href="../references.html#pocs-dykstra" id="id4"><span>[PoCS_Dykstra]</span></a>.)</p>
-<p>This function assumes <span class="math notranslate nohighlight">\(\mathcal{C}_{1} \cap \cdots \cap \mathcal{C}_{K} \ne \emptyset\)</span>.
-<a class="reference internal" href="#pyxu.operator.ConvexSetIntersection.prox" title="pyxu.operator.ConvexSetIntersection.prox"><code class="xref py py-meth docutils literal notranslate"><span class="pre">prox()</span></code></a> will loop indefinitely if this condition is violated.</p>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-
-<span class="n">op</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">ConvexSetIntersection</span><span class="p">(</span>             <span class="c1"># intersection of</span>
-    <span class="n">pxo</span><span class="o">.</span><span class="n">LInfinityBall</span><span class="p">(),</span>                    <span class="c1">#   L-\infty ball centered at (0,0)</span>
-    <span class="n">pxo</span><span class="o">.</span><span class="n">L2Ball</span><span class="p">()</span><span class="o">.</span><span class="n">asloss</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])),</span>  <span class="c1">#   L2 ball centered at (1,0)</span>
-<span class="p">)</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span>
-    <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
-    <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
-    <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>  <span class="c1"># not in LInfinity ball -&gt; \infty</span>
-    <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
-    <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span>
-    <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>  <span class="c1"># not in L2 ball -&gt; \infty</span>
- <span class="p">])</span>
-<span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># [0 0 inf 0 0 inf]</span>
-</pre></div>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>args</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em>]</em>) – </p>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.ConvexSetIntersection.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#ConvexSetIntersection.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.ConvexSetIntersection.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>args</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a> ( <a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a> )) – Sequence of indicator functions encoding convex domains.</p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.ConvexSetIntersection.prox">
-<span class="sig-name descname"><span class="pre">prox</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tau</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/func/indicator.html#ConvexSetIntersection.prox"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.ConvexSetIntersection.prox" title="Link to this definition">#</a></dt>
-<dd><p>Evaluate proximity operator of <span class="math notranslate nohighlight">\(\tau f\)</span> at specified point(s).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, M) input points.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive scale factor.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>out</strong> – (…, M) proximal evaluations.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>For <span class="math notranslate nohighlight">\(\tau &gt;0\)</span>, the <em>proximity operator</em> of a scaled functional <span class="math notranslate nohighlight">\(f: \mathbb{R}^{M} \to \mathbb{R}\)</span> is
-defined as:</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{\text{prox}}_{\tau f}(\mathbf{z})
-:=
-\arg\min_{\mathbf{x}\in\mathbb{R}^{M}} f(x)+\frac{1}{2\tau} \|\mathbf{x}-\mathbf{z}\|_{2}^{2},
-\quad
-\forall \mathbf{z} \in \mathbb{R}^{M}.\]</div>
-</dd></dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.stack">
-<span class="sig-name descname"><span class="pre">stack</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ops</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axis</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/blocks.html#stack"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.stack" title="Link to this definition">#</a></dt>
-<dd><p>Construct a stacked operator.</p>
-<p>A stacked-operator <span class="math notranslate nohighlight">\(V: \mathbb{R}^{d} \to \mathbb{R}^{c}\)</span> is an operator containing (vertically or
-horizontally) blocks of smaller operators <span class="math notranslate nohighlight">\(\{O_{1}, \ldots, O_{N}\}\)</span>.</p>
-<p>This is a convenience function around <a class="reference internal" href="#pyxu.operator.hstack" title="pyxu.operator.hstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">hstack()</span></code></a> and <a class="reference internal" href="#pyxu.operator.vstack" title="pyxu.operator.vstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">vstack()</span></code></a>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>ops</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a> ( <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-attr docutils literal notranslate"><span class="pre">OpT</span></code></a> )) – [op1(c1, d1), …, opN(cN, dN)] operators to join.</p></li>
-<li><p><strong>axis</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – <p>The axis along which operators will be joined, i.e.</p>
-<ul>
-<li><p>0: stack vertically (row-wise)</p></li>
-<li><p>1: stack horizontally (column-wise)</p></li>
-</ul>
-</p></li>
-<li><p><strong>kwargs</strong> – Extra keyword-arguments forwarded to <code class="xref py py-class docutils literal notranslate"><span class="pre">_COOBlock</span></code>.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Stacked operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.hstack" title="pyxu.operator.hstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">hstack()</span></code></a>, <a class="reference internal" href="#pyxu.operator.vstack" title="pyxu.operator.vstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">vstack()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.vstack">
-<span class="sig-name descname"><span class="pre">vstack</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ops</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/blocks.html#vstack"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.vstack" title="Link to this definition">#</a></dt>
-<dd><p>Construct a vertically-stacked operator.</p>
-<p>A vstacked-operator <span class="math notranslate nohighlight">\(V: \mathbb{R}^{d} \to \mathbb{R}^{c_{1} + \cdots + c_{N}}\)</span> is an operator containing
-(vertically) blocks of smaller operators <span class="math notranslate nohighlight">\(\{O_{1}: \mathbb{R}^{d} \to \mathbb{R}^{c_{1}}, \ldots, O_{N}:
-\mathbb{R}^{d} \to \mathbb{R}^{c_{N}}\}\)</span>, i.e.</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}V
-=
-\left[
-    \begin{array}{c}
-        O_{1}  \\
-        \vdots \\
-        O_{N}  \\
-    \end{array}
-\right]\end{split}\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>ops</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a> ( <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-attr docutils literal notranslate"><span class="pre">OpT</span></code></a> )) – [op1(c1, d), …, opN(cN, d)] operators to concatenate.</p></li>
-<li><p><strong>kwargs</strong> – Extra keyword-arguments forwarded to <code class="xref py py-class docutils literal notranslate"><span class="pre">_COOBlock</span></code>.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Vertically-stacked (c1+…+cN, d) operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p>All sub-operator domains must have compatible shapes, i.e. all integer-valued <code class="docutils literal notranslate"><span class="pre">dim</span></code> s must be identical.</p></li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.hstack" title="pyxu.operator.hstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">hstack()</span></code></a>, <a class="reference internal" href="#pyxu.operator.stack" title="pyxu.operator.stack"><code class="xref py py-func docutils literal notranslate"><span class="pre">stack()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.hstack">
-<span class="sig-name descname"><span class="pre">hstack</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ops</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/blocks.html#hstack"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.hstack" title="Link to this definition">#</a></dt>
-<dd><p>Construct a horizontally-stacked operator.</p>
-<p>A hstacked-operator <span class="math notranslate nohighlight">\(H: \mathbb{R}^{d_{1} + \cdots + d_{N}} \to \mathbb{R}^{c}\)</span> is an operator containing
-(horizontally) blocks of smaller operators <span class="math notranslate nohighlight">\(\{O_{1}: \mathbb{R}^{d_{1}} \to \mathbb{R}^{c}, \ldots, O_{N}:
-\mathbb{R}^{d_{N}} \to \mathbb{R}^{c}\}\)</span>, i.e.</p>
-<div class="math notranslate nohighlight">
-\[H
-=
-\left[
-    \begin{array}{ccc}
-        O_{1} &amp; \cdots &amp; O_{N}
-    \end{array}
-\right]\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>ops</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a> ( <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-attr docutils literal notranslate"><span class="pre">OpT</span></code></a> )) – [op1(c, d1), …, opN(c, dN)] operators to concatenate.</p></li>
-<li><p><strong>kwargs</strong> – Extra keyword-arguments forwarded to <code class="xref py py-class docutils literal notranslate"><span class="pre">_COOBlock</span></code>.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Horizontally-stacked (c, d1+….+dN) operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p>All sub-operator domains must have compatible shapes, i.e. all <code class="docutils literal notranslate"><span class="pre">codim</span></code> s must be identical.</p></li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.vstack" title="pyxu.operator.vstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">vstack()</span></code></a>, <a class="reference internal" href="#pyxu.operator.stack" title="pyxu.operator.stack"><code class="xref py py-func docutils literal notranslate"><span class="pre">stack()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.block_diag">
-<span class="sig-name descname"><span class="pre">block_diag</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ops</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/blocks.html#block_diag"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.block_diag" title="Link to this definition">#</a></dt>
-<dd><p>Construct a block-diagonal operator.</p>
-<p>A block-diagonal operator <span class="math notranslate nohighlight">\(D: \mathbb{R}^{d_{1} + \cdots + d_{N}} \to \mathbb{R}^{c_{1} + \cdots + c_{N}}\)</span> is
-an operator containing (diagonally) blocks of smaller operators <span class="math notranslate nohighlight">\(\{O_{1}: \mathbb{R}^{d_{1}} \to
-\mathbb{R}^{c_{1}}, \ldots, O_{N}: \mathbb{R}^{d_{N}} \to \mathbb{R}^{c_{N}}\}\)</span>, i.e.</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}D
-=
-\left[
-    \begin{array}{ccc}
-        O_{1} &amp;        &amp;       \\
-              &amp; \ddots &amp;       \\
-              &amp;        &amp; O_{N} \\
-    \end{array}
-\right]\end{split}\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>ops</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a> ( <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-attr docutils literal notranslate"><span class="pre">OpT</span></code></a> )) – [op1(c1, d1), …, opN(cN, dN)] operators to concatenate.</p></li>
-<li><p><strong>kwargs</strong> – Extra keyword-arguments forwarded to <code class="xref py py-class docutils literal notranslate"><span class="pre">_COOBlock</span></code>.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Block-diagonal (c1+…+cN, d1+…+dN) operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.block" title="pyxu.operator.block"><code class="xref py py-func docutils literal notranslate"><span class="pre">block()</span></code></a>, <a class="reference internal" href="#pyxu.operator.coo_block" title="pyxu.operator.coo_block"><code class="xref py py-func docutils literal notranslate"><span class="pre">coo_block()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.block">
-<span class="sig-name descname"><span class="pre">block</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ops</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/blocks.html#block"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.block" title="Link to this definition">#</a></dt>
-<dd><p>Construct a (dense) block-defined operator.</p>
-<p>A block-defined operator is an operator containing blocks of smaller operators.  Blocks are stacked
-horizontally/vertically in a user-specified order to obtain the final shape.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>ops</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a> ( <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a> ( <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-attr docutils literal notranslate"><span class="pre">OpT</span></code></a> ) )) – 2D nested sequence of (ck, dk)-shaped operators.</p></li>
-<li><p><strong>order</strong> (<code class="docutils literal notranslate"><span class="pre">0</span></code>, <code class="docutils literal notranslate"><span class="pre">1</span></code>) – <p>Order in which the nested operators are specified/concatenated:</p>
-<ul>
-<li><p>0: concatenate inner-most blocks via <a class="reference internal" href="#pyxu.operator.vstack" title="pyxu.operator.vstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">vstack()</span></code></a>, then <a class="reference internal" href="#pyxu.operator.hstack" title="pyxu.operator.hstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">hstack()</span></code></a>.</p></li>
-<li><p>1: concatenate inner-most blocks via <a class="reference internal" href="#pyxu.operator.hstack" title="pyxu.operator.hstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">hstack()</span></code></a>, then <a class="reference internal" href="#pyxu.operator.vstack" title="pyxu.operator.vstack"><code class="xref py py-func docutils literal notranslate"><span class="pre">vstack()</span></code></a>.</p></li>
-</ul>
-</p></li>
-<li><p><strong>kwargs</strong> – Extra keyword-arguments forwarded to <code class="xref py py-class docutils literal notranslate"><span class="pre">_COOBlock</span></code>.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Block-defined operator. (See below for examples.)</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p>Each row/column may contain a different number of operators.</p></li>
-</ul>
-<p class="rubric">Examples</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">block</span><span class="p">(</span>
-<span class="gp">... </span>   <span class="p">[</span>
-<span class="gp">... </span>    <span class="p">[</span><span class="n">A</span><span class="p">],</span>        <span class="c1"># ABEEGGG</span>
-<span class="gp">... </span>    <span class="p">[</span><span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">D</span><span class="p">],</span>  <span class="c1"># ACEEHHH</span>
-<span class="gp">... </span>    <span class="p">[</span><span class="n">E</span><span class="p">,</span> <span class="n">F</span><span class="p">],</span>     <span class="c1"># ADFFHHH</span>
-<span class="gp">... </span>    <span class="p">[</span><span class="n">G</span><span class="p">,</span> <span class="n">H</span><span class="p">],</span>
-<span class="gp">... </span>   <span class="p">],</span>
-<span class="gp">... </span>   <span class="n">order</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
-<span class="gp">... </span><span class="p">)</span>
-
-<span class="gp">&gt;&gt;&gt; </span><span class="n">block</span><span class="p">(</span>
-<span class="gp">... </span>   <span class="p">[</span>
-<span class="gp">... </span>    <span class="p">[</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">D</span><span class="p">],</span>  <span class="c1"># ABBCD</span>
-<span class="gp">... </span>    <span class="p">[</span><span class="n">E</span><span class="p">],</span>           <span class="c1"># EEEEE</span>
-<span class="gp">... </span>    <span class="p">[</span><span class="n">F</span><span class="p">,</span> <span class="n">G</span><span class="p">],</span>        <span class="c1"># FFGGG</span>
-<span class="gp">... </span>   <span class="p">],</span>
-<span class="gp">... </span>   <span class="n">order</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
-<span class="gp">... </span><span class="p">)</span>
-</pre></div>
-</div>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.block_diag" title="pyxu.operator.block_diag"><code class="xref py py-func docutils literal notranslate"><span class="pre">block_diag()</span></code></a>, <a class="reference internal" href="#pyxu.operator.coo_block" title="pyxu.operator.coo_block"><code class="xref py py-func docutils literal notranslate"><span class="pre">coo_block()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.coo_block">
-<span class="sig-name descname"><span class="pre">coo_block</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ops</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">grid_shape</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/blocks.html#coo_block"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.coo_block" title="Link to this definition">#</a></dt>
-<dd><p>Constuct a (possibly-sparse) block-defined operator in COOrdinate format.</p>
-<p>A block-defined operator is an operator containing blocks of smaller operators.  Blocks must align on a coarse grid,
-akin to the COO format used to define sparse arrays.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>ops</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a><em>]</em><em>, </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em><em>, </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em><em>]</em><em>]</em>) – <p>(data, (i, j)) sequences defining block placement, i.e.</p>
-<ul>
-<li><p><code class="code docutils literal notranslate"><span class="pre">data[:]</span></code> are <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-attr docutils literal notranslate"><span class="pre">OpT</span></code></a> instances, in any order.</p></li>
-<li><p><code class="code docutils literal notranslate"><span class="pre">i[:]</span></code> are the row indices of the block entries on the coarse grid.</p></li>
-<li><p><code class="code docutils literal notranslate"><span class="pre">j[:]</span></code> are the column indices of the block entries on the coarse grid.</p></li>
-</ul>
-</p></li>
-<li><p><strong>grid_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpShape" title="pyxu.info.ptype.OpShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpShape</span></code></a>) – (M, N) shape of the coarse grid.</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – <p>If <code class="docutils literal notranslate"><span class="pre">true</span></code> , use Dask to evaluate the following methods:</p>
-<ul>
-<li><p><code class="docutils literal notranslate"><span class="pre">.apply()</span></code></p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">.prox()</span></code></p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">.grad()</span></code></p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">.adjoint()</span></code></p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">.[co]gram().[apply,adjoint]()</span></code></p></li>
-</ul>
-</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Block-defined operator. (See below for examples.)</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p>Blocks on the same row/column must have the same <code class="docutils literal notranslate"><span class="pre">codim</span></code> / <code class="docutils literal notranslate"><span class="pre">dim</span></code> s.</p></li>
-<li><p>Each row/column of the coarse grid <strong>must</strong> contain at least one entry.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">parallel=True</span></code> only parallelizes execution when inputs to listed methods are NUMPY arrays.</p></li>
-</ul>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>When processing Dask inputs, or when <code class="docutils literal notranslate"><span class="pre">parallel=True</span></code>, operators which are not thread-safe may produce incorrect
-results.  There is no easy way to ensure thread-safety at the level of <code class="xref py py-mod docutils literal notranslate"><span class="pre">blocks</span></code> without
-impacting performance of all operators involved.  Users are thus responsible for executing block-defined
-operators correctly, i.e., if thread-unsafe operators are involved, stick to NumPy/CuPy inputs.</p>
-</div>
-<p class="rubric">Examples</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">coo_block</span><span class="p">(</span>
-<span class="gp">... </span>    <span class="p">([</span><span class="n">A</span><span class="p">(</span><span class="mi">500</span><span class="p">,</span><span class="mi">1000</span><span class="p">),</span> <span class="n">B</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1000</span><span class="p">),</span> <span class="n">C</span><span class="p">(</span><span class="mi">500</span><span class="p">,</span><span class="mi">500</span><span class="p">),</span> <span class="n">D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">)],</span>  <span class="c1"># data</span>
-<span class="gp">... </span>     <span class="p">[</span>
-<span class="gp">... </span>      <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span>  <span class="c1"># i</span>
-<span class="gp">... </span>      <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>  <span class="c1"># j</span>
-<span class="gp">... </span>     <span class="p">]),</span>
-<span class="gp">... </span>    <span class="n">grid_shape</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span>
-<span class="gp">... </span><span class="p">)</span>
-
-<span class="go">| coarse_idx |      0       |    1    |      2      |</span>
-<span class="go">|------------|--------------|---------|-------------|</span>
-<span class="go">|          0 | A(500, 1000) |         | C(500, 500) |</span>
-<span class="go">|          1 | B(1, 1000)   |         |             |</span>
-<span class="go">|          2 |              | D(1, 3) |             |</span>
-</pre></div>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.sin">
-<span class="sig-name descname"><span class="pre">sin</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#sin"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.sin" title="Link to this definition">#</a></dt>
-<dd><p>Trigonometric sine, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \sin(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = \cos(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f'(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(L\)</span> at <span class="math notranslate nohighlight">\(x = k \pi, \, k \in \mathbb{Z}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 1\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> at <span class="math notranslate nohighlight">\(x = (2k + 1) \frac{\pi}{2}, \, k
-\in \mathbb{Z}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.cos">
-<span class="sig-name descname"><span class="pre">cos</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#cos"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.cos" title="Link to this definition">#</a></dt>
-<dd><p>Trigonometric cosine, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \cos(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = -\sin(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f'(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(L\)</span> at <span class="math notranslate nohighlight">\(x = (2k + 1) \frac{\pi}{2}, \, k \in
-\mathbb{Z}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 1\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> at <span class="math notranslate nohighlight">\(x = k \pi, \, k \in \mathbb{Z}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.tan">
-<span class="sig-name descname"><span class="pre">tan</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#tan"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.tan" title="Link to this definition">#</a></dt>
-<dd><p>Trigonometric tangent, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \tan(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = \cos^{-2}(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [-\pi, \pi]\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [-\pi, \pi]\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.arcsin">
-<span class="sig-name descname"><span class="pre">arcsin</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#arcsin"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.arcsin" title="Link to this definition">#</a></dt>
-<dd><p>Inverse sine, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \arcsin(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = (1 - x^{2})^{-\frac{1}{2}}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [-1, 1]\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [-1, 1]\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.arccos">
-<span class="sig-name descname"><span class="pre">arccos</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#arccos"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.arccos" title="Link to this definition">#</a></dt>
-<dd><p>Inverse cosine, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \arccos(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = -(1 - x^{2})^{-\frac{1}{2}}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [-1, 1]\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [-1, 1]\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.arctan">
-<span class="sig-name descname"><span class="pre">arctan</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#arctan"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.arctan" title="Link to this definition">#</a></dt>
-<dd><p>Inverse tangent, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \arctan(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = (1 + x^{2})^{-1}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f'(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(L\)</span> at <span class="math notranslate nohighlight">\(x = 0\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 3 \sqrt{3} / 8\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> at <span class="math notranslate nohighlight">\(x = \pm \frac{1}{\sqrt{3}}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.sinh">
-<span class="sig-name descname"><span class="pre">sinh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#sinh"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.sinh" title="Link to this definition">#</a></dt>
-<dd><p>Hyperbolic sine, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \sinh(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = \cosh(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.cosh">
-<span class="sig-name descname"><span class="pre">cosh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#cosh"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.cosh" title="Link to this definition">#</a></dt>
-<dd><p>Hyperbolic cosine, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \cosh(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = \sinh(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.tanh">
-<span class="sig-name descname"><span class="pre">tanh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#tanh"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.tanh" title="Link to this definition">#</a></dt>
-<dd><p>Hyperbolic tangent, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \tanh(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = 1 - \tanh^{2}(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f'(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(L\)</span> at <span class="math notranslate nohighlight">\(x = 0\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 4 / 3 \sqrt{3}\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> at <span class="math notranslate nohighlight">\(x = \frac{1}{2} \ln(2 \pm
-\sqrt{3})\)</span>.</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.arcsinh">
-<span class="sig-name descname"><span class="pre">arcsinh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#arcsinh"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.arcsinh" title="Link to this definition">#</a></dt>
-<dd><p>Inverse hyperbolic sine, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \sinh^{-1}(x) = \ln(x + \sqrt{x^{2} + 1})\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = (x^{2} + 1)^{-\frac{1}{2}}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f'(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(L\)</span> at <span class="math notranslate nohighlight">\(x = 0\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \frac{2}{3 \sqrt{3}}\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> at <span class="math notranslate nohighlight">\(x = \pm \frac{1}{\sqrt{2}}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.arccosh">
-<span class="sig-name descname"><span class="pre">arccosh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#arccosh"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.arccosh" title="Link to this definition">#</a></dt>
-<dd><p>Inverse hyperbolic cosine, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \cosh^{-1}(x) = \ln(x + \sqrt{x^{2} - 1})\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = (x^{2} - 1)^{-\frac{1}{2}}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [1, \infty[\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [1, \infty[\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.arctanh">
-<span class="sig-name descname"><span class="pre">arctanh</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#arctanh"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.arctanh" title="Link to this definition">#</a></dt>
-<dd><p>Inverse hyperbolic tangent, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \tanh^{-1}(x) = \frac{1}{2}\ln\left(\frac{1+x}{1-x}\right)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = (1 - x^{2})^{-1}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [-1, 1]\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = [-1, 1]\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.exp">
-<span class="sig-name descname"><span class="pre">exp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">base</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#exp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.exp" title="Link to this definition">#</a></dt>
-<dd><p>Exponential, element-wise. (Default: base-E exponential.)</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f_{b}(x) = b^{x}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f_{b}'(x) = b^{x} \ln(b)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f_{b}(x) - f_{b}(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f_{b}'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f_{b}) = \mathbb{R}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f_{b}'(x) - f_{b}'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant
-<span class="math notranslate nohighlight">\(\partial L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f_{b}''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f_{b}) = \mathbb{R}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
-<li><p><strong>base</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.log">
-<span class="sig-name descname"><span class="pre">log</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">base</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#log"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.log" title="Link to this definition">#</a></dt>
-<dd><p>Logarithm, element-wise. (Default: base-E logarithm.)</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f_{b}(x) = \log_{b}(x)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f_{b}'(x) = x^{-1} / \ln(b)\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f_{b}(x) - f_{b}(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f_{b}'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f_{b}) = \mathbb{R}_{+}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f_{b}'(x) - f_{b}'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant
-<span class="math notranslate nohighlight">\(\partial L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f_{b}''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f_{b}) = \mathbb{R}_{+}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
-<li><p><strong>base</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.clip">
-<span class="sig-name descname"><span class="pre">clip</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">a_min</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">a_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#clip"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.clip" title="Link to this definition">#</a></dt>
-<dd><p>Clip (limit) values in an array, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><div class="math notranslate nohighlight">
-\[\begin{split}f_{[a,b]}(x) =
-\begin{cases}
-    a, &amp; \text{if} \ x \leq a, \\
-    x, &amp; a &lt; x &lt; b, \\
-    b, &amp; \text{if} \ x \geq b.
-\end{cases}\end{split}\]</div>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p></li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
-<li><p><strong>a_min</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-<li><p><strong>a_max</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.sqrt">
-<span class="sig-name descname"><span class="pre">sqrt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#sqrt"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.sqrt" title="Link to this definition">#</a></dt>
-<dd><p>Non-negative square-root, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \sqrt{x}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = 1 / 2 \sqrt{x}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}_{+}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}_{+}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.cbrt">
-<span class="sig-name descname"><span class="pre">cbrt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#cbrt"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.cbrt" title="Link to this definition">#</a></dt>
-<dd><p>Cube-root, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \sqrt[3]{x}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = 1 / 3 \sqrt[3]{x^{2}}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f''(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.square">
-<span class="sig-name descname"><span class="pre">square</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#square"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.square" title="Link to this definition">#</a></dt>
-<dd><p>Square, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = x^{2}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = 2 x\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \infty\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(f'(x)\)</span> is unbounded on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 2\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> everywhere.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.abs">
-<span class="sig-name descname"><span class="pre">abs</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#abs"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.abs" title="Link to this definition">#</a></dt>
-<dd><p>Absolute value, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(f(x) = \vert x \vert\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p></li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.sign">
-<span class="sig-name descname"><span class="pre">sign</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#sign"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.sign" title="Link to this definition">#</a></dt>
-<dd><p>Number sign indicator, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(f(x) = x / \vert x \vert\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 2\)</span>.</p></li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.gaussian">
-<span class="sig-name descname"><span class="pre">gaussian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#gaussian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.gaussian" title="Link to this definition">#</a></dt>
-<dd><p>Gaussian, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \exp(-x^{2})\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = -2 x \exp(-x^{2})\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \sqrt{2 / e}\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f'(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(L\)</span> at <span class="math notranslate nohighlight">\(x = \pm 1 / \sqrt{2}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 2\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> at <span class="math notranslate nohighlight">\(x = 0\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.sigmoid">
-<span class="sig-name descname"><span class="pre">sigmoid</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#sigmoid"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.sigmoid" title="Link to this definition">#</a></dt>
-<dd><p>Sigmoid, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = (1 + e^{-x})^{-1}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = f(x) [ f(x) - 1 ]\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1 / 4\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f'(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(L\)</span> at <span class="math notranslate nohighlight">\(x = 0\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 1 / 6 \sqrt{3}\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> at <span class="math notranslate nohighlight">\(x = \ln(2 \pm \sqrt{3})\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.softplus">
-<span class="sig-name descname"><span class="pre">softplus</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#softplus"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.softplus" title="Link to this definition">#</a></dt>
-<dd><p>Softplus operator.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = \ln(1 + e^{x})\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = (1 + e^{-x})^{-1}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f'(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(L\)</span> on <span class="math notranslate nohighlight">\(\text{dom}(f) = \mathbb{R}\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 1 / 4\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> at <span class="math notranslate nohighlight">\(x = 0\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.leakyrelu">
-<span class="sig-name descname"><span class="pre">leakyrelu</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#leakyrelu"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.leakyrelu" title="Link to this definition">#</a></dt>
-<dd><p>Leaky rectified linear unit, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(f(x) = x \left[\mathbb{1}_{\ge 0}(x) + \alpha \mathbb{1}_{&lt; 0}(x)\right], \quad \alpha \ge 0\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = \max(1, \alpha)\)</span>.</p></li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p></li>
-<li><p><strong>alpha</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.relu">
-<span class="sig-name descname"><span class="pre">relu</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#relu"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.relu" title="Link to this definition">#</a></dt>
-<dd><p>Rectified linear unit, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(f(x) = \lfloor x \rfloor_{+}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p></li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.silu">
-<span class="sig-name descname"><span class="pre">silu</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#silu"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.silu" title="Link to this definition">#</a></dt>
-<dd><p>Sigmoid linear unit, element-wise.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(f(x) = x / (1 + e^{-x})\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(f'(x) = (1 + e^{-x} + x e^{-x}) / (1 + e^{-x})^{2}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1.1\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f'(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(L\)</span> at <span class="math notranslate nohighlight">\(x \approx 2.4\)</span>.)</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 1 / 2\)</span>.</p>
-<p>(Reason: <span class="math notranslate nohighlight">\(\vert f''(x) \vert\)</span> is bounded by <span class="math notranslate nohighlight">\(\partial L\)</span> at <span class="math notranslate nohighlight">\(x = 0\)</span>.)</p>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.softmax">
-<span class="sig-name descname"><span class="pre">softmax</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/map/ufunc.html#softmax"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.softmax" title="Link to this definition">#</a></dt>
-<dd><p>Softmax operator.</p>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\([f(x_{1},\ldots,x_{N})]_{i} = e^{x_{i}} / \sum_{k=1}^{N} e^{x_{k}}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(J_{f}(\mathbf{x}) = \text{diag}(f(\mathbf{x})) - f(\mathbf{x}) f(\mathbf{x})^{T}\)</span></p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f(x) - f(y) \vert \le L \vert x - y \vert\)</span>, with Lipschitz constant <span class="math notranslate nohighlight">\(L = 1\)</span>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\vert f'(x) - f'(y) \vert \le \partial L \vert x - y \vert\)</span>, with diff-Lipschitz constant <span class="math notranslate nohighlight">\(\partial L
-= 1\)</span>.</p></li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>op</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.SubSample">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SubSample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">indices</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/select.html#SubSample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SubSample" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
-<p>Multi-dimensional sub-sampling operator.</p>
-<p>This operator extracts a subset of the input matching the provided subset specifier.
-Its Lipschitz constant is 1.</p>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1">### Extract even samples of a 1D signal.</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
-<span class="n">S</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">SubSample</span><span class="p">(</span>
-      <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
-      <span class="nb">slice</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span>
-<span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">S</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># array([0, 2, 4, 6, 8])</span>
-</pre></div>
-</div>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1">### Extract columns[1, 3, -1] from a 2D matrix</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="mi">40</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">40</span><span class="p">)</span>  <span class="c1"># the input</span>
-<span class="n">S</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">SubSample</span><span class="p">(</span>
-      <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
-      <span class="nb">slice</span><span class="p">(</span><span class="kc">None</span><span class="p">),</span>  <span class="c1"># take all rows</span>
-      <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span>   <span class="c1"># and these columns</span>
-<span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">S</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>  <span class="c1"># array([[  1.,   3.,  39.],</span>
-                                    <span class="c1">#        [ 41.,  43.,  79.],</span>
-                                    <span class="c1">#        [ 81.,  83., 119.]])</span>
-</pre></div>
-</div>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1">### Extract all red rows of an (D,H,W) RGB image matching a boolean mask.</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="mi">5</span> <span class="o">*</span> <span class="mi">4</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
-<span class="n">mask</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
-<span class="n">S</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">SubSample</span><span class="p">(</span>
-      <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
-      <span class="mi">0</span><span class="p">,</span>            <span class="c1"># red channel</span>
-      <span class="n">mask</span><span class="p">,</span>         <span class="c1"># row selector</span>
-      <span class="nb">slice</span><span class="p">(</span><span class="kc">None</span><span class="p">),</span>  <span class="c1"># all columns; this field can be omitted.</span>
-<span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">S</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">mask</span><span class="o">.</span><span class="n">sum</span><span class="p">(),</span> <span class="mi">4</span><span class="p">)</span>  <span class="c1"># array([[[ 0.,  1.,  2.,  3.],</span>
-                                                <span class="c1">#         [12., 13., 14., 15.]]])</span>
-</pre></div>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>indices</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#slice" title="(in Python v3.11)"><em>slice</em></a><em> | </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.operator.SubSample.IndexSpec">
-<span class="sig-name descname"><span class="pre">IndexSpec</span></span><a class="headerlink" href="#pyxu.operator.SubSample.IndexSpec" title="Link to this definition">#</a></dt>
-<dd><p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>], <a class="reference external" href="https://docs.python.org/3/library/functions.html#slice" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">slice</span></code></a>, <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NDArray</span></code></a>]</p>
-</dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.operator.SubSample.TrimSpec">
-<span class="sig-name descname"><span class="pre">TrimSpec</span></span><a class="headerlink" href="#pyxu.operator.SubSample.TrimSpec" title="Link to this definition">#</a></dt>
-<dd><p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>], <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>]]]</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.SubSample.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">indices</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/select.html#SubSample.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SubSample.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the data to be sub-sampled.</p></li>
-<li><p><strong>indices</strong> (<a class="reference internal" href="#pyxu.operator.SubSample.IndexSpec" title="pyxu.operator.SubSample.IndexSpec"><code class="xref py py-class docutils literal notranslate"><span class="pre">IndexSpec</span></code></a>) – <p>Sub-sample specifier per dimension. (See examples.)</p>
-<p>Valid specifiers are:</p>
-<ul>
-<li><p>integers</p></li>
-<li><p>lists (or arrays) of indices</p></li>
-<li><p>slices</p></li>
-<li><p>1D boolean masks</p></li>
-</ul>
-<p>Unspecified trailing dimensions are not sub-sampled.</p>
-</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.SubSample.apply">
-<span class="sig-name descname"><span class="pre">apply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/select.html#SubSample.apply"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SubSample.apply" title="Link to this definition">#</a></dt>
-<dd><p>Sub-sample the data.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, arg_shape.prod()) data</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>out</strong> – (…, sub_shape.prod()) sub-sampled data points.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.SubSample.adjoint">
-<span class="sig-name descname"><span class="pre">adjoint</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/select.html#SubSample.adjoint"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SubSample.adjoint" title="Link to this definition">#</a></dt>
-<dd><p>Up-sample the data.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, sub_shape.prod()) data points.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>out</strong> – (…, arg_shape.prod()) up-sampled data points. (Zero-filled.)</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Trim">
-<span class="sig-name descname"><span class="pre">Trim</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">trim_width</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/select.html#Trim"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Trim" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional trimming operator.</p>
-<p>This operator trims the input array in each dimension according to specified widths.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>trim_width</strong> (<a class="reference internal" href="#pyxu.operator.SubSample.TrimSpec" title="pyxu.operator.SubSample.TrimSpec"><code class="xref py py-class docutils literal notranslate"><span class="pre">TrimSpec</span></code></a>) – <p>Number of values trimmed from the edges of each axis.
-Multiple forms are accepted:</p>
-<ul>
-<li><p><code class="docutils literal notranslate"><span class="pre">int</span></code>: trim each dimension’s head/tail by <code class="code docutils literal notranslate"><span class="pre">trim_width</span></code>.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuple[int,</span> <span class="pre">...]</span></code>: trim dimension[k]’s head/tail by <code class="code docutils literal notranslate"><span class="pre">trim_width[k]</span></code>.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuple[tuple[int,</span> <span class="pre">int],</span> <span class="pre">...]</span></code>: trim dimension[k]’s head/tail by <code class="code docutils literal notranslate"><span class="pre">trim_width[k][0]</span></code> / <code class="code docutils literal notranslate"><span class="pre">trim_width[k][1]</span></code>
-respectively.</p></li>
-</ul>
-</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong></p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Sum">
-<span class="sig-name descname"><span class="pre">Sum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/reduce.html#Sum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Sum" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional sum reduction.</p>
-<p>This operator re-arranges the input array to a multi-dimensional array of shape <code class="code docutils literal notranslate"><span class="pre">arg_shape</span></code>, then reduces it via
-summation across one or more <code class="code docutils literal notranslate"><span class="pre">axis</span></code>.</p>
-<p>For example, assuming the input array <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_1 \times N_2 \times N_3}\)</span> and <code class="docutils literal notranslate"><span class="pre">axis=-1</span></code>,
-then</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{y}_{i,j} = \sum_{k}{\mathbf{x}_{i,j,k}}.\]</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the data to be reduced.</p></li>
-<li><p><strong>axis</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayAxis" title="pyxu.info.ptype.NDArrayAxis"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayAxis</span></code></a>) – Axis or axes along which a sum is performed.  The default, axis=None, will sum all the elements of the input
-array.  If axis is negative it counts from the last to the first axis.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>The matrix operator of a 1D reduction applied to <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N}\)</span> is given by</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{A}(x) = \mathbf{1}^{T} \mathbf{x},\]</div>
-<p>where <span class="math notranslate nohighlight">\(\sigma_{\max}(\mathbf{A}) = \sqrt{N}\)</span>.  An ND reduction is a chain of 1D reductions in orthogonal
-dimensions.  Hence the Lipschitz constant of an ND reduction is the product of Lipschitz constants of all 1D
-reductions involved, i.e.:</p>
-<div class="math notranslate nohighlight">
-\[L = \sqrt{\prod_{i_{k}} N_{i_{k}}},\]</div>
-<p>where <span class="math notranslate nohighlight">\(\{i_{k}\}_{k}\)</span> denotes the axes being summed over.</p>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.kron">
-<span class="sig-name descname"><span class="pre">kron</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">B</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/kron.html#kron"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.kron" title="Link to this definition">#</a></dt>
-<dd><p><a class="reference external" href="https://en.wikipedia.org/wiki/Kronecker_product#Definition">Kronecker product</a> <span class="math notranslate nohighlight">\(A \otimes B\)</span> between two
-linear operators.</p>
-<p>The Kronecker product <span class="math notranslate nohighlight">\(A \otimes B\)</span> is defined as</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}A \otimes B
-=
-\left[
-    \begin{array}{ccc}
-        A_{11} B     &amp; \cdots &amp; A_{1N_{A}} B \\
-        \vdots       &amp; \ddots &amp; \vdots   \\
-        A_{M_{A}1} B &amp; \cdots &amp; A_{M_{A}N_{A}} B \\
-    \end{array}
-\right],\end{split}\]</div>
-<p>where <span class="math notranslate nohighlight">\(A : \mathbb{R}^{N_{A}} \to \mathbb{R}^{M_{A}}\)</span>, and <span class="math notranslate nohighlight">\(B : \mathbb{R}^{N_{B}} \to
-\mathbb{R}^{M_{B}}\)</span>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a>) – (mA, nA) linear operator</p></li>
-<li><p><strong>B</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a>) – (mB, nB) linear operator</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (mA*mB, nA*nB) linear operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>This implementation is <strong>matrix-free</strong> by leveraging properties of the Kronecker product, i.e.  <span class="math notranslate nohighlight">\(A\)</span> and
-<span class="math notranslate nohighlight">\(B\)</span> need not be known explicitly.  In particular <span class="math notranslate nohighlight">\((A \otimes B) x\)</span> and <span class="math notranslate nohighlight">\((A \otimes B)^{*} x\)</span> are
-computed implicitly via the relation:</p>
-<div class="math notranslate nohighlight">
-\[\text{vec}(\mathbf{A}\mathbf{B}\mathbf{C})
-=
-(\mathbf{C}^{T} \otimes \mathbf{A}) \text{vec}(\mathbf{B}),\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathbf{A}\)</span>, <span class="math notranslate nohighlight">\(\mathbf{B}\)</span>, and <span class="math notranslate nohighlight">\(\mathbf{C}\)</span> are matrices.</p>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.khatri_rao">
-<span class="sig-name descname"><span class="pre">khatri_rao</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">B</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/kron.html#khatri_rao"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.khatri_rao" title="Link to this definition">#</a></dt>
-<dd><p><a class="reference external" href="https://en.wikipedia.org/wiki/Khatri%E2%80%93Rao_product#Column-wise_Kronecker_product">Column-wise Khatri-Rao product</a> <span class="math notranslate nohighlight">\(A \circ B\)</span> between
-two linear operators.</p>
-<p>The Khatri-Rao product <span class="math notranslate nohighlight">\(A \circ B\)</span> is defined as</p>
-<div class="math notranslate nohighlight">
-\[A \circ B
-=
-\left[
-    \begin{array}{ccc}
-    \mathbf{a}_{1} \otimes \mathbf{b}_{1} &amp; \cdots &amp; \mathbf{a}_{N} \otimes \mathbf{b}_{N}
-    \end{array}
-\right],\]</div>
-<p>where <span class="math notranslate nohighlight">\(A : \mathbb{R}^{N} \to \mathbb{R}^{M_{A}}\)</span>, <span class="math notranslate nohighlight">\(B : \mathbb{R}^{N} \to \mathbb{R}^{M_{B}}\)</span>, and
-<span class="math notranslate nohighlight">\(\mathbf{a}_{k}\)</span> (repectively <span class="math notranslate nohighlight">\(\mathbf{b}_{k}\)</span>) denotes the <span class="math notranslate nohighlight">\(k\)</span>-th column of <span class="math notranslate nohighlight">\(A\)</span>
-(respectively <span class="math notranslate nohighlight">\(B\)</span>).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a>) – (mA, n) linear operator</p></li>
-<li><p><strong>B</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a>) – (mB, n) linear operator</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (mA*mB, n) linear operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>This implementation is <strong>matrix-free</strong> by leveraging properties of the Khatri-Rao product, i.e.  <span class="math notranslate nohighlight">\(A\)</span> and
-<span class="math notranslate nohighlight">\(B\)</span> need not be known explicitly.  In particular <span class="math notranslate nohighlight">\((A \circ B) x\)</span> and <span class="math notranslate nohighlight">\((A \circ B)^{*} x\)</span> are
-computed implicitly via the relation:</p>
-<div class="math notranslate nohighlight">
-\[\text{vec}(\mathbf{A}\text{diag}(\mathbf{b})\mathbf{C})
-=
-(\mathbf{C}^{T} \circ \mathbf{A}) \mathbf{b},\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathbf{A}\)</span>, <span class="math notranslate nohighlight">\(\mathbf{C}\)</span> are matrices, and <span class="math notranslate nohighlight">\(\mathbf{b}\)</span> is a vector.</p>
-<p>Note however that a matrix-free implementation of the Khatri-Rao product does not permit the same optimizations as a
-matrix-based implementation.  Thus the Khatri-Rao product as implemented here is only marginally more efficient than
-applying <a class="reference internal" href="#pyxu.operator.kron" title="pyxu.operator.kron"><code class="xref py py-func docutils literal notranslate"><span class="pre">kron()</span></code></a> and pruning its output.</p>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.IdentityOp">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">IdentityOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/base.html#IdentityOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.IdentityOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.OrthProjOp" title="pyxu.abc.operator.OrthProjOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">OrthProjOp</span></code></a></p>
-<p>Identity operator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.NullOp">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NullOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/base.html#NullOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NullOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
-<p>Null operator.</p>
-<p>This operator maps any input vector on the null vector.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.NullFunc">
-<span class="sig-name descname"><span class="pre">NullFunc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/base.html#NullFunc"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NullFunc" title="Link to this definition">#</a></dt>
-<dd><p>Null functional.</p>
-<p>This functional maps any input vector on the null scalar.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>dim</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.HomothetyOp">
-<span class="sig-name descname"><span class="pre">HomothetyOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cst</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/base.html#HomothetyOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.HomothetyOp" title="Link to this definition">#</a></dt>
-<dd><p>Scaling operator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>dim</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Dimension of the domain.</p></li>
-<li><p><strong>cst</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Scaling factor.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (dim, dim) scaling operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>This operator is not defined in terms of <a class="reference internal" href="#pyxu.operator.DiagonalOp" title="pyxu.operator.DiagonalOp"><code class="xref py py-func docutils literal notranslate"><span class="pre">DiagonalOp()</span></code></a> since it is array-backend-agnostic.</p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.DiagonalOp">
-<span class="sig-name descname"><span class="pre">DiagonalOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vec</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/base.html#DiagonalOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.DiagonalOp" title="Link to this definition">#</a></dt>
-<dd><p>Element-wise scaling operator.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p><a class="reference internal" href="#pyxu.operator.DiagonalOp" title="pyxu.operator.DiagonalOp"><code class="xref py py-func docutils literal notranslate"><span class="pre">DiagonalOp()</span></code></a> instances are <strong>not arraymodule-agnostic</strong>:
-they will only work with NDArrays belonging to the same array module as <code class="code docutils literal notranslate"><span class="pre">vec</span></code>.  Moreover, inner computations may
-cast input arrays when the precision of <code class="code docutils literal notranslate"><span class="pre">vec</span></code> does not match the user-requested precision.  If such a situation
-occurs, a warning is raised.</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>vec</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (N,) diagonal scale factors.</p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.Pad">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Pad</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pad_width</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/pad.html#Pad"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Pad" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
-<p>Multi-dimensional padding operator.</p>
-<p>This operator pads the input array in each dimension according to specified widths.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p>If inputs are D-dimensional, then some of the padding of later axes are calculated from padding of previous axes.</p></li>
-<li><p>The <em>adjoint</em> of the padding operator performs a cumulative summation over the original positions used to pad.
-Its effect is clear from its matrix form.  For example the matrix-form of <code class="docutils literal notranslate"><span class="pre">Pad(arg_shape=(3,),</span> <span class="pre">mode="wrap",</span>
-<span class="pre">pad_width=(1,</span> <span class="pre">1))</span></code> is:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{A}
-=
-\left[
-   \begin{array}{ccc}
-       0 &amp; 0 &amp; 1 \\
-       1 &amp; 0 &amp; 0 \\
-       0 &amp; 1 &amp; 0 \\
-       0 &amp; 0 &amp; 1 \\
-       1 &amp; 0 &amp; 0
-   \end{array}
-\right].\end{split}\]</div>
-<p>The adjoint of <span class="math notranslate nohighlight">\(\mathbf{A}\)</span> corresponds to its matrix transpose:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{A}^{\ast}
-=
-\left[
-    \begin{array}{ccccc}
-        0 &amp; 1 &amp; 0 &amp; 0 &amp; 1 \\
-        0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 \\
-        1 &amp; 0 &amp; 0 &amp; 1 &amp; 0
-    \end{array}
-\right].\end{split}\]</div>
-<p>This operation can be seen as a trimming (<span class="math notranslate nohighlight">\(\mathbf{T}\)</span>) plus a cumulative summation (<span class="math notranslate nohighlight">\(\mathbf{S}\)</span>):</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{A}^{\ast}
-=
-\mathbf{T} + \mathbf{S}
-=
-\left[
-   \begin{array}{ccccc}
-       0 &amp; 1 &amp; 0 &amp; 0 &amp; 0 \\
-       0 &amp; 0 &amp; 1 &amp; 0 &amp; 0 \\
-       0 &amp; 0 &amp; 0 &amp; 1 &amp; 0
-   \end{array}
-\right]
-+
-\left[
-   \begin{array}{ccccc}
-       0 &amp; 0 &amp; 0 &amp; 0 &amp; 1 \\
-       0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 \\
-       1 &amp; 0 &amp; 0 &amp; 0 &amp; 0
-   \end{array}
-\right],\end{split}\]</div>
-<p>where both <span class="math notranslate nohighlight">\(\mathbf{T}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{S}\)</span> are efficiently implemented in matrix-free form.</p>
-</li>
-<li><p>The Lipschitz constant of the multi-dimensional padding operator is upper-bounded by the product of Lipschitz
-constants of the uni-dimensional paddings applied per dimension, i.e.:</p>
-<div class="math notranslate nohighlight">
-\[L \le \prod_{i} L_{i}, \qquad i \in \{0, \dots, N-1\},\]</div>
-<p>where <span class="math notranslate nohighlight">\(L_{i}\)</span> depends on the boundary condition at the <span class="math notranslate nohighlight">\(i\)</span>-th axis.</p>
-<p><span class="math notranslate nohighlight">\(L_{i}^{2}\)</span> corresponds to the maximum singular value of the diagonal matrix</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{A}_{i}^{\ast} \mathbf{A}_{i}
-=
-\mathbf{T}_{i}^{\ast} \mathbf{T}_{i} + \mathbf{S}_{i}^{\ast} \mathbf{S}_{i}
-=
-\mathbf{I}_{N} + \mathbf{S}_{i}^{\ast} \mathbf{S}_{i}.\]</div>
-<ul>
-<li><p>In mode=”constant”, <span class="math notranslate nohighlight">\(\text{diag}(\mathbf{S}_{i}^{\ast} \mathbf{S}_{i}) = \mathbf{0}\)</span>, hence <span class="math notranslate nohighlight">\(L_{i} =
-1\)</span>.</p></li>
-<li><p>In mode=”edge”,</p>
-<div class="math notranslate nohighlight">
-\[\text{diag}(\mathbf{S}_{i}^{\ast} \mathbf{S}_{i})
-=
-\left[p_{lhs}, 0, \ldots, 0, p_{rhs} \right],\]</div>
-<p>hence <span class="math notranslate nohighlight">\(L_{i} = \sqrt{1 + \min(p_{lhs}, p_{rhs})}\)</span>.</p>
-</li>
-<li><p>In mode=”symmetric”, “wrap”, “reflect”, <span class="math notranslate nohighlight">\(\text{diag}(\mathbf{S}_{i}^{\ast} \mathbf{S}_{i})\)</span> equals (up to
-a mode-dependant permutation)</p>
-<div class="math notranslate nohighlight">
-\[\text{diag}(\mathbf{S}_{i}^{\ast} \mathbf{S}_{i})
-=
-\left[1, \ldots, 1, 0, \ldots, 0\right]
-+
-\left[0, \ldots, 0, 1, \ldots, 1\right],\]</div>
-<p>hence</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}L^{\text{wrap, symmetric}}_{i} = \sqrt{1 + \lceil\frac{p_{lhs} + p_{rhs}}{N}\rceil}, \\
-L^{\text{reflect}}_{i} = \sqrt{1 + \lceil\frac{p_{lhs} + p_{rhs}}{N-2}\rceil}.\end{split}\]</div>
-</li>
-</ul>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>pad_width</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em><em>]</em>) – </p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.operator.Pad.WidthSpec">
-<span class="sig-name descname"><span class="pre">WidthSpec</span></span><a class="headerlink" href="#pyxu.operator.Pad.WidthSpec" title="Link to this definition">#</a></dt>
-<dd><p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>], <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>]]]</p>
-</dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.operator.Pad.ModeSpec">
-<span class="sig-name descname"><span class="pre">ModeSpec</span></span><a class="headerlink" href="#pyxu.operator.Pad.ModeSpec" title="Link to this definition">#</a></dt>
-<dd><p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>]]</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.Pad.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pad_width</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/pad.html#Pad.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Pad.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>pad_width</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">WidthSpec</span></code>) – <p>Number of values padded to the edges of each axis.
-Multiple forms are accepted:</p>
-<ul>
-<li><p><code class="docutils literal notranslate"><span class="pre">int</span></code>: pad each dimension’s head/tail by <code class="code docutils literal notranslate"><span class="pre">pad_width</span></code>.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuple[int,</span> <span class="pre">...]</span></code>: pad dimension[k]’s head/tail by <code class="code docutils literal notranslate"><span class="pre">pad_width[k]</span></code>.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuple[tuple[int,</span> <span class="pre">int],</span> <span class="pre">...]</span></code>: pad dimension[k]’s head/tail by <code class="code docutils literal notranslate"><span class="pre">pad_width[k][0]</span></code> /
-<code class="code docutils literal notranslate"><span class="pre">pad_width[k][1]</span></code> respectively.</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a> ( str )) – <p>Padding mode.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (zero-padding)</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: pad dimension[k] using <code class="code docutils literal notranslate"><span class="pre">mode[k]</span></code>.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator._Stencil">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">_Stencil</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">kernel</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">center</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/stencil/_stencil.html#_Stencil"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator._Stencil" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
-<p>Multi-dimensional JIT-compiled stencil. (Low-level function.)</p>
-<p>This low-level class creates a gu-vectorized stencil applicable on multiple inputs simultaneously.</p>
-<p>Create instances via factory method <a class="reference internal" href="#pyxu.operator._Stencil.init" title="pyxu.operator._Stencil.init"><code class="xref py py-meth docutils literal notranslate"><span class="pre">init()</span></code></a>.</p>
-<p class="rubric">Example</p>
-<p>Correlate a stack of images <code class="code docutils literal notranslate"><span class="pre">A</span></code> with a (3, 3) kernel such that:</p>
-<div class="math notranslate nohighlight">
-\[B[n, m] = A[n-1, m] + A[n, m-1] + A[n, m+1] + A[n+1, m]\]</div>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator.linop.stencil._stencil</span> <span class="kn">import</span> <span class="n">_Stencil</span>
-
-<span class="c1"># create the stencil</span>
-<span class="n">kernel</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
-                   <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
-                   <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
-<span class="n">center</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="n">stencil</span> <span class="o">=</span> <span class="n">_Stencil</span><span class="o">.</span><span class="n">init</span><span class="p">(</span><span class="n">kernel</span><span class="p">,</span> <span class="n">center</span><span class="p">)</span>
-
-<span class="c1"># apply it to the data</span>
-<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">()</span>
-<span class="n">A</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="mi">30</span><span class="p">))</span>  <span class="c1"># 24 images of size (30, 30)</span>
-<span class="n">B</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
-<span class="n">stencil</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">)</span>  <span class="c1"># (2, 3, 4, 30, 30)</span>
-</pre></div>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>kernel</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>) – </p></li>
-<li><p><strong>center</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.operator._Stencil.IndexSpec">
-<span class="sig-name descname"><span class="pre">IndexSpec</span></span><a class="headerlink" href="#pyxu.operator._Stencil.IndexSpec" title="Link to this definition">#</a></dt>
-<dd><p>alias of <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integral</span></code></a>]</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator._Stencil.init">
-<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">init</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">kernel</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">center</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/stencil/_stencil.html#_Stencil.init"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator._Stencil.init" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>kernel</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – <p>(k_1, …, k_D) kernel coefficients.</p>
-<p>Only float32/64 kernels are supported.</p>
-</p></li>
-<li><p><strong>center</strong> (<a class="reference internal" href="#pyxu.operator._Stencil.IndexSpec" title="pyxu.operator._Stencil.IndexSpec"><code class="xref py py-class docutils literal notranslate"><span class="pre">IndexSpec</span></code></a>) – (D,) index of the kernel’s center.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>st</strong> – Rank-D stencil.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="#pyxu.operator._Stencil" title="pyxu.operator.linop.stencil._stencil._Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">_Stencil</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator._Stencil.apply">
-<span class="sig-name descname"><span class="pre">apply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/stencil/_stencil.html#_Stencil.apply"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator._Stencil.apply" title="Link to this definition">#</a></dt>
-<dd><p>Evaluate stencil on multiple inputs.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, N_1, …, N_D) data to process.</p></li>
-<li><p><strong>out</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, N_1, …, N_D) array to which outputs are written.</p></li>
-<li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>Extra kwargs to configure <code class="code docutils literal notranslate"><span class="pre">f_jit()</span></code>, the Dispatcher instance created by Numba.</p>
-<p>Only relevant for GPU stencils, with values:</p>
-<ul>
-<li><p>blockspergrid: int</p></li>
-<li><p>threadsperblock: int</p></li>
-</ul>
-<p>Default values are chosen if unspecified.</p>
-</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>out</strong> – (…, N_1, …, N_D) outputs.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<ul>
-<li><p><code class="code docutils literal notranslate"><span class="pre">arr</span></code> and <code class="code docutils literal notranslate"><span class="pre">out</span></code> must have the same type/dtype as the kernel used during instantiation.</p></li>
-<li><p>Index regions in <code class="code docutils literal notranslate"><span class="pre">out</span></code> where the stencil is not fully supported are set to 0.</p></li>
-<li><p><a class="reference internal" href="#pyxu.operator._Stencil.apply" title="pyxu.operator._Stencil.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> may raise <code class="docutils literal notranslate"><span class="pre">CUDA_ERROR_LAUNCH_OUT_OF_RESOURCES</span></code> when the number of
-GPU registers required exceeds resource limits.  There are 2 solutions to this problem:</p>
-<blockquote>
-<div><ol class="arabic simple">
-<li><p>Pass the <code class="code docutils literal notranslate"><span class="pre">max_registers</span></code> kwarg to f_jit()’s decorator; or</p></li>
-<li><p><a class="reference external" href="https://stackoverflow.com/a/68659008">Limit the number of threads per block</a>.</p></li>
-</ol>
-</div></blockquote>
-<ol class="arabic simple">
-<li><p>must be set at compile time; it is thus left unbounded.</p></li>
-<li><p>is accessible through .apply(**kwargs).</p></li>
-</ol>
-</li>
-</ul>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.Stencil">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Stencil</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kernel</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">center</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/stencil/stencil.html#Stencil"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Stencil" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.SquareOp" title="pyxu.abc.operator.SquareOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareOp</span></code></a></p>
-<p>Multi-dimensional JIT-compiled stencil.</p>
-<p>Stencils are a common computational pattern in which array elements are updated according to some fixed pattern
-called the <em>stencil kernel</em>.  Notable examples include multi-dimensional convolutions, correlations and finite
-differences.  (See Notes for a definition.)</p>
-<p>Stencils can be evaluated efficiently on CPU/GPU architectures.</p>
-<p>Several boundary conditions are supported.  Moreover boundary conditions may differ per axis.</p>
-<p class="rubric">Implementation Notes</p>
-<ul class="simple">
-<li><p>Numba (and its <code class="docutils literal notranslate"><span class="pre">@stencil</span></code> decorator) is used behind the scenes to compile efficient machine code from a stencil
-kernel specification.  This has 2 consequences:</p>
-<ul>
-<li><dl class="simple">
-<dt><a class="reference internal" href="#pyxu.operator.Stencil" title="pyxu.operator.Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stencil</span></code></a> instances are <strong>not arraymodule-agnostic</strong>: they will only work with NDArrays</dt><dd><p>belonging to the same array module as <code class="code docutils literal notranslate"><span class="pre">kernel</span></code>.</p>
-</dd>
-</dl>
-</li>
-<li><p>Compiled stencils are not <strong>precision-agnostic</strong>: they will only work on NDArrays with the same dtype as
-<code class="code docutils literal notranslate"><span class="pre">kernel</span></code>.  A warning is emitted if inputs must be cast to the kernel dtype.</p></li>
-</ul>
-</li>
-<li><p>Stencil kernels can be specified in two forms: (See <a class="reference internal" href="#pyxu.operator.Stencil.__init__" title="pyxu.operator.Stencil.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__init__()</span></code></a> for details.)</p>
-<ul>
-<li><p>A single non-separable <span class="math notranslate nohighlight">\(D\)</span>-dimensional kernel <span class="math notranslate nohighlight">\(k[i_{1},\ldots,i_{D}]\)</span> of shape
-<span class="math notranslate nohighlight">\((K_{1},\ldots,K_{D})\)</span>.</p></li>
-<li><p>A sequence of separable <span class="math notranslate nohighlight">\(1\)</span>-dimensional kernel(s) <span class="math notranslate nohighlight">\(k_{d}[i]\)</span> of shapes
-<span class="math notranslate nohighlight">\((K_{1},),\ldots,(K_{D},)\)</span> such that <span class="math notranslate nohighlight">\(k[i_{1},\ldots,i_{D}] = \Pi_{d=1}^{D} k_{d}[i_{d}]\)</span>.</p></li>
-</ul>
-</li>
-</ul>
-<p class="rubric">Mathematical Notes</p>
-<p>Given a <span class="math notranslate nohighlight">\(D\)</span>-dimensional array <span class="math notranslate nohighlight">\(x\in\mathbb{R}^{N_1\times\cdots\times N_D}\)</span> and kernel
-<span class="math notranslate nohighlight">\(k\in\mathbb{R}^{K_1\times\cdots\times K_D}\)</span> with center <span class="math notranslate nohighlight">\((c_1, \ldots, c_D)\)</span>, the output of the stencil
-operator is an array <span class="math notranslate nohighlight">\(y\in\mathbb{R}^{N_1\times\cdots\times N_D}\)</span> given by:</p>
-<div class="math notranslate nohighlight">
-\[y[i_{1},\ldots,i_{D}]
-=
-\sum_{q_{1},\ldots,q_{D}=0}^{K_{1},\ldots,K_{D}}
-x[i_{1} - c_{1} + q_{1},\ldots,i_{D} - c_{D} + q_{D}]
-\,\cdot\,
-k[q_{1},\ldots,q_{D}].\]</div>
-<p>This corresponds to a <em>correlation</em> with a shifted version of the kernel <span class="math notranslate nohighlight">\(k\)</span>.</p>
-<p>Numba stencils assume summation terms involving out-of-bound indices of <span class="math notranslate nohighlight">\(x\)</span> are set to zero.
-<a class="reference internal" href="#pyxu.operator.Stencil" title="pyxu.operator.Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stencil</span></code></a> lifts this constraint by extending the stencil to boundary values via pre-padding
-and post-trimming.  Concretely, any stencil operator <span class="math notranslate nohighlight">\(S\)</span> instantiated with <a class="reference internal" href="#pyxu.operator.Stencil" title="pyxu.operator.Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stencil</span></code></a>
-can be written as the composition <span class="math notranslate nohighlight">\(S = TS_0P\)</span>, where <span class="math notranslate nohighlight">\((T, S_0, P)\)</span> are trimming, stencil with
-zero-padding conditions, and padding operators respectively.  This construct allows
-<a class="reference internal" href="#pyxu.operator.Stencil" title="pyxu.operator.Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stencil</span></code></a> to handle complex boundary conditions under which <span class="math notranslate nohighlight">\(S\)</span> <em>may not be a proper
-stencil</em> (i.e., varying kernel) but can still be implemented efficiently via a proper stencil upon appropriate
-trimming/padding.</p>
-<p>For example consider the decomposition of the following (improper) stencil operator:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">S</span> <span class="o">=</span> <span class="n">Stencil</span><span class="p">(</span>
-<span class="gp">... </span>     <span class="n">arg_shape</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,),</span>
-<span class="gp">... </span>     <span class="n">kernel</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">3</span><span class="p">],</span>
-<span class="gp">... </span>     <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,),</span>
-<span class="gp">... </span>     <span class="n">mode</span><span class="o">=</span><span class="s2">"reflect"</span><span class="p">,</span>
-<span class="gp">... </span><span class="p">)</span>
-
-<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span><span class="o">.</span><span class="n">asarray</span><span class="p">()</span>
-<span class="go">[[-3   2   1   0   0]</span>
-<span class="go"> [ 2  -2   0   0   0]</span>
-<span class="go"> [ 1   2  -3   0   0]</span>
-<span class="go"> [ 0   1   2  -3   0]</span>
-<span class="go"> [ 0   0   1   2  -3]] # Improper stencil (kernel varies across rows)</span>
-<span class="go">=</span>
-<span class="go">[[0  0  1  0  0  0  0  0  0]</span>
-<span class="go"> [0  0  0  1  0  0  0  0  0]</span>
-<span class="go"> [0  0  0  0  1  0  0  0  0]</span>
-<span class="go"> [0  0  0  0  0  1  0  0  0]</span>
-<span class="go"> [0  0  0  0  0  0  1  0  0]]  # Trimming</span>
-<span class="go">@</span>
-<span class="go">[[-3   0   0   0   0   0   0   0   0]</span>
-<span class="go"> [ 2  -3   0   0   0   0   0   0   0]</span>
-<span class="go"> [ 1   2  -3   0   0   0   0   0   0]</span>
-<span class="go"> [ 0   1   2  -3   0   0   0   0   0]</span>
-<span class="go"> [ 0   0   1   2  -3   0   0   0   0]</span>
-<span class="go"> [ 0   0   0   1   2  -3   0   0   0]</span>
-<span class="go"> [ 0   0   0   0   1   2  -3   0   0]</span>
-<span class="go"> [ 0   0   0   0   0   1   2  -3   0]</span>
-<span class="go"> [ 0   0   0   0   0   0   1   2  -3]]  # Proper stencil (Toeplitz structure)</span>
-<span class="go">@</span>
-<span class="go">[[0  0  1  0  0]</span>
-<span class="go"> [0  1  0  0  0]</span>
-<span class="go"> [1  0  0  0  0]</span>
-<span class="go"> [0  1  0  0  0]</span>
-<span class="go"> [0  0  1  0  0]</span>
-<span class="go"> [0  0  0  1  0]</span>
-<span class="go"> [0  0  0  0  1]</span>
-<span class="go"> [0  0  0  1  0]</span>
-<span class="go"> [0  0  1  0  0]]  # Padding with reflect mode.</span>
-</pre></div>
-</div>
-<p>Note that the adjoint of a stencil operator may not necessarily be a stencil operator, or the associated center and
-boundary conditions may be hard to predict.  For example, the adjoint of the stencil operator defined above is given
-by:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">S</span><span class="o">.</span><span class="n">T</span><span class="o">.</span><span class="n">asarray</span><span class="p">()</span>
-<span class="go">[[-3   2   1   0   0],</span>
-<span class="go"> [ 2  -2   2   1   0],</span>
-<span class="go"> [ 1   0  -3   2   1],</span>
-<span class="go"> [ 0   0   0  -3   2],</span>
-<span class="go"> [ 0   0   0   0  -3]]</span>
-</pre></div>
-</div>
-<p>which resembles a stencil with time-reversed kernel, but with weird (if not improper) boundary conditions.  This can
-also be seen from the fact that <span class="math notranslate nohighlight">\(S^\ast = P^\ast S_0^\ast T^\ast = P^\ast S_0^\ast P_0,\)</span> and <span class="math notranslate nohighlight">\(P^\ast\)</span> is
-in general not a trimming operator.  (See <a class="reference internal" href="#pyxu.operator.Pad" title="pyxu.operator.Pad"><code class="xref py py-class docutils literal notranslate"><span class="pre">Pad</span></code></a>.)</p>
-<p>The same holds for gram/cogram operators.  Consider indeed the following order-1 backward finite-difference operator
-with zero-padding:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">S</span> <span class="o">=</span> <span class="n">Stencil</span><span class="p">(</span>
-<span class="gp">... </span>     <span class="n">arg_shape</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,),</span>
-<span class="gp">... </span>     <span class="n">kernel</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
-<span class="gp">... </span>     <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,),</span>
-<span class="gp">... </span>     <span class="n">mode</span><span class="o">=</span><span class="s1">'constant'</span><span class="p">,</span>
-<span class="gp">... </span><span class="p">)</span>
-
-<span class="gp">&gt;&gt;&gt; </span><span class="n">S</span><span class="o">.</span><span class="n">gram</span><span class="p">()</span><span class="o">.</span><span class="n">asarray</span><span class="p">()</span>
-<span class="go">[[ 1  -1   0   0   0]</span>
-<span class="go"> [-1   2  -1   0   0]</span>
-<span class="go"> [ 0  -1   2  -1   0]</span>
-<span class="go"> [ 0   0  -1   2  -1]</span>
-<span class="go"> [ 0   0   0  -1   2]]</span>
-</pre></div>
-</div>
-<p>We observe that the Gram differs from the order 2 centered finite-difference operator.  (Reduced-order derivative on
-one side.)</p>
-<p class="rubric">Example</p>
-<ul>
-<li><p><strong>Moving average of a 1D signal</strong></p>
-<p>Let <span class="math notranslate nohighlight">\(x[n]\)</span> denote a 1D signal.  The weighted moving average</p>
-<div class="math notranslate nohighlight">
-\[y[n] = x[n-2] + 2 x[n-1] + 3 x[n]\]</div>
-<p>can be viewed as the output of the 3-point stencil of kernel <span class="math notranslate nohighlight">\(k = [1, 2, 3]\)</span>.</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">Stencil</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>  <span class="c1"># [0  1  2  3  4  5  6  7  8  9]</span>
-
-<span class="n">op</span> <span class="o">=</span> <span class="n">Stencil</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
-    <span class="n">kernel</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]),</span>
-    <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,),</span>  <span class="c1"># k[2] applies on x[n]</span>
-<span class="p">)</span>
-
-<span class="n">y</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># [0  3  8  14  20  26  32  38  44  50]</span>
-</pre></div>
-</div>
-</li>
-<li><p><strong>Non-seperable image filtering</strong></p>
-<p>Let <span class="math notranslate nohighlight">\(x[n, m]\)</span> denote a 2D image.  The blurred image</p>
-<div class="math notranslate nohighlight">
-\[y[n, m] = 2 x[n-1,m-1] + 3 x[n-1,m+1] + 4 x[n+1,m-1] + 5 x[n+1,m+1]\]</div>
-<p>can be viewed as the output of the 9-point stencil</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}k =
-\left[
-\begin{array}{ccc}
-   2 &amp; 0 &amp; 3 \\
-   0 &amp; 0 &amp; 0 \\
-   4 &amp; 0 &amp; 5
-\end{array}
-\right].\end{split}\]</div>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">Stencil</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">64</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span>  <span class="c1"># square image</span>
-<span class="c1"># [[ 0   1   2   3   4   5   6   7]</span>
-<span class="c1">#  [ 8   9  10  11  12  13  14  15]</span>
-<span class="c1">#  [16  17  18  19  20  21  22  23]</span>
-<span class="c1">#  [24  25  26  27  28  29  30  31]</span>
-<span class="c1">#  [32  33  34  35  36  37  38  39]</span>
-<span class="c1">#  [40  41  42  43  44  45  46  47]</span>
-<span class="c1">#  [48  49  50  51  52  53  54  55]</span>
-<span class="c1">#  [56  57  58  59  60  61  62  63]]</span>
-
-<span class="n">op</span> <span class="o">=</span> <span class="n">Stencil</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
-    <span class="n">kernel</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span>
-        <span class="p">[[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span>
-         <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
-         <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">]]),</span>
-    <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span>  <span class="c1"># k[1, 1] applies on x[n, m]</span>
-<span class="p">)</span>
-
-<span class="n">y</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span>
-<span class="c1"># [[ 45   82   91  100  109  118  127   56 ]</span>
-<span class="c1">#  [ 88  160  174  188  202  216  230  100 ]</span>
-<span class="c1">#  [152  272  286  300  314  328  342  148 ]</span>
-<span class="c1">#  [216  384  398  412  426  440  454  196 ]</span>
-<span class="c1">#  [280  496  510  524  538  552  566  244 ]</span>
-<span class="c1">#  [344  608  622  636  650  664  678  292 ]</span>
-<span class="c1">#  [408  720  734  748  762  776  790  340 ]</span>
-<span class="c1">#  [147  246  251  256  261  266  271  108 ]]</span>
-</pre></div>
-</div>
-</li>
-<li><p><strong>Seperable image filtering</strong></p>
-<p>Let <span class="math notranslate nohighlight">\(x[n, m]\)</span> denote a 2D image.  The warped image</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\begin{align*}
-    y[n, m] = &amp; +  4 x[n-1,m-1] +  5 x[n-1,m] +  6 x[n-1,m+1] \\
-              &amp; +  8 x[n  ,m-1] + 10 x[n  ,m] + 12 x[n  ,m+1] \\
-              &amp; + 12 x[n+1,m-1] + 15 x[n+1,m] + 18 x[n+1,m+1]
-\end{align*}\end{split}\]</div>
-<p>can be viewed as the output of the 9-point stencil</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}k_{2D} =
-\left[
-\begin{array}{ccc}
-    4 &amp;  5 &amp;  6 \\
-    8 &amp; 10 &amp; 12 \\
-   12 &amp; 15 &amp; 18 \\
-\end{array}
-\right].\end{split}\]</div>
-<p>Notice however that <span class="math notranslate nohighlight">\(y[n, m]\)</span> can be implemented more efficiently by factoring the 9-point stencil as a
-cascade of two 3-point stencils:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}k_{2D}
-= k_{1} k_{2}^{T}
-= \left[
-\begin{array}{c}
-   1 \\ 2 \\ 3
-\end{array}
-\right]
-\left[
-\begin{array}{c}
-   4 &amp; 5 &amp; 6
-\end{array}
-\right].\end{split}\]</div>
-<p>Seperable stencils are supported and should be preferred when applicable.</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">Stencil</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">64</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span>  <span class="c1"># square image</span>
-<span class="c1"># [[ 0   1   2   3   4   5   6   7]</span>
-<span class="c1">#  [ 8   9  10  11  12  13  14  15]</span>
-<span class="c1">#  [16  17  18  19  20  21  22  23]</span>
-<span class="c1">#  [24  25  26  27  28  29  30  31]</span>
-<span class="c1">#  [32  33  34  35  36  37  38  39]</span>
-<span class="c1">#  [40  41  42  43  44  45  46  47]</span>
-<span class="c1">#  [48  49  50  51  52  53  54  55]</span>
-<span class="c1">#  [56  57  58  59  60  61  62  63]]</span>
-
-<span class="n">op_2D</span> <span class="o">=</span> <span class="n">Stencil</span><span class="p">(</span>  <span class="c1"># using non-seperable kernel</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
-    <span class="n">kernel</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span>
-        <span class="p">[[</span> <span class="mi">4</span><span class="p">,</span>  <span class="mi">5</span><span class="p">,</span>  <span class="mi">6</span><span class="p">],</span>
-         <span class="p">[</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">12</span><span class="p">],</span>
-         <span class="p">[</span><span class="mi">12</span><span class="p">,</span> <span class="mi">15</span><span class="p">,</span> <span class="mi">18</span><span class="p">]]),</span>
-    <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span>  <span class="c1"># k[1, 1] applies on x[n, m]</span>
-<span class="p">)</span>
-<span class="n">op_sep</span> <span class="o">=</span> <span class="n">Stencil</span><span class="p">(</span>  <span class="c1"># using seperable kernels</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
-    <span class="n">kernel</span><span class="o">=</span><span class="p">[</span>
-        <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]),</span>  <span class="c1"># k1: stencil along 1st axis</span>
-        <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">]),</span>  <span class="c1"># k2: stencil along 2nd axis</span>
-    <span class="p">],</span>
-    <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span>  <span class="c1"># k1[1] * k2[1] applies on x[n, m]</span>
-<span class="p">)</span>
-
-<span class="n">y_2D</span> <span class="o">=</span> <span class="n">op_2D</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span>
-<span class="n">y_sep</span> <span class="o">=</span> <span class="n">op_sep</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span>  <span class="c1"># np.allclose(y_2D, y_sep) -&gt; True</span>
-<span class="c1"># [[ 294   445   520   595   670   745   820   511 ]</span>
-<span class="c1">#  [ 740  1062  1152  1242  1332  1422  1512   930 ]</span>
-<span class="c1">#  [1268  1782  1872  1962  2052  2142  2232  1362 ]</span>
-<span class="c1">#  [1796  2502  2592  2682  2772  2862  2952  1794 ]</span>
-<span class="c1">#  [2324  3222  3312  3402  3492  3582  3672  2226 ]</span>
-<span class="c1">#  [2852  3942  4032  4122  4212  4302  4392  2658 ]</span>
-<span class="c1">#  [3380  4662  4752  4842  4932  5022  5112  3090 ]</span>
-<span class="c1">#  [1778  2451  2496  2541  2586  2631  2676  1617 ]]</span>
-</pre></div>
-</div>
-</li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Convolve" title="pyxu.operator.Convolve"><code class="xref py py-class docutils literal notranslate"><span class="pre">Convolve</span></code></a>, <a class="reference internal" href="#pyxu.operator._Stencil" title="pyxu.operator._Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">_Stencil</span></code></a></p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>kernel</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
-<li><p><strong>center</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.operator.Stencil.KernelSpec">
-<span class="sig-name descname"><span class="pre">KernelSpec</span></span><a class="headerlink" href="#pyxu.operator.Stencil.KernelSpec" title="Link to this definition">#</a></dt>
-<dd><p>alias of <a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Union" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Union</span></code></a>[<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sequence</span></code></a>[<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NDArray</span></code></a>]]</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.Stencil.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kernel</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">center</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/stencil/stencil.html#Stencil.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Stencil.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the rank-<span class="math notranslate nohighlight">\(D\)</span> input array.</p></li>
-<li><p><strong>kernel</strong> (<a class="reference internal" href="#pyxu.operator.Stencil.KernelSpec" title="pyxu.operator.Stencil.KernelSpec"><code class="xref py py-class docutils literal notranslate"><span class="pre">KernelSpec</span></code></a>) – <p>Stencil coefficients.  Two forms are accepted:</p>
-<ul>
-<li><p>NDArray of rank-<span class="math notranslate nohighlight">\(D\)</span>: denotes a non-seperable stencil.</p></li>
-<li><p>tuple[NDArray_1, …, NDArray_D]: a sequence of 1D stencils such that dimension[k] is filtered by stencil
-<code class="code docutils literal notranslate"><span class="pre">kernel[k]</span></code>, that is:</p>
-<div class="math notranslate nohighlight">
-\[k = k_1\otimes \cdots\otimes k_D,\]</div>
-<p>or in Python: <code class="docutils literal notranslate"><span class="pre">k</span> <span class="pre">=</span> <span class="pre">functools.reduce(numpy.multiply.outer,</span> <span class="pre">kernel)</span></code>.</p>
-</li>
-</ul>
-</p></li>
-<li><p><strong>center</strong> (<a class="reference internal" href="#pyxu.operator._Stencil.IndexSpec" title="pyxu.operator._Stencil.IndexSpec"><code class="xref py py-class docutils literal notranslate"><span class="pre">IndexSpec</span></code></a>) – <p>(i_1, …, i_D) index of the stencil’s center.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">center</span></code> defines how a kernel is overlaid on inputs to produce outputs.</p>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a> ( str )) – <p>Boundary conditions.  Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (zero-padding)</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: dimension[k] uses <code class="code docutils literal notranslate"><span class="pre">mode[k]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.Stencil.configure_dispatcher">
-<span class="sig-name descname"><span class="pre">configure_dispatcher</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/stencil/stencil.html#Stencil.configure_dispatcher"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Stencil.configure_dispatcher" title="Link to this definition">#</a></dt>
-<dd><p>(Only applies if <code class="code docutils literal notranslate"><span class="pre">kernel</span></code> is a CuPy array.)</p>
-<p>Configure stencil Dispatcher.</p>
-<p>See <a class="reference internal" href="#pyxu.operator._Stencil.apply" title="pyxu.operator._Stencil.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> for accepted options.</p>
-<p class="rubric">Example</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">cupy</span> <span class="k">as</span> <span class="nn">cp</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">Stencil</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">cp</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
-
-<span class="n">op</span> <span class="o">=</span> <span class="n">Stencil</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
-    <span class="n">kernel</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]),</span>
-    <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,),</span>
-<span class="p">)</span>
-
-<span class="n">y</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># uses default threadsperblock/blockspergrid values</span>
-
-<span class="n">op</span><span class="o">.</span><span class="n">configure_dispatcher</span><span class="p">(</span>
-    <span class="n">threadsperblock</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
-    <span class="n">blockspergrid</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
-<span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># supplied values used instead</span>
-</pre></div>
-</div>
-</dd></dl>
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.operator.Stencil.kernel">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">kernel</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><span class="pre">NDArray</span></a><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><span class="pre">Sequence</span></a><span class="p"><span class="pre">[</span></span><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><span class="pre">NDArray</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#pyxu.operator.Stencil.kernel" title="Link to this definition">#</a></dt>
-<dd><p>Stencil kernel coefficients.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><p><strong>kern</strong> – Stencil coefficients.</p>
-<p>If the kernel is non-seperable, a single array is returned.
-Otherwise <span class="math notranslate nohighlight">\(D\)</span> arrays are returned, one per axis.</p>
-</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="#pyxu.operator.Stencil.KernelSpec" title="pyxu.operator.Stencil.KernelSpec"><code class="xref py py-class docutils literal notranslate"><span class="pre">KernelSpec</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.operator.Stencil.center">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">center</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><span class="pre">Sequence</span></a><span class="p"><span class="pre">[</span></span><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><span class="pre">Integral</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#pyxu.operator.Stencil.center" title="Link to this definition">#</a></dt>
-<dd><p>Stencil central position.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>ctr</strong> – Stencil central position.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="#pyxu.operator._Stencil.IndexSpec" title="pyxu.operator._Stencil.IndexSpec"><code class="xref py py-class docutils literal notranslate"><span class="pre">IndexSpec</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py property">
-<dt class="sig sig-object py" id="pyxu.operator.Stencil.relative_indices">
-<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">relative_indices</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><span class="pre">Sequence</span></a><span class="p"><span class="pre">[</span></span><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><span class="pre">NDArray</span></a><span class="p"><span class="pre">]</span></span></em><a class="headerlink" href="#pyxu.operator.Stencil.relative_indices" title="Link to this definition">#</a></dt>
-<dd><p>Relative indices of the stencil.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>r_idx</strong> – Relative indices of the stencil’s kernel in each dimension.</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a> ( <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a> )</p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">S</span> <span class="o">=</span> <span class="n">Stencil</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">9</span><span class="p">),</span>
-    <span class="n">kernel</span><span class="o">=</span><span class="p">[</span>
-        <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span>
-        <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
-        <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
-    <span class="p">],</span>
-    <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span>
-<span class="p">)</span>
-<span class="n">S</span><span class="o">.</span><span class="n">relative_indices</span>  <span class="c1"># [array([-1,  0]), array([0, 1, 2]), array([-3, -2, -1,  0])]</span>
-</pre></div>
-</div>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.Stencil.visualize">
-<span class="sig-name descname"><span class="pre">visualize</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/stencil/stencil.html#Stencil.visualize"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Stencil.visualize" title="Link to this definition">#</a></dt>
-<dd><p>Show the <span class="math notranslate nohighlight">\(D\)</span>-dimensional stencil kernel.</p>
-<p>The stencil’s center is identified by surrounding parentheses.</p>
-<p class="rubric">Example</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">Stencil</span>
-
-<span class="n">S</span> <span class="o">=</span> <span class="n">Stencil</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">),</span>
-    <span class="n">kernel</span><span class="o">=</span><span class="p">[</span>
-        <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
-        <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
-    <span class="p">],</span>
-    <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span>
-<span class="p">)</span>
-<span class="nb">print</span><span class="p">(</span><span class="n">S</span><span class="o">.</span><span class="n">visualize</span><span class="p">())</span>  <span class="c1"># [[6.0 -3.0  9.0  3.0]</span>
-                      <span class="c1">#  [4.0 -2.0 (6.0) 2.0]</span>
-                      <span class="c1">#  [2.0 -1.0  3.0 1.0]]</span>
-</pre></div>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)">str</a></p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.operator.Correlate">
-<span class="sig-name descname"><span class="pre">Correlate</span></span><a class="headerlink" href="#pyxu.operator.Correlate" title="Link to this definition">#</a></dt>
-<dd><p>alias of <a class="reference internal" href="#pyxu.operator.Stencil" title="pyxu.operator.linop.stencil.stencil.Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stencil</span></code></a></p>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Convolve">
-<span class="sig-name descname"><span class="pre">Convolve</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kernel</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">center</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/stencil/stencil.html#Convolve"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Convolve" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional JIT-compiled convolution.</p>
-<p>Inputs are convolved with the given kernel.</p>
-<p class="rubric">Notes</p>
-<p>Given a <span class="math notranslate nohighlight">\(D\)</span>-dimensional array <span class="math notranslate nohighlight">\(x\in\mathbb{R}^{N_1\times\cdots\times N_D}\)</span> and kernel
-<span class="math notranslate nohighlight">\(k\in\mathbb{R}^{K_1\times\cdots\times K_D}\)</span> with center <span class="math notranslate nohighlight">\((c_1, \ldots, c_D)\)</span>, the output of the
-convolution operator is an array <span class="math notranslate nohighlight">\(y\in\mathbb{R}^{N_1\times\cdots\times N_D}\)</span> given by:</p>
-<div class="math notranslate nohighlight">
-\[y[i_{1},\ldots,i_{D}]
-=
-\sum_{q_{1},\ldots,q_{D}=0}^{K_{1},\ldots,K_{D}}
-x[i_{1} - q_{1} + c_{1},\ldots,i_{D} - q_{D} + c_{D}]
-\,\cdot\,
-k[q_{1},\ldots,q_{D}].\]</div>
-<p>The convolution is implemented via <a class="reference internal" href="#pyxu.operator.Stencil" title="pyxu.operator.Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stencil</span></code></a>.  To do so, the convolution kernel is
-transformed to the equivalent correlation kernel:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}y[i_{1},\ldots,i_{D}]
-=
-\sum_{q_{1},\ldots,q_{D}=0}^{K_{1},\ldots,K_{D}}
-&amp;x[i_{1} + q_{1} - (K_{1} - c_{1}),\ldots,i_{D} + q_{D} - (K_{D} - c_{D})] \\
-&amp;\cdot\,
-k[K_{1}-q_{1},\ldots,K_{D}-q_{D}].\end{split}\]</div>
-<p>This corresponds to a correlation with a flipped kernel and center.</p>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">from</span> <span class="nn">scipy.ndimage</span> <span class="kn">import</span> <span class="n">convolve</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">Convolve</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span>
-     <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
-     <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">4</span><span class="p">],</span>
-     <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">7</span><span class="p">],</span>
-     <span class="p">[</span><span class="mi">9</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
-<span class="p">])</span>
-<span class="n">k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span>
-     <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
-     <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
-     <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
-<span class="p">])</span>
-<span class="n">op</span> <span class="o">=</span> <span class="n">Convolve</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
-    <span class="n">kernel</span><span class="o">=</span><span class="n">k</span><span class="p">,</span>
-    <span class="n">center</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span>
-    <span class="n">mode</span><span class="o">=</span><span class="s2">"constant"</span><span class="p">,</span>
-<span class="p">)</span>
-
-<span class="n">y_op</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
-<span class="n">y_sp</span> <span class="o">=</span> <span class="n">convolve</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s2">"constant"</span><span class="p">,</span> <span class="n">origin</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>  <span class="c1"># np.allclose(y_op, y_sp) -&gt; True</span>
-<span class="c1"># [[11  10   7   4],</span>
-<span class="c1">#  [10   3  11  11],</span>
-<span class="c1">#  [15  12  14   7],</span>
-<span class="c1">#  [12   3   7   0]]</span>
-</pre></div>
-</div>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Stencil" title="pyxu.operator.Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stencil</span></code></a></p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>kernel</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
-<li><p><strong>center</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.FFT">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">FFT</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/fft.html#FFT"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.FFT" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
-<p>Multi-dimensional Discrete Fourier Transform (DFT) <span class="math notranslate nohighlight">\(A: \mathbb{C}^{N_{1} \times \cdots \times N_{D}} \to
-\mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span>.</p>
-<p>The FFT is defined as follows:</p>
-<div class="math notranslate nohighlight">
-\[(A \, \mathbf{x})[\mathbf{k}]
-=
-\sum_{\mathbf{n}} \mathbf{x}[\mathbf{n}]
-\exp\left[-j 2 \pi \langle \frac{\mathbf{n}}{\mathbf{N}}, \mathbf{k} \rangle \right],\]</div>
-<div class="math notranslate nohighlight">
-\[(A^{*} \, \hat{\mathbf{x}})[\mathbf{n}]
-=
-\sum_{\mathbf{k}} \hat{\mathbf{x}}[\mathbf{k}]
-\exp\left[j 2 \pi \langle \frac{\mathbf{n}}{\mathbf{N}}, \mathbf{k} \rangle \right],\]</div>
-<div class="math notranslate nohighlight">
-\[(\mathbf{x}, \, \hat{\mathbf{x}}) \in \mathbb{C}^{N_{1} \times \cdots \times N_{D}},
-\quad
-(\mathbf{n}, \, \mathbf{k}) \in \{0, \ldots, N_{1}-1\} \times \cdots \times \{0, \ldots, N_{D}-1\}.\]</div>
-<p>The DFT is taken over any number of axes by means of the Fast Fourier Transform algorithm (FFT).</p>
-<p class="rubric">Implementation Notes</p>
-<ul class="simple">
-<li><p>The CPU implementation uses <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/fft.html">SciPy’s FFT implementation</a>.</p></li>
-<li><p>The GPU implementation uses cuFFT via <a class="reference external" href="https://docs.cupy.dev/en/latest/reference/scipy_fft.html">CuPy</a>.</p></li>
-</ul>
-<p class="rubric">Examples</p>
-<ul>
-<li><p>1D DFT of a cosine pulse.</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">FFT</span>
-<span class="kn">import</span> <span class="nn">pyxu.util</span> <span class="k">as</span> <span class="nn">pxu</span>
-
-<span class="n">N</span> <span class="o">=</span> <span class="mi">10</span>
-<span class="n">op</span> <span class="o">=</span> <span class="n">FFT</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N</span><span class="p">,),</span>
-    <span class="n">real</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
-<span class="p">)</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="n">N</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">N</span><span class="p">))</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
-<span class="c1"># [0, N/2, 0, 0, 0, 0, 0, 0, 0, N/2]</span>
-
-<span class="n">z</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
-<span class="c1"># np.allclose(z, N * x) -&gt; True</span>
-</pre></div>
-</div>
-</li>
-<li><p>1D DFT of a complex exponential pulse.</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">FFT</span>
-<span class="kn">import</span> <span class="nn">pyxu.util</span> <span class="k">as</span> <span class="nn">pxu</span>
-
-<span class="n">N</span> <span class="o">=</span> <span class="mi">10</span>
-<span class="n">op</span> <span class="o">=</span> <span class="n">FFT</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N</span><span class="p">,),</span>
-    <span class="n">real</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>  <span class="c1"># complex-valued inputs</span>
-<span class="p">)</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="n">N</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">N</span><span class="p">))</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span>
-        <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span>
-            <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_real</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-        <span class="p">)</span>
-    <span class="p">)</span>
-<span class="c1"># [0, N, 0, 0, 0, 0, 0, 0, 0, 0]</span>
-
-<span class="n">z</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span>
-        <span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span>
-            <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span>
-                <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_real</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-            <span class="p">)</span>
-        <span class="p">)</span>
-    <span class="p">)</span>
-<span class="c1"># np.allclose(z, N * x) -&gt; True</span>
-</pre></div>
-</div>
-</li>
-<li><p>2D DFT of an image</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">FFT</span>
-<span class="kn">import</span> <span class="nn">pyxu.util</span> <span class="k">as</span> <span class="nn">pxu</span>
-
-<span class="n">N_h</span><span class="p">,</span> <span class="n">N_w</span> <span class="o">=</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">8</span>
-<span class="n">op</span> <span class="o">=</span> <span class="n">FFT</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_h</span><span class="p">,</span> <span class="n">N_w</span><span class="p">),</span>
-    <span class="n">real</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
-<span class="p">)</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span>  <span class="c1"># an image</span>
-    <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N_h</span><span class="o">//</span><span class="mi">2</span><span class="p">,</span> <span class="n">N_w</span><span class="o">//</span><span class="mi">2</span><span class="p">)),</span>
-    <span class="n">pad_width</span><span class="o">=</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="n">N_h</span><span class="o">//</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N_w</span><span class="o">//</span><span class="mi">2</span><span class="p">)),</span>
-<span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span>  <span class="c1"># sinc</span>
-        <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
-    <span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">N_h</span><span class="p">,</span> <span class="n">N_w</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span>
-        <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
-    <span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">N_h</span><span class="p">,</span> <span class="n">N_w</span><span class="p">)</span>
-<span class="c1"># np.allclose(z, (N_h * N_w) * x) -&gt; True</span>
-</pre></div>
-</div>
-</li>
-<li><p>1D DFT of an image’s rows</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">FFT</span>
-<span class="kn">import</span> <span class="nn">pyxu.util</span> <span class="k">as</span> <span class="nn">pxu</span>
-
-<span class="n">N_h</span><span class="p">,</span> <span class="n">N_w</span> <span class="o">=</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">8</span>
-<span class="n">op</span> <span class="o">=</span> <span class="n">FFT</span><span class="p">(</span>
-    <span class="n">arg_shape</span><span class="o">=</span><span class="p">(</span><span class="n">N_h</span><span class="p">,</span> <span class="n">N_w</span><span class="p">),</span>
-    <span class="n">axes</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span>
-    <span class="n">real</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
-<span class="p">)</span>
-
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span>  <span class="c1"># an image</span>
-    <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N_h</span><span class="o">//</span><span class="mi">2</span><span class="p">,</span> <span class="n">N_w</span><span class="o">//</span><span class="mi">2</span><span class="p">)),</span>
-    <span class="n">pad_width</span><span class="o">=</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="n">N_h</span><span class="o">//</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N_w</span><span class="o">//</span><span class="mi">2</span><span class="p">)),</span>
-<span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span>  <span class="c1"># sinc</span>
-        <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
-    <span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">N_h</span><span class="p">,</span> <span class="n">N_w</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span>
-        <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span>
-    <span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">N_h</span><span class="p">,</span> <span class="n">N_w</span><span class="p">)</span>
-<span class="c1"># np.allclose(z, N_w * x) -&gt; True</span>
-</pre></div>
-</div>
-</li>
-</ul>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>axes</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>real</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.FFT.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/fft.html#FFT.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.FFT.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – (N_1, …, N_D) shape of the input array <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_{1} \times \cdots \times
-N_{D}}\)</span> or <span class="math notranslate nohighlight">\(\mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span>.</p></li>
-<li><p><strong>axes</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayAxis" title="pyxu.info.ptype.NDArrayAxis"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayAxis</span></code></a>) – Axis or axes along which the DFT is performed.  The default, axes=None, will transform all dimensions of the
-input array.</p></li>
-<li><p><strong>real</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – <p>If <code class="docutils literal notranslate"><span class="pre">True</span></code>, assumes <a class="reference internal" href="#pyxu.operator.FFT.apply" title="pyxu.operator.FFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> takes (…, N.prod()) inputs in
-<span class="math notranslate nohighlight">\(\mathbb{R}^{N}\)</span>.</p>
-<p>If <code class="docutils literal notranslate"><span class="pre">False</span></code>, then <a class="reference internal" href="#pyxu.operator.FFT.apply" title="pyxu.operator.FFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> takes (…, 2N.prod()) inputs, i.e.
-<span class="math notranslate nohighlight">\(\mathbb{C}^{N}\)</span> vectors viewed as bijections with <span class="math notranslate nohighlight">\(\mathbb{R}^{2N}\)</span>.</p>
-</p></li>
-<li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>Extra kwargs passed to <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.fft.fftn.html#scipy.fft.fftn" title="(in SciPy v1.11.2)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.fft.fftn()</span></code></a> or <a class="reference external" href="https://docs.cupy.dev/en/latest/reference/generated/cupyx.scipy.fft.fftn.html#cupyx.scipy.fft.fftn" title="(in CuPy v13.0.0b1)"><code class="xref py py-func docutils literal notranslate"><span class="pre">cupyx.scipy.fft.fftn()</span></code></a>.</p>
-<p>Supported parameters for <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.fft.fftn.html#scipy.fft.fftn" title="(in SciPy v1.11.2)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.fft.fftn()</span></code></a> are:</p>
-<blockquote>
-<div><ul>
-<li><p>workers: int = 1</p></li>
-</ul>
-</div></blockquote>
-<p>Supported parameters for <a class="reference external" href="https://docs.cupy.dev/en/latest/reference/generated/cupyx.scipy.fft.fftn.html#cupyx.scipy.fft.fftn" title="(in CuPy v13.0.0b1)"><code class="xref py py-func docutils literal notranslate"><span class="pre">cupyx.scipy.fft.fftn()</span></code></a> are:</p>
-<blockquote>
-<div><ul>
-<li><p>NOT SUPPORTED FOR NOW</p></li>
-</ul>
-</div></blockquote>
-<p>Default values are chosen if unspecified.</p>
-</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.FFT.apply">
-<span class="sig-name descname"><span class="pre">apply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/fft.html#FFT.apply"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.FFT.apply" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – <ul class="simple">
-<li><p>(…,  N.prod()) inputs <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_{1} \times \cdots \times N_{D}}\)</span>
-(<code class="docutils literal notranslate"><span class="pre">real=True</span></code>.)</p></li>
-<li><p>(…, 2N.prod()) inputs <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span> viewed as a
-real array. (See <a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
-</ul>
-</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>out</strong> – (…, 2N.prod()) outputs <span class="math notranslate nohighlight">\(\hat{\mathbf{x}} \in \mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span> viewed
-as a real array. (See <a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.FFT.adjoint">
-<span class="sig-name descname"><span class="pre">adjoint</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/fft.html#FFT.adjoint"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.FFT.adjoint" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, 2N.prod()) outputs <span class="math notranslate nohighlight">\(\hat{\mathbf{x}} \in \mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span> viewed
-as a real array. (See <a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><p><strong>out</strong> –</p>
-<ul class="simple">
-<li><p>(…,  N.prod()) inputs <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_{1} \times \cdots \times N_{D}}\)</span>
-(<code class="docutils literal notranslate"><span class="pre">real=True</span></code>.)</p></li>
-<li><p>(…, 2N.prod()) inputs <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span> viewed as a
-real array. (See <a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
-</ul>
-</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NUFFT</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
-<p>Non-Uniform Fast Fourier Transform (NUFFT) of Type 1/2/3 (for <span class="math notranslate nohighlight">\(d=\{1,2,3\}\)</span>).</p>
-<p>The <em>Non-Uniform Fast Fourier Transform (NUFFT)</em> generalizes the FFT to off-grid data.  There are three types of
-NUFFTs proposed in the literature:</p>
-<ul class="simple">
-<li><p>Type 1 (<em>non-uniform to uniform</em>),</p></li>
-<li><p>Type 2 (<em>uniform to non-uniform</em>),</p></li>
-<li><p>Type 3 (<em>non-uniform to non-uniform</em>).</p></li>
-</ul>
-<p>See the notes below, including <a class="reference internal" href="../references.html#finufft" id="id5"><span>[FINUFFT]</span></a>, for definitions of the various transforms and algorithmic details.</p>
-<p>The transforms should be instantiated via <a class="reference internal" href="#pyxu.operator.NUFFT.type1" title="pyxu.operator.NUFFT.type1"><code class="xref py py-meth docutils literal notranslate"><span class="pre">type1()</span></code></a>,
-<a class="reference internal" href="#pyxu.operator.NUFFT.type2" title="pyxu.operator.NUFFT.type2"><code class="xref py py-meth docutils literal notranslate"><span class="pre">type2()</span></code></a>, and <a class="reference internal" href="#pyxu.operator.NUFFT.type3" title="pyxu.operator.NUFFT.type3"><code class="xref py py-meth docutils literal notranslate"><span class="pre">type3()</span></code></a> respectively.  (See each method for
-usage examples.)</p>
-<p>The dimension of each transform is inferred from the dimensions of the input arguments, with support for
-<span class="math notranslate nohighlight">\(d=\{1,2,3\}\)</span>.</p>
-<p class="rubric">Notes</p>
-<p>We adopt here the same notational conventions as in <a class="reference internal" href="../references.html#finufft" id="id6"><span>[FINUFFT]</span></a>.</p>
-<ul>
-<li><p><strong>Mathematical Definition.</strong>
-Let <span class="math notranslate nohighlight">\(d\in\{1,2,3\}\)</span> and consider the mesh</p>
-<div class="math notranslate nohighlight">
-\[\mathcal{I}_{N_1,\ldots,N_d}
-=
-\mathcal{I}_{N_1} \times \cdots \times \mathcal{I}_{N_d}
-\subset \mathbb{Z}^d,\]</div>
-<p>where the mesh indices <span class="math notranslate nohighlight">\(\mathcal{I}_{N_i}\subset\mathbb{Z}\)</span> are given for each dimension <span class="math notranslate nohighlight">\(i=1,\dots,
-d\)</span> by:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathcal{I}_{N_i}
-=
-\begin{cases}
-    [[-N_i/2, N_i/2-1]], &amp; N_i\in 2\mathbb{N} \text{ (even)}, \\
-    [[-(N_i-1)/2, (N_i-1)/2]], &amp; N_i\in 2\mathbb{N}+1 \text{ (odd)}.
-\end{cases}\end{split}\]</div>
-<p>Then the NUFFT operators approximate, up to a requested relative accuracy <span class="math notranslate nohighlight">\(\varepsilon \geq 0\)</span>, <a class="footnote-reference brackets" href="#id13" id="id7" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> the
-following exponential sums:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\begin{align}
-    (1)\; &amp;u_{\mathbf{n}} = \sum_{j=1}^{M} w_{j} e^{\sigma i\langle \mathbf{n}, \mathbf{x}_{j} \rangle}, \quad &amp;\mathbf{n}\in \mathcal{I}_{N_1,\ldots, N_d},\qquad &amp;\text{Type 1 (non-uniform to uniform)}\\
-    (2)\; &amp;w_{j} = \sum_{\mathbf{n}\in\mathcal{I}_{N_1,\ldots, N_d}} u_{\mathbf{n}} e^{\sigma i\langle \mathbf{n}, \mathbf{x}_{j} \rangle }, \quad &amp;j=1,\ldots, M,\qquad  &amp;\text{Type 2 (uniform to non-uniform)}\\
-    (3)\; &amp;v_{k} = \sum_{j=1}^{M} w_{j} e^{\sigma i\langle \mathbf{z}_k, \mathbf{x}_{j} \rangle }, \quad &amp;k=1,\ldots, N, \qquad &amp;\text{Type 3 (non-uniform to non-uniform)}
-\end{align}\end{split}\]</div>
-<p>where <span class="math notranslate nohighlight">\(\sigma \in \{+1, -1\}\)</span> defines the sign of the transform and <span class="math notranslate nohighlight">\(u_{\mathbf{n}}, v_{k}, w_{j}\in
-\mathbb{C}\)</span>.  For the type-1 and type-2 NUFFTs, the non-uniform samples <span class="math notranslate nohighlight">\(\mathbf{x}_{j}\)</span> are assumed to lie
-in <span class="math notranslate nohighlight">\([-\pi,\pi)^{d}\)</span>.  For the type-3 NUFFT, the non-uniform samples <span class="math notranslate nohighlight">\(\mathbf{x}_{j}\)</span> and
-<span class="math notranslate nohighlight">\(\mathbf{z}_{k}\)</span> are arbitrary points in <span class="math notranslate nohighlight">\(\mathbb{R}^{d}\)</span>.</p>
-</li>
-<li><p><strong>Adjoint NUFFTs.</strong>
-The type-1 and type-2 NUFFTs with opposite signs form an <em>adjoint pair</em>.  The adjoint of the type-3 NUFFT is
-obtained by flipping the transform’s sign and switching the roles of <span class="math notranslate nohighlight">\(\mathbf{z}_k\)</span> and
-<span class="math notranslate nohighlight">\(\mathbf{x}_{j}\)</span> in (3).</p></li>
-<li><p><strong>Lipschitz Constants.</strong>
-We bound the Lipschitz constant by the Frobenius norm of the operators, which yields <span class="math notranslate nohighlight">\(L \leq \sqrt{NM}\)</span>.
-Note that these Lipschitz constants are cheap to compute but may be pessimistic.  Tighter Lipschitz constants can
-be computed by calling <a class="reference internal" href="abc.html#pyxu.abc.Map.estimate_lipschitz" title="pyxu.abc.Map.estimate_lipschitz"><code class="xref py py-meth docutils literal notranslate"><span class="pre">estimate_lipschitz()</span></code></a>.</p></li>
-<li><p><strong>Error Analysis.</strong>
-Let <span class="math notranslate nohighlight">\(\tilde{\mathbf{u}}\in\mathbb{C}^{\mathcal{I}_{N_1,\ldots, N_d}}\)</span> and
-<span class="math notranslate nohighlight">\(\tilde{\mathbf{w}}\in\mathbb{C}^{M}\)</span> be the outputs of the type-1 and type-2 NUFFT algorithms which
-approximate the sequences <span class="math notranslate nohighlight">\({\mathbf{u}}\in\mathbb{C}^{\mathcal{I}_{N_1,\ldots, N_d}}\)</span> and
-<span class="math notranslate nohighlight">\({\mathbf{w}}\in\mathbb{C}^{M}\)</span> defined in (1) and (2) respectively.  Then <a class="reference internal" href="../references.html#finufft" id="id8"><span>[FINUFFT]</span></a> shows that the
-relative errors <span class="math notranslate nohighlight">\(\|\tilde{\mathbf{u}}-{\mathbf{u}}\|_2/\|{\mathbf{u}}\|_2\)</span> and
-<span class="math notranslate nohighlight">\(\|\tilde{\mathbf{w}}-{\mathbf{w}}\|_2/\|{\mathbf{w}}\|_2\)</span> are <em>almost always similar to the user-requested
-tolerance</em> <span class="math notranslate nohighlight">\(\varepsilon\)</span>, except when round-off error dominates (i.e. very small user-requested tolerances).
-The same holds approximately for the type-3 NUFFT.  Note however that this is a <em>typical error analysis</em>: some
-degenerate (but rare) worst-case scenarios can result in higher errors.</p></li>
-<li><p><strong>Complexity.</strong>
-Naive evaluation of the exponential sums (1), (2) and (3) above costs <span class="math notranslate nohighlight">\(O(NM)\)</span>, where <span class="math notranslate nohighlight">\(N=N_{1}\ldots
-N_{d}\)</span> for the type-1 and type-2 NUFFTs.  NUFFT algorithms approximate these sums to a user-specified relative
-tolerance <span class="math notranslate nohighlight">\(\varepsilon\)</span> in log-linear complexity in <span class="math notranslate nohighlight">\(N\)</span> and <span class="math notranslate nohighlight">\(M\)</span>.  The complexity of the various
-NUFFTs are given by (see <a class="reference internal" href="../references.html#finufft" id="id9"><span>[FINUFFT]</span></a>):</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}&amp;\mathcal{O}\left(N \log(N) + M|\log(\varepsilon)|^d\right)\qquad &amp;\text{(Type 1 and 2)}\\
-&amp;\mathcal{O}\left(\Pi_{i=1}^dX_iZ_i\sum_{i=1}^d\log(X_iZ_i) + (M + N)|\log(\varepsilon)|^d\right)\qquad &amp;\text{(Type 3)}\end{split}\]</div>
-<p>where <span class="math notranslate nohighlight">\(X_i = \max_{j=1,\ldots,M}|(\mathbf{x}_{j})_i|\)</span> and <span class="math notranslate nohighlight">\(Z_i =
-\max_{k=1,\ldots,N}|(\mathbf{z}_k)_i|\)</span> for <span class="math notranslate nohighlight">\(i=1,\ldots,d\)</span>.  The terms above correspond to the complexities
-of the FFT and spreading/interpolation steps respectively.</p>
-</li>
-<li><p><strong>Memory footprint.</strong>
-The complexity and memory footprint of the type-3 NUFFT can be arbitrarily large for poorly-centered data, or for
-data with a large spread.  An easy fix consists in centering the data before/after the NUFFT via pre/post-phasing
-operations, as described in equation (3.24) of <a class="reference internal" href="../references.html#finufft" id="id10"><span>[FINUFFT]</span></a>.  This optimization is automatically carried out by
-FINUFFT if the compute/memory gains are non-negligible.</p>
-<p>Additionally the type-3 summation (eq. 3) can be evaluated block-wise by partitioning the non-uniform samples
-<span class="math notranslate nohighlight">\((x_{j}, z_{k})\)</span>:</p>
-<div class="math notranslate nohighlight">
-\[\begin{align}
-    (4)\;\; &amp;v_{k}
-    =
-    \sum_{p=1}^{P}
-    \sum_{j\in \mathcal{M}_{p}} w_{j}
-    e^{\sigma i\langle \mathbf{z}_{k}, \mathbf{x}_{j} \rangle },
-    \quad &amp;
-    k\in \mathcal{N}_{q}, \quad q=1,\ldots, Q, \quad &amp; \text{Type 3 (chunked)}
-\end{align}\]</div>
-<p>where <span class="math notranslate nohighlight">\(\{\mathcal{M}_1, \ldots, \mathcal{M}_P\}\)</span> and <span class="math notranslate nohighlight">\(\{\mathcal{N}_1, \ldots, \mathcal{N}_Q\}\)</span> are
-<em>partitions</em> of the sets <span class="math notranslate nohighlight">\(\{1, \ldots, M\}\)</span> and  <span class="math notranslate nohighlight">\(\{1, \ldots, N\}\)</span> respectively.  In the chunked
-setting, the partial sums in (4)</p>
-<div class="math notranslate nohighlight">
-\[\left\{\sum_{j\in \mathcal{M}_p} w_{j} e^{\sigma i\langle \mathbf{z}_k, \mathbf{x}_{j} \rangle }, \, k\in \mathcal{N}_q\right\}_{p,q}\]</div>
-<p>are each evaluated via a type-3 NUFFT involving a subset of the non-uniform samples.  Sub-problems can be
-evaluated in parallel.  Moreover, for wisely chosen data partitions, the memory budget of each NUFFT can be
-explicitly controlled and capped to a maximal value.  This allows one to perform out-of-core NUFFTs with
-(theoretically) no complexity overhead w.r.t a single large NUFFT. (See note below however.)</p>
-<p>Chunking of the type-3 NUFFT is activated by passing <code class="docutils literal notranslate"><span class="pre">chunked=True</span></code> to <a class="reference internal" href="#pyxu.operator.NUFFT.type3" title="pyxu.operator.NUFFT.type3"><code class="xref py py-meth docutils literal notranslate"><span class="pre">type3()</span></code></a>
-(together with <code class="docutils literal notranslate"><span class="pre">parallel=True</span></code> for parallel computations).  Finally, <a class="reference internal" href="#pyxu.operator.NUFFT.auto_chunk" title="pyxu.operator.NUFFT.auto_chunk"><code class="xref py py-meth docutils literal notranslate"><span class="pre">auto_chunk()</span></code></a>
-can be used to compute a good partition of the X/Z-domains.</p>
-<div class="admonition-hint admonition">
-<p class="admonition-title">Hint</p>
-<p>The current implementation of the chunked type-3 NUFFT has computational complexity:</p>
-<div class="math notranslate nohighlight">
-\[\mathcal{O}\left(
-    \sum_{p,q=1}^{P}\Pi_{i=1}^{d} X^{(p)}_{i}Z^{(q)}_{i}
-    \sum_{i=1}^{d} \log(X^{(p)}_{i} Z^{(q)}_{i})
-    +
-    (M_p + N_q)|\log(\varepsilon)|^{d}
-\right),\]</div>
-<p>where</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\begin{align*}
-    X^{(p)}_{i} &amp; = \max_{j\in \mathcal{M}_{p}}|(\mathbf{x}_{j})_{i}|, \quad i = \{1,\ldots,d\} \\
-    Z^{(p)}_{i} &amp; = \max_{k\in \mathcal{N}_{q}}|(\mathbf{z}_k)_{i}|, \quad i = \{1,\ldots,d\}
-\end{align*}\end{split}\]</div>
-<p>and <span class="math notranslate nohighlight">\(M_{p}, N_{q}\)</span> denote the number of elements in the sets <span class="math notranslate nohighlight">\(\mathcal{M}_{p}, \mathcal{N}_{q}\)</span>,
-respectively.</p>
-<p>For perfectly balanced and uniform chunks (i.e. <span class="math notranslate nohighlight">\(M_{p}=M/P\)</span>, <span class="math notranslate nohighlight">\(N_{q}=N/Q\)</span>, <span class="math notranslate nohighlight">\(X^{(p)}_{i} =
-X_{i}/P\)</span>, <span class="math notranslate nohighlight">\(Z^{(q)}_{i} = Z_{i}/Q\)</span> and <span class="math notranslate nohighlight">\(P=Q\)</span>) the complexity reduces to</p>
-<div class="math notranslate nohighlight">
-\[\mathcal{O}\left(
-    \Pi_{i=1}^{d} X_{i}Z_{i}\sum_{i=1}^{d}\log(X_{i}Z_{i})
-    +
-    P(M + N)|\log(\varepsilon)|^{d}
-\right).\]</div>
-<p>This shows that the spreading/interpolation is <span class="math notranslate nohighlight">\(P\)</span> times more expensive than in the non-chunked case.
-This overhead is usually acceptable if the number of chunks remains small.  With explicit control on the
-spreading/interpolation steps (which the Python interface to the FINUFFT backend does not currently offer), the
-spreading/interpolation overhead can be removed so as to obtain a computational complexity on par to that of
-the non-chunked type-3 NUFFT.  This will be implemented in a future release.</p>
-</div>
-</li>
-<li><p><strong>Backend.</strong>
-The NUFFT transforms are computed via Python wrappers to <a class="reference external" href="https://github.com/flatironinstitute/finufft">FINUFFT</a>
-and <a class="reference external" href="https://github.com/flatironinstitute/cufinufft">cuFINUFFT</a>.  (See also <a class="reference internal" href="../references.html#finufft" id="id11"><span>[FINUFFT]</span></a> and <a class="reference internal" href="../references.html#cufinufft" id="id12"><span>[cuFINUFFT]</span></a>.) These
-librairies perform the expensive spreading/interpolation between nonuniform points and the fine grid via the
-“exponential of semicircle” kernel.</p></li>
-<li><p><strong>Optional Parameters.</strong>
-[cu]FINUFFT exposes many optional parameters to adjust the performance of the algorithms, change the output
-format, or provide debug/timing information.  While the default options are sensible for most setups, advanced
-users may overwrite them via the <code class="docutils literal notranslate"><span class="pre">kwargs</span></code> parameter of <a class="reference internal" href="#pyxu.operator.NUFFT.type1" title="pyxu.operator.NUFFT.type1"><code class="xref py py-meth docutils literal notranslate"><span class="pre">type1()</span></code></a>,
-<a class="reference internal" href="#pyxu.operator.NUFFT.type2" title="pyxu.operator.NUFFT.type2"><code class="xref py py-meth docutils literal notranslate"><span class="pre">type2()</span></code></a>, and <a class="reference internal" href="#pyxu.operator.NUFFT.type3" title="pyxu.operator.NUFFT.type3"><code class="xref py py-meth docutils literal notranslate"><span class="pre">type3()</span></code></a>.  See the <a class="reference external" href="https://finufft.readthedocs.io/en/latest/python.html#finufft.Plan">guru interface</a> from FINUFFT and its <a class="reference external" href="https://finufft.readthedocs.io/en/latest/opts.html#options-parameters">companion page</a> for details.</p>
-<div class="admonition-hint admonition">
-<p class="admonition-title">Hint</p>
-<p>FINUFFT exposes a <code class="docutils literal notranslate"><span class="pre">dtype</span></code> keyword to control the precision (single or double) at which transforms are
-performed.  This parameter is ignored by <a class="reference internal" href="#pyxu.operator.NUFFT" title="pyxu.operator.NUFFT"><code class="xref py py-class docutils literal notranslate"><span class="pre">NUFFT</span></code></a>: use the context manager
-<a class="reference internal" href="runtime.html#pyxu.runtime.Precision" title="pyxu.runtime.Precision"><code class="xref py py-class docutils literal notranslate"><span class="pre">Precision</span></code></a> to control floating point precision.</p>
-</div>
-<div class="admonition-hint admonition">
-<p class="admonition-title">Hint</p>
-<p>The NUFFT is performed in <strong>batches of (n_trans,)</strong>, where <code class="code docutils literal notranslate"><span class="pre">n_trans</span></code> denotes the number of simultaneous
-transforms requested.  (See the <code class="docutils literal notranslate"><span class="pre">n_trans</span></code> parameter of <a class="reference external" href="https://finufft.readthedocs.io/en/latest/python.html#finufft.Plan">finufft.Plan</a>.)</p>
-<p>Good performance is obtained when each batch fits easily in memory. This recommendation also applies to Dask
-inputs which are re-chunked internally to be <code class="code docutils literal notranslate"><span class="pre">n_trans</span></code>-compliant.</p>
-<p>This parameter also affects performance of the <code class="docutils literal notranslate"><span class="pre">eps=0</span></code> case: increasing <code class="docutils literal notranslate"><span class="pre">n_trans</span></code> may improve performance
-when doing several transforms in parallel.</p>
-</div>
-</li>
-</ul>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>Since FINUFFT plans cannot be shared among different processes, this class is <strong>only compatible</strong> with Dask’s
-thread-based schedulers, i.e.:</p>
-<ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">scheduler='thread'</span></code></p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">scheduler='synchronous'</span></code></p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">distributed.Client(processes=False)</span></code></p></li>
-</ul>
-<p>Batches are hence processed serially.  (Each batch is multi-threaded however.)</p>
-</div>
-<aside class="footnote-list brackets">
-<aside class="footnote brackets" id="id13" role="doc-footnote">
-<span class="label"><span class="fn-bracket">[</span><a href="#id7" role="doc-backlink">1</a><span class="fn-bracket">]</span></span>
-<p><span class="math notranslate nohighlight">\(\varepsilon= 0\)</span> means that no approximation is performed: the exponential sums
-are naively computed by direct evaluation.</p>
-</aside>
-</aside>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.FFT" title="pyxu.operator.FFT"><code class="xref py py-class docutils literal notranslate"><span class="pre">FFT</span></code></a></p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>]</em>) – </p>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.type1">
-<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">type1</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">isign</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plan_fw</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plan_bw</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.type1"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.type1" title="Link to this definition">#</a></dt>
-<dd><p>Type-1 NUFFT (non-uniform to uniform).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (M, [d]) d-dimensional sample points <span class="math notranslate nohighlight">\(\mathbf{x}_{j} \in [-\pi,\pi)^{d}\)</span>.</p></li>
-<li><p><strong>N</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a> ( Integer )) – <p>([d],) mesh size in each dimension <span class="math notranslate nohighlight">\((N_1, \ldots, N_d)\)</span>.</p>
-<p>If <code class="code docutils literal notranslate"><span class="pre">N</span></code> is an integer, then the mesh is assumed to have the same size in each dimension.</p>
-</p></li>
-<li><p><strong>isign</strong> (<code class="docutils literal notranslate"><span class="pre">1</span></code>, <code class="docutils literal notranslate"><span class="pre">-1</span></code>) – Sign <span class="math notranslate nohighlight">\(\sigma\)</span> of the transform.</p></li>
-<li><p><strong>eps</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – <p>Requested relative accuracy <span class="math notranslate nohighlight">\(\varepsilon \geq 0\)</span>.</p>
-<p>If <code class="docutils literal notranslate"><span class="pre">eps=0</span></code>, the transform is computed exactly via direct evaluation of the exponential sum using a Numba
-JIT-compiled kernel.</p>
-</p></li>
-<li><p><strong>real</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – <p>If <code class="docutils literal notranslate"><span class="pre">True</span></code>, assumes <a class="reference internal" href="#pyxu.operator.NUFFT.apply" title="pyxu.operator.NUFFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> takes (…, M) inputs in <span class="math notranslate nohighlight">\(\mathbb{R}^{M}\)</span>.</p>
-<p>If <code class="docutils literal notranslate"><span class="pre">False</span></code>, then <a class="reference internal" href="#pyxu.operator.NUFFT.apply" title="pyxu.operator.NUFFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> takes (…, 2M) inputs, i.e. <span class="math notranslate nohighlight">\(\mathbb{C}^{M}\)</span>
-vectors viewed as bijections with <span class="math notranslate nohighlight">\(\mathbb{R}^{2M}\)</span>.</p>
-</p></li>
-<li><p><strong>plan_fw/bw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, allocate FINUFFT resources to do the forward (fw) and/or backward (bw) transform.  These are
-advanced options: use them with care.  Some public methods in the <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> interface may
-not work if fw/bw transforms are disabled.  These options only take effect if <code class="docutils literal notranslate"><span class="pre">eps</span> <span class="pre">&gt;</span> <span class="pre">0</span></code>.</p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
-<li><p><strong>**kwargs</strong> – <p>Extra kwargs to <a class="reference external" href="https://finufft.readthedocs.io/en/latest/python.html#finufft.Plan">finufft.Plan</a>.
-(Illegal keywords are dropped silently.) Most useful are <code class="docutils literal notranslate"><span class="pre">n_trans</span></code>, <code class="docutils literal notranslate"><span class="pre">nthreads</span></code> and <code class="docutils literal notranslate"><span class="pre">debug</span></code>.</p>
-</p></li>
-<li><p><strong>plan_fw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-<li><p><strong>plan_bw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (2N.prod(), M) or (2N.prod(), 2M) type-1 NUFFT.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="kn">import</span> <span class="nn">pyxu.runtime</span> <span class="k">as</span> <span class="nn">pxrt</span>
-<span class="kn">import</span> <span class="nn">pyxu.util</span> <span class="k">as</span> <span class="nn">pxu</span>
-
-<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<span class="n">D</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">5</span>  <span class="c1"># D denotes the dimension of the data</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fmod</span><span class="p">(</span><span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="n">D</span><span class="p">)),</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
-
-<span class="k">with</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">Precision</span><span class="p">(</span><span class="n">pxrt</span><span class="o">.</span><span class="n">Width</span><span class="o">.</span><span class="n">SINGLE</span><span class="p">):</span>
-    <span class="c1"># The NUFFT dimension (1/2/3) is inferred from the trailing dimension of x.</span>
-    <span class="c1"># Its precision is controlled by the context manager.</span>
-    <span class="n">N_trans</span> <span class="o">=</span> <span class="mi">5</span>
-    <span class="n">A</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">NUFFT</span><span class="o">.</span><span class="n">type1</span><span class="p">(</span>
-            <span class="n">x</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span>
-            <span class="n">n_trans</span><span class="o">=</span><span class="n">N_trans</span><span class="p">,</span>
-            <span class="n">isign</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span>
-            <span class="n">eps</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
-        <span class="p">)</span>
-
-    <span class="c1"># Pyxu operators only support real inputs/outputs, so we use the functions</span>
-    <span class="c1"># pxu.view_as_[complex/real] to interpret complex arrays as real arrays (and</span>
-    <span class="c1"># vice-versa).</span>
-    <span class="n">arr</span> <span class="o">=</span>        <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">N_trans</span><span class="p">,</span> <span class="n">M</span><span class="p">))</span> \
-          <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">N_trans</span><span class="p">,</span> <span class="n">M</span><span class="p">))</span>
-    <span class="n">A_out_fw</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">pxu</span><span class="o">.</span><span class="n">view_as_real</span><span class="p">(</span><span class="n">arr</span><span class="p">)))</span>
-    <span class="n">A_out_bw</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">pxu</span><span class="o">.</span><span class="n">view_as_real</span><span class="p">(</span><span class="n">A_out_fw</span><span class="p">)))</span>
-</pre></div>
-</div>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.type2">
-<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">type2</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">isign</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plan_fw</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plan_bw</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.type2"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.type2" title="Link to this definition">#</a></dt>
-<dd><p>Type-2 NUFFT (uniform to non-uniform).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (M, [d]) d-dimensional sample points <span class="math notranslate nohighlight">\(\mathbf{x}_{j} \in [-\pi,\pi]^{d}\)</span>.</p></li>
-<li><p><strong>N</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a> ( Integer )) – <p>([d],) mesh size in each dimension <span class="math notranslate nohighlight">\((N_1, \ldots, N_d)\)</span>.</p>
-<p>If <code class="code docutils literal notranslate"><span class="pre">N</span></code> is an integer, then the mesh is assumed to have the same size in each dimension.</p>
-</p></li>
-<li><p><strong>isign</strong> (<code class="docutils literal notranslate"><span class="pre">1</span></code>, <code class="docutils literal notranslate"><span class="pre">-1</span></code>) – Sign <span class="math notranslate nohighlight">\(\sigma\)</span> of the transform.</p></li>
-<li><p><strong>eps</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – <p>Requested relative accuracy <span class="math notranslate nohighlight">\(\varepsilon \geq 0\)</span>.</p>
-<p>If <code class="docutils literal notranslate"><span class="pre">eps=0</span></code>, the transform is computed exactly via direct evaluation of the exponential sum using a Numba
-JIT-compiled kernel.</p>
-</p></li>
-<li><p><strong>real</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – <p>If <code class="docutils literal notranslate"><span class="pre">True</span></code>, assumes <a class="reference internal" href="#pyxu.operator.NUFFT.apply" title="pyxu.operator.NUFFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> takes (…, N.prod()) inputs in
-<span class="math notranslate nohighlight">\(\mathbb{R}^{N}\)</span>.</p>
-<p>If <code class="docutils literal notranslate"><span class="pre">False</span></code>, then <a class="reference internal" href="#pyxu.operator.NUFFT.apply" title="pyxu.operator.NUFFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> takes (…, 2N.prod()) inputs, i.e.
-<span class="math notranslate nohighlight">\(\mathbb{C}^{N}\)</span> vectors viewed as bijections with <span class="math notranslate nohighlight">\(\mathbb{R}^{2N}\)</span>.</p>
-</p></li>
-<li><p><strong>plan_fw/bw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, allocate FINUFFT resources to do the forward (fw) and/or backward (bw) transform.  These are
-advanced options: use them with care.  Some public methods in the <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> interface may
-not work if fw/bw transforms are disabled.  These options only take effect if <code class="docutils literal notranslate"><span class="pre">eps</span> <span class="pre">&gt;</span> <span class="pre">0</span></code>.</p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
-<li><p><strong>**kwargs</strong> – <p>Extra kwargs to <a class="reference external" href="https://finufft.readthedocs.io/en/latest/python.html#finufft.Plan">finufft.Plan</a>.
-(Illegal keywords are dropped silently.) Most useful are <code class="docutils literal notranslate"><span class="pre">n_trans</span></code>, <code class="docutils literal notranslate"><span class="pre">nthreads</span></code> and <code class="docutils literal notranslate"><span class="pre">debug</span></code>.</p>
-</p></li>
-<li><p><strong>plan_fw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-<li><p><strong>plan_bw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (2M, N.prod()) or (2M, 2N.prod()) type-2 NUFFT.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="kn">import</span> <span class="nn">pyxu.runtime</span> <span class="k">as</span> <span class="nn">pxrt</span>
-<span class="kn">import</span> <span class="nn">pyxu.util</span> <span class="k">as</span> <span class="nn">pxu</span>
-
-<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<span class="n">D</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">5</span>  <span class="c1"># D denotes the dimension of the data</span>
-<span class="n">N_full</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="p">,)</span> <span class="o">*</span> <span class="n">D</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fmod</span><span class="p">(</span><span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="n">D</span><span class="p">)),</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
-
-<span class="k">with</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">Precision</span><span class="p">(</span><span class="n">pxrt</span><span class="o">.</span><span class="n">Width</span><span class="o">.</span><span class="n">SINGLE</span><span class="p">):</span>
-    <span class="c1"># The NUFFT dimension (1/2/3) is inferred from the trailing dimension of x.</span>
-    <span class="c1"># Its precision is controlled by the context manager.</span>
-    <span class="n">N_trans</span> <span class="o">=</span> <span class="mi">5</span>
-    <span class="n">A</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">NUFFT</span><span class="o">.</span><span class="n">type2</span><span class="p">(</span>
-            <span class="n">x</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span>
-            <span class="n">n_trans</span><span class="o">=</span><span class="n">N_trans</span><span class="p">,</span>
-            <span class="n">isign</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span>
-            <span class="n">eps</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
-        <span class="p">)</span>
-
-    <span class="c1"># Pyxu operators only support real inputs/outputs, so we use the functions</span>
-    <span class="c1"># pxu.view_as_[complex/real] to interpret complex arrays as real arrays (and</span>
-    <span class="c1"># vice-versa).</span>
-    <span class="n">arr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span>
-               <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">N_trans</span><span class="p">,</span> <span class="o">*</span><span class="n">N_full</span><span class="p">))</span>
-        <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">N_trans</span><span class="p">,</span> <span class="o">*</span><span class="n">N_full</span><span class="p">)),</span>
-        <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">N_trans</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">),</span>
-    <span class="p">)</span>
-    <span class="n">A_out_fw</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">pxu</span><span class="o">.</span><span class="n">view_as_real</span><span class="p">(</span><span class="n">arr</span><span class="p">)))</span>
-    <span class="n">A_out_bw</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">pxu</span><span class="o">.</span><span class="n">view_as_real</span><span class="p">(</span><span class="n">A_out_fw</span><span class="p">)))</span>
-</pre></div>
-</div>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.type3">
-<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">type3</span></span><span class="sig-paren">(</span>
-<dl>
-<dd><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">z</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">isign</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">eps</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0001</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">real</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">plan_fw</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">plan_bw</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">chunked</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em>,</dd>
-</dl>
-<span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.type3"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.type3" title="Link to this definition">#</a></dt>
-<dd><p>Type-3 NUFFT (non-uniform to non-uniform).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (M, [d]) d-dimensional sample points <span class="math notranslate nohighlight">\(\mathbf{x}_{j} \in \mathbb{R}^{d}\)</span>.</p></li>
-<li><p><strong>z</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (N, [d]) d-dimensional query points <span class="math notranslate nohighlight">\(\mathbf{z}_{k} \in \mathbb{R}^{d}\)</span>.</p></li>
-<li><p><strong>isign</strong> (<code class="docutils literal notranslate"><span class="pre">1</span></code>, <code class="docutils literal notranslate"><span class="pre">-1</span></code>) – Sign <span class="math notranslate nohighlight">\(\sigma\)</span> of the transform.</p></li>
-<li><p><strong>eps</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – <p>Requested relative accuracy <span class="math notranslate nohighlight">\(\varepsilon \geq 0\)</span>.</p>
-<p>If <code class="docutils literal notranslate"><span class="pre">eps=0</span></code>, the transform is computed exactly via direct evaluation of the exponential sum using a Numba
-JIT-compiled kernel.</p>
-</p></li>
-<li><p><strong>real</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – <p>If <code class="docutils literal notranslate"><span class="pre">True</span></code>, assumes <a class="reference internal" href="#pyxu.operator.NUFFT.apply" title="pyxu.operator.NUFFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> takes (…, M) inputs in <span class="math notranslate nohighlight">\(\mathbb{R}^{M}\)</span>.</p>
-<p>If <code class="docutils literal notranslate"><span class="pre">False</span></code>, then <a class="reference internal" href="#pyxu.operator.NUFFT.apply" title="pyxu.operator.NUFFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> takes (…, 2M) inputs, i.e. <span class="math notranslate nohighlight">\(\mathbb{C}^{M}\)</span>
-vectors viewed as bijections with <span class="math notranslate nohighlight">\(\mathbb{R}^{2M}\)</span>.</p>
-</p></li>
-<li><p><strong>plan_fw/bw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, allocate FINUFFT resources to do the forward (fw) and/or backward (bw) transform.  These are
-advanced options: use them with care.  Some public methods in the <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> interface may
-not work if fw/bw transforms are disabled.  These options only take effect if <code class="docutils literal notranslate"><span class="pre">eps</span> <span class="pre">&gt;</span> <span class="pre">0</span></code>.</p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
-<li><p><strong>chunked</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, the transform is performed in small chunks. (See Notes for details.)</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – This option only applies to chunked transforms.  If <code class="docutils literal notranslate"><span class="pre">True</span></code>, evaluate chunks in parallel.</p></li>
-<li><p><strong>**kwargs</strong> – <p>Extra kwargs to <a class="reference external" href="https://finufft.readthedocs.io/en/latest/python.html#finufft.Plan">finufft.Plan</a>.
-(Illegal keywords are dropped silently.) Most useful are <code class="docutils literal notranslate"><span class="pre">n_trans</span></code>, <code class="docutils literal notranslate"><span class="pre">nthreads</span></code> and <code class="docutils literal notranslate"><span class="pre">debug</span></code>.</p>
-</p></li>
-<li><p><strong>plan_fw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-<li><p><strong>plan_bw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (2N, M) or (2N, 2M) type-3 NUFFT.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="kn">import</span> <span class="nn">pyxu.runtime</span> <span class="k">as</span> <span class="nn">pxrt</span>
-<span class="kn">import</span> <span class="nn">pyxu.util</span> <span class="k">as</span> <span class="nn">pxu</span>
-
-<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<span class="n">D</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">200</span><span class="p">,</span> <span class="mi">5</span>  <span class="c1"># D denotes the dimension of the data</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="n">D</span><span class="p">))</span> <span class="o">+</span> <span class="mi">2000</span>  <span class="c1"># Poorly-centered data</span>
-<span class="n">z</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">D</span><span class="p">))</span>
-<span class="k">with</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">Precision</span><span class="p">(</span><span class="n">pxrt</span><span class="o">.</span><span class="n">Width</span><span class="o">.</span><span class="n">SINGLE</span><span class="p">):</span>
-    <span class="c1"># The NUFFT dimension (1/2/3) is inferred from the trailing dimension of x/z.</span>
-    <span class="c1"># Its precision is controlled by the context manager.</span>
-    <span class="n">N_trans</span> <span class="o">=</span> <span class="mi">20</span>
-    <span class="n">A</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">NUFFT</span><span class="o">.</span><span class="n">type3</span><span class="p">(</span>
-            <span class="n">x</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span>
-            <span class="n">n_trans</span><span class="o">=</span><span class="n">N_trans</span><span class="p">,</span>
-            <span class="n">isign</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span>
-            <span class="n">eps</span><span class="o">=</span><span class="mf">1e-6</span><span class="p">,</span>
-         <span class="p">)</span>
-
-    <span class="c1"># Pyxu operators only support real inputs/outputs, so we use the functions</span>
-    <span class="c1"># pxu.view_as_[complex/real] to interpret complex arrays as real arrays (and</span>
-    <span class="c1"># vice-versa).</span>
-    <span class="n">arr</span> <span class="o">=</span>        <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">N_trans</span><span class="p">,</span> <span class="n">M</span><span class="p">))</span> \
-          <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">N_trans</span><span class="p">,</span> <span class="n">M</span><span class="p">))</span>
-    <span class="n">A_out_fw</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">pxu</span><span class="o">.</span><span class="n">view_as_real</span><span class="p">(</span><span class="n">arr</span><span class="p">)))</span>
-    <span class="n">A_out_bw</span> <span class="o">=</span> <span class="n">pxu</span><span class="o">.</span><span class="n">view_as_complex</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">pxu</span><span class="o">.</span><span class="n">view_as_real</span><span class="p">(</span><span class="n">A_out_fw</span><span class="p">)))</span>
-</pre></div>
-</div>
-<p class="rubric">Notes (chunked-transform)</p>
-<ul>
-<li><p>An extra initialization step is required before using a chunked-transform:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">pxl</span><span class="o">.</span><span class="n">NUFFT</span><span class="o">.</span><span class="n">type3</span><span class="p">(</span>
-        <span class="n">x</span><span class="p">,</span> <span class="n">z</span>
-        <span class="n">isign</span>
-        <span class="n">chunked</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>   <span class="c1"># with chunk specified</span>
-        <span class="n">parallel</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>  <span class="c1"># for extra speed (chunked-only)</span>
-        <span class="o">**</span><span class="n">finufft_kwargs</span><span class="p">,</span>
-     <span class="p">)</span>
-<span class="n">x_chunks</span><span class="p">,</span> <span class="n">z_chunks</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">auto_chunk</span><span class="p">()</span>  <span class="c1"># auto-determine a good x/z chunking strategy</span>
-<span class="n">A</span><span class="o">.</span><span class="n">allocate</span><span class="p">(</span><span class="n">x_chunks</span><span class="p">,</span> <span class="n">z_chunks</span><span class="p">)</span>  <span class="c1"># apply the chunking strategy.</span>
-</pre></div>
-</div>
-<p><a class="reference internal" href="#pyxu.operator.NUFFT.auto_chunk" title="pyxu.operator.NUFFT.auto_chunk"><code class="xref py py-meth docutils literal notranslate"><span class="pre">auto_chunk()</span></code></a> is a helper method to auto-determine a good chunking strategy.</p>
-<p>Its runtime is significant when the number of sub-problems grows large. (1000+) In these contexts, assuming a
-good-enough x/z-split is known in advance, users can directly supply them to
-<a class="reference internal" href="#pyxu.operator.NUFFT.allocate" title="pyxu.operator.NUFFT.allocate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">allocate()</span></code></a>.</p>
-</li>
-<li><p><a class="reference internal" href="#pyxu.operator.NUFFT.apply" title="pyxu.operator.NUFFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> / <a class="reference internal" href="#pyxu.operator.NUFFT.adjoint" title="pyxu.operator.NUFFT.adjoint"><code class="xref py py-func docutils literal notranslate"><span class="pre">adjoint()</span></code></a> runtime is minimized when x/z
-are well-ordered, i.e.  when sub-problems can sub-sample inputs to <a class="reference internal" href="#pyxu.operator.NUFFT.apply" title="pyxu.operator.NUFFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> /
-<a class="reference internal" href="#pyxu.operator.NUFFT.adjoint" title="pyxu.operator.NUFFT.adjoint"><code class="xref py py-func docutils literal notranslate"><span class="pre">adjoint()</span></code></a> via slice operators.</p>
-<p>To reduce runtime of chunked transforms, <a class="reference internal" href="#pyxu.operator.NUFFT.allocate" title="pyxu.operator.NUFFT.allocate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">allocate()</span></code></a> automatically re-orders x/z
-when appropriate.</p>
-<p>The side-effect is the cost of a permutation before/after calls to <a class="reference internal" href="#pyxu.operator.NUFFT.apply" title="pyxu.operator.NUFFT.apply"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply()</span></code></a> /
-<a class="reference internal" href="#pyxu.operator.NUFFT.adjoint" title="pyxu.operator.NUFFT.adjoint"><code class="xref py py-func docutils literal notranslate"><span class="pre">adjoint()</span></code></a>.  This cost becomes significant when the number of non-uniform points
-x/z is large. (&gt; 1e6)</p>
-<p>To avoid paying the re-ordering cost at each transform, it is recommended to supply x/z and apply/adjoint
-inputs in the “correct” order from the start.</p>
-<p>A good re-ordering is computed automatically by <a class="reference internal" href="#pyxu.operator.NUFFT.allocate" title="pyxu.operator.NUFFT.allocate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">allocate()</span></code></a> and can be used to
-initialize a new chunked-transform with better runtime properties as such:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1">### Initialize a chunked transform (1st try; as above)</span>
-<span class="n">A</span> <span class="o">=</span> <span class="n">pxl</span><span class="o">.</span><span class="n">NUFFT</span><span class="o">.</span><span class="n">type3</span><span class="p">(</span>
-        <span class="n">x</span><span class="p">,</span> <span class="n">z</span>
-        <span class="n">isign</span>
-        <span class="n">chunked</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
-        <span class="n">parallel</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
-        <span class="o">**</span><span class="n">finufft_kwargs</span><span class="p">,</span>
-     <span class="p">)</span>
-<span class="n">x_chunks</span><span class="p">,</span> <span class="n">z_chunks</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">auto_chunk</span><span class="p">()</span>  <span class="c1"># auto-determine a good x/z chunking strategy</span>
-<span class="n">A</span><span class="o">.</span><span class="n">allocate</span><span class="p">(</span><span class="n">x_chunks</span><span class="p">,</span> <span class="n">z_chunks</span><span class="p">)</span>  <span class="c1"># will raise warning if bad x/z-order detected</span>
-
-<span class="c1">### Now initialize a better transform (2nd try)</span>
-<span class="n">x_idx</span><span class="p">,</span> <span class="n">x_chunks</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">order</span><span class="p">(</span><span class="s2">"x"</span><span class="p">)</span>  <span class="c1"># get a good x-ordering</span>
-<span class="n">z_idx</span><span class="p">,</span> <span class="n">z_chunks</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">order</span><span class="p">(</span><span class="s2">"z"</span><span class="p">)</span>  <span class="c1"># get a good z-ordering</span>
-<span class="n">A</span> <span class="o">=</span> <span class="n">pxl</span><span class="o">.</span><span class="n">NUFFT</span><span class="o">.</span><span class="n">type3</span><span class="p">(</span>
-        <span class="n">x</span><span class="p">[</span><span class="n">x_idx</span><span class="p">],</span> <span class="n">z</span><span class="p">[</span><span class="n">z_idx</span><span class="p">]</span>  <span class="c1"># re-order x/z accordingly</span>
-        <span class="o">...</span>                 <span class="c1"># same as before</span>
-     <span class="p">)</span>
-<span class="n">A</span><span class="o">.</span><span class="n">allocate</span><span class="p">(</span><span class="n">x_chunks</span><span class="p">,</span> <span class="n">z_chunks</span><span class="p">)</span>  <span class="c1"># skip auto-chunking and apply</span>
-                                <span class="c1"># optimal x/z_chunks provided.</span>
-</pre></div>
-</div>
-</li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.NUFFT.auto_chunk" title="pyxu.operator.NUFFT.auto_chunk"><code class="xref py py-meth docutils literal notranslate"><span class="pre">auto_chunk()</span></code></a>, <a class="reference internal" href="#pyxu.operator.NUFFT.allocate" title="pyxu.operator.NUFFT.allocate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">allocate()</span></code></a>, <a class="reference internal" href="#pyxu.operator.NUFFT.diagnostic_plot" title="pyxu.operator.NUFFT.diagnostic_plot"><code class="xref py py-meth docutils literal notranslate"><span class="pre">diagnostic_plot()</span></code></a>, <a class="reference internal" href="#pyxu.operator.NUFFT.stats" title="pyxu.operator.NUFFT.stats"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stats()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.apply">
-<span class="sig-name descname"><span class="pre">apply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.apply"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.apply" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – <ul class="simple">
-<li><dl class="simple">
-<dt><strong>Type 1 and 3:</strong></dt><dd><ul>
-<li><p>(…,  M) input weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{R}^{M}\)</span> (real transform).</p></li>
-<li><p>(…, 2M) input weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{C}^{M}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
-</ul>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt><strong>Type 2:</strong></dt><dd><ul>
-<li><p>(…,  N.prod()) input weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{R}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-(real transform).</p></li>
-<li><p>(…, 2N.prod()) input weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{C}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-viewed as a real array.  (See <a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
-</ul>
-</dd>
-</dl>
-</li>
-</ul>
-</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><p><strong>out</strong> –</p>
-<ul class="simple">
-<li><dl class="simple">
-<dt><strong>Type 1:</strong></dt><dd><p>(…, 2N.prod()) output weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{C}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-viewed as a real array.  (See <a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt><strong>Type 2:</strong></dt><dd><p>(…, 2M) output weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{C}^{M}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt><strong>Type 3:</strong></dt><dd><p>(…, 2N) output weights <span class="math notranslate nohighlight">\(\mathbf{v} \in \mathbb{C}^{N}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
-</dd>
-</dl>
-</li>
-</ul>
-</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.adjoint">
-<span class="sig-name descname"><span class="pre">adjoint</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.adjoint"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.adjoint" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – <ul class="simple">
-<li><dl class="simple">
-<dt><strong>Type 1:</strong></dt><dd><p>(…, 2N.prod()) output weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{C}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-viewed as a real array.  (See <a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt><strong>Type 2:</strong></dt><dd><p>(…, 2M) output weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{C}^{M}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt><strong>Type 3:</strong></dt><dd><p>(…, 2N) output weights <span class="math notranslate nohighlight">\(\mathbf{v} \in \mathbb{C}^{N}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
-</dd>
-</dl>
-</li>
-</ul>
-</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><p><strong>out</strong> –</p>
-<ul class="simple">
-<li><dl class="simple">
-<dt><strong>Type 1 and 3:</strong></dt><dd><ul>
-<li><p>(…,  M) input weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{R}^{M}\)</span> (real transform).</p></li>
-<li><p>(…, 2M) input weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{C}^{M}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
-</ul>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt><strong>Type 2:</strong></dt><dd><ul>
-<li><p>(…,  N.prod()) input weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{R}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-(real transform).</p></li>
-<li><p>(…, 2N.prod()) input weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{C}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-viewed as a real array.  (See <a class="reference internal" href="util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
-</ul>
-</dd>
-</dl>
-</li>
-</ul>
-</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.ascomplexarray">
-<span class="sig-name descname"><span class="pre">ascomplexarray</span></span><span class="sig-paren">(</span>
-<dl>
-<dd><em class="sig-param"><span class="n"><span class="pre">xp=&lt;module</span> <span class="pre">'numpy'</span> <span class="pre">from</span> <span class="pre">'/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/numpy/__init__.py'&gt;</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">dtype=None</span></span></em>,</dd>
-</dl>
-<span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.ascomplexarray"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.ascomplexarray" title="Link to this definition">#</a></dt>
-<dd><p>Matrix representation (complex-valued) of the linear operator.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>xp</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArrayModule</span></code></a>) – Which array module to use to represent the output.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Optional (complex-valued) type of the array.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><p><strong>A</strong> – Array representation of the operator (NUFFT type-dependant).</p>
-<ul class="simple">
-<li><p><strong>Type 1:</strong> (N.prod(), M)</p></li>
-<li><p><strong>Type 2:</strong> (M, N.prod())</p></li>
-<li><p><strong>Type 3:</strong> (N, M)</p></li>
-</ul>
-</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.mesh">
-<span class="sig-name descname"><span class="pre">mesh</span></span><span class="sig-paren">(</span>
-<dl>
-<dd><em class="sig-param"><span class="n"><span class="pre">xp=&lt;module</span> <span class="pre">'numpy'</span> <span class="pre">from</span> <span class="pre">'/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/numpy/__init__.py'&gt;</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">dtype=None</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">scale='unit'</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">upsampled=False</span></span></em>,</dd>
-</dl>
-<span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.mesh"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.mesh" title="Link to this definition">#</a></dt>
-<dd><p>For type-1/2 NUFFT: compute the transform’s meshgrid <span class="math notranslate nohighlight">\(\mathcal{I}_{N_{1} \times \cdots \times N_{d}} =
-\mathcal{I}_{N_{1}} \times \cdots \times \mathcal{I}_{N_{d}}\)</span>.</p>
-<p>For type-3 NUFFT: compute the (shifted) meshgrid used for internal FFT computations.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>xp</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArrayModule</span></code></a>) – Which array module to use to represent the output.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Optional type of the array.</p></li>
-<li><p><strong>scale</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>) – <p>Grid scale. Options are:</p>
-<ul>
-<li><dl class="simple">
-<dt><strong>Type1 and 2:</strong></dt><dd><ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">unit</span></code>, i.e. <span class="math notranslate nohighlight">\(\mathcal{I} = [[-N_{d}//2, \ldots, (N_{d}-1)//2 + 1))^{d}\)</span></p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">source</span></code>, i.e. <span class="math notranslate nohighlight">\(\mathcal{I} \subset [-\pi, \pi)^{d}\)</span></p></li>
-</ul>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt><strong>Type 3:</strong></dt><dd><ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">unit</span></code>, i.e. <span class="math notranslate nohighlight">\(\mathcal{I} = [[-N_{d}//2, \ldots, (N_{d}-1)//2 + 1))^{d}\)</span></p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">source</span></code>, i.e. <span class="math notranslate nohighlight">\(\mathcal{I}_{\text{source}} \subset x^{c} + [-X_{d}, X_{d})^{d}\)</span></p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">target</span></code>, i.e. <span class="math notranslate nohighlight">\(\mathcal{I}_{\text{target}} \subset z^{c} + [-Z_{d}, Z_{d})^{d}\)</span>,</p></li>
-</ul>
-</dd>
-</dl>
-<p>where <span class="math notranslate nohighlight">\(x^{c}\)</span>, <span class="math notranslate nohighlight">\(z^{c}\)</span> denote the source/target centroids, and <span class="math notranslate nohighlight">\(X\)</span>, <span class="math notranslate nohighlight">\(Z\)</span> the
-source/target half-widths.</p>
-</li>
-</ul>
-</p></li>
-<li><p><strong>upsampled</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Use the upsampled meshgrid.  (See <a class="reference internal" href="../references.html#finufft" id="id17"><span>[FINUFFT]</span></a> for details.)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>grid</strong> – (N1, …, Nd, d) grid.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-
-<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<span class="n">D</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span>  <span class="c1"># D denotes the dimension of the data</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">fmod</span><span class="p">(</span><span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="n">D</span><span class="p">)),</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
-<span class="n">A</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">NUFFT</span><span class="o">.</span><span class="n">type1</span><span class="p">(</span>
-    <span class="n">x</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span>
-    <span class="n">isign</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span>
-    <span class="n">eps</span><span class="o">=</span><span class="mf">1e-3</span>
-<span class="p">)</span>
-<span class="n">A</span><span class="o">.</span><span class="n">mesh</span><span class="p">()</span>  <span class="c1"># array([[-1.],</span>
-          <span class="c1">#        [ 0.],</span>
-          <span class="c1">#        [ 1.]])</span>
-</pre></div>
-</div>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.plot_kernel">
-<span class="sig-name descname"><span class="pre">plot_kernel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.plot_kernel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.plot_kernel" title="Link to this definition">#</a></dt>
-<dd><p>Plot the spreading/interpolation kernel (along each dimension) on its support.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>ax</strong> (<a class="reference external" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="(in Matplotlib v3.7.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Axes</span></code></a>) – Axes to draw on.  If <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>, a new axes is used.</p></li>
-<li><p><strong>**kwargs</strong> – Keyword arguments forwarded to <a class="reference external" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="(in Matplotlib v3.7.2)"><code class="xref py py-meth docutils literal notranslate"><span class="pre">matplotlib.axes.Axes.plot()</span></code></a>.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>ax</strong></p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="(in Matplotlib v3.7.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Axes</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-
-<span class="n">rng</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/random/generator.html#numpy.random.default_rng" title="numpy.random.default_rng"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span></a><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-<span class="n">D</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span>  <span class="c1"># D denotes the dimension of the data</span>
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.fmod.html#numpy.fmod" title="numpy.fmod"><span class="n">np</span><span class="o">.</span><span class="n">fmod</span></a><span class="p">(</span><span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="n">D</span><span class="p">)),</span> <span class="mi">2</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/constants.html#numpy.pi" title="numpy.pi"><span class="n">np</span><span class="o">.</span><span class="n">pi</span></a><span class="p">)</span>
-<span class="n">A</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">NUFFT</span><span class="o">.</span><span class="n">type1</span><span class="p">(</span>
-    <span class="n">x</span><span class="p">,</span> <span class="n">N</span><span class="p">,</span>
-    <span class="n">isign</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span>
-    <span class="n">eps</span><span class="o">=</span><span class="mf">1e-9</span>
-<span class="p">)</span>
-<span class="n">A</span><span class="o">.</span><span class="n">plot_kernel</span><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/9c8347663ec88378aaae5057c1ae3264/operator-1.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/8b695d494c85f1c4793c328b97cbc021/operator-1.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ca2090d31fc0a86e6382087c1b5955b0/operator-1.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ee7aa894b3da122692fdf69beafcbe37/operator-1.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-1.png" class="plot-directive" src="../_images/operator-1.png"/>
-</figure>
-<p class="rubric">Notes</p>
-<p>Requires <a class="reference external" href="https://matplotlib.org/">Matplotlib</a> to be installed.</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.params">
-<span class="sig-name descname"><span class="pre">params</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.params"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.params" title="Link to this definition">#</a></dt>
-<dd><p>Compute internal parameters of the <a class="reference internal" href="../references.html#finufft" id="id18"><span>[FINUFFT]</span></a> implementation.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><p><strong>p</strong> – Internal parameters of the FINUFFT implementation, with fields:</p>
-<ul class="simple">
-<li><dl class="simple">
-<dt>upsample_factor: <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a></dt><dd><p>FFT upsampling factor &gt; 1</p>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt>kernel_width: <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Integer</span></code></a></dt><dd><p>Width of the spreading/interpolation kernels (in number of samples).</p>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt>kernel_beta: <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a></dt><dd><p>Kernel decay parameter <span class="math notranslate nohighlight">\(\beta &gt; 0\)</span>.</p>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt>fft_shape: (d,) [<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Integer</span></code></a>]</dt><dd><p>Size of the D-dimensional FFT(s) performed internally.</p>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt>dilation_factor: (d,) [<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>]</dt><dd><p>Dilation factor(s) <span class="math notranslate nohighlight">\(\gamma_{d}\)</span>. (Type-3 only)</p>
-</dd>
-</dl>
-</li>
-</ul>
-</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/collections.html#collections.namedtuple" title="(in Python v3.11)"><code class="xref py py-func docutils literal notranslate"><span class="pre">namedtuple()</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>When called from a chunked type-3 transform, <a class="reference internal" href="#pyxu.operator.NUFFT.params" title="pyxu.operator.NUFFT.params"><code class="xref py py-meth docutils literal notranslate"><span class="pre">params()</span></code></a> returns parameters of the
-equivalent monolithic type-3 transform.  The monolithic transform is seldom instantiable due to its large memory
-requirements.  This method can hence be used to estimate the memory savings induced by chunking.</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.auto_chunk">
-<span class="sig-name descname"><span class="pre">auto_chunk</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">max_mem</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_anisotropy</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">5</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.auto_chunk"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.auto_chunk" title="Link to this definition">#</a></dt>
-<dd><p>(Only applies to chunked type-3 transforms.)</p>
-<p>Auto-determine chunk indices per domain.</p>
-<p>Use this function if you don’t know how to optimally ‘cut’ x/z manually.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>max_mem</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Max FFT memory (MiB) allowed per sub-block. (Default = 10 MiB)</p></li>
-<li><p><strong>max_anisotropy</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – <p>Max tolerated (normalized) anisotropy ratio &gt;= 1.</p>
-<ul>
-<li><p>Setting close to 1 favors cubeoid-shaped partitions of x/z space.</p></li>
-<li><p>Setting large allows x/z-partitions to be highly-rectangular.</p></li>
-</ul>
-</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><ul class="simple">
-<li><p><strong>x_chunks</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[NDArray[int]]</span></code>) – (x_idx[0], …, x_idx[A-1]) x-coordinate chunk specifier.
-<code class="code docutils literal notranslate"><span class="pre">x_idx[k]</span></code> contains indices of <code class="code docutils literal notranslate"><span class="pre">x</span></code> which participate in the k-th NUFFT sub-problem.</p></li>
-<li><p><strong>z_chunks</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[NDArray[int]]</span></code>) – (z_idx[0], …, z_idx[B-1]) z-coordinate chunk specifier.
-<code class="code docutils literal notranslate"><span class="pre">z_idx[k]</span></code> contains indices of <code class="code docutils literal notranslate"><span class="pre">z</span></code> which participate in the k-th NUFFT sub-problem.</p></li>
-</ul>
-</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)">tuple</a>[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)">list</a>[<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>], <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)">list</a>[<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>]]</p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>Chunks are identified by a custom hierarchical clustering method, with main steps:</p>
-<ol class="arabic">
-<li><p><strong>Partition the NUFFT domains.</strong>
-Given a maximum FFT memory budget <span class="math notranslate nohighlight">\(B&gt;0\)</span> and chunk anisotropy <span class="math notranslate nohighlight">\(\alpha\geq 1\)</span>, partition the
-source/target domains into uniform rectangular cells.  The (half) widths of the source/target cells
-<span class="math notranslate nohighlight">\(h_{k}&gt;0\)</span> and <span class="math notranslate nohighlight">\(\eta_{k}&gt;0\)</span> in each dimension <span class="math notranslate nohighlight">\(k=\{1,\ldots d\}\)</span> are chosen so as to:</p>
-<p>Minimize the total number of partitions:</p>
-<div class="math notranslate nohighlight">
-\[N_{c}
-=
-\underbrace{\prod_{k=1}^{d} \frac{X_k}{h_k}}_{\text{Source partition count}}
-\times
-\underbrace{\prod_{k=1}^{d} \frac{Z_k}{\eta_k}}_{\text{Target partition count}}\]</div>
-<p>subject to:</p>
-<blockquote>
-<div><ol class="loweralpha">
-<li><div class="math notranslate nohighlight">
-\[\prod_{k=1}^{d} \eta_k h_k
-\leq
-(\pi/2\upsilon)^{d} \frac{B}{\delta \; \texttt{n_trans}},\]</div>
-<p>where</p>
-<blockquote>
-<div><ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\upsilon\)</span> denotes the NUFFT’s grid upsampling factor,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\delta\)</span> the number of bytes occupied by a complex number,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\texttt{n_trans}\)</span> the number of simultaneous transforms performed.</p></li>
-</ul>
-</div></blockquote>
-</li>
-<li><div class="math notranslate nohighlight">
-\[\begin{split}\begin{align*}
-    h_{k} &amp; \leq X_{k}, \quad k=\{1,\ldots,d\} \\
-    \eta_{k} &amp; \leq Z_{k}, \quad k=\{1,\ldots,d\}
-\end{align*}\end{split}\]</div>
-</li>
-<li><div class="math notranslate nohighlight">
-\[N_{c} \ge 1.\]</div>
-</li>
-<li><div class="math notranslate nohighlight">
-\[\begin{split}\begin{align*}
-    \frac{1}{\alpha} &amp; \leq \frac{h_{k}}{h_{j}} \frac{X_{j}}{X_{k}} \leq \alpha, \quad k \ne j, \\
-    \frac{1}{\alpha} &amp; \leq \frac{\eta_{k}}{\eta_{j}} \frac{Z_{j}}{Z_{k}} \leq \alpha, \quad k \ne j.
-\end{align*}\end{split}\]</div>
-</li>
-<li><div class="math notranslate nohighlight">
-\[\begin{align*}
-    \frac{1}{\alpha} &amp; \leq \frac{h_{k}}{\eta_{j}} \frac{Z_{j}}{X_{k}} \leq \alpha, \quad (j, k) = \{1,\ldots,d\}^{2}.
-\end{align*}\]</div>
-</li>
-</ol>
-</div></blockquote>
-<p>Constraint (a) ensures type-3 NUFFTs performed in each sub-problem do not exceed the FFT memory budget.
-Constraints (b-c) ensure that partitions are non-degenerate/non-trivial respectively.
-Constraints (d-e) limit the anisotropy of the partitioning cells in each domain and across domains.</p>
-</li>
-<li><p><strong>Data-independent Chunking.</strong>
-Chunk the data by assigning non-uniform samples to their enclosing cell in the partition.
-Empty partitions are dropped.</p></li>
-<li><p><strong>Data-dependent Chunk Fusion.</strong>
-Since (1) is data-independent, data chunks obtained in (2) may split clusters among adjacent chunks, which is
-undesirable.  Clusters whose joint-spread is small enough are hence fused hierarchically.</p></li>
-</ol>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>This procedure yields a small number of memory-capped and well-separated data chunks in source/target
-domains.  However, it may result in unbalanced chunks, with some chunks containing significantly more
-data-points than others.  FINUFFT mitigates the unbalanced-chunk problem by spawning multiple threads to
-process dense clusters.</p>
-</div>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.NUFFT.allocate" title="pyxu.operator.NUFFT.allocate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">allocate()</span></code></a>, <a class="reference internal" href="#pyxu.operator.NUFFT.diagnostic_plot" title="pyxu.operator.NUFFT.diagnostic_plot"><code class="xref py py-meth docutils literal notranslate"><span class="pre">diagnostic_plot()</span></code></a>, <a class="reference internal" href="#pyxu.operator.NUFFT.stats" title="pyxu.operator.NUFFT.stats"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stats()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.allocate">
-<span class="sig-name descname"><span class="pre">allocate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x_chunks</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z_chunks</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">direct_eval_threshold</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10000</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.allocate"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.allocate" title="Link to this definition">#</a></dt>
-<dd><p>(Only applies to chunked type-3 transforms.)</p>
-<p>Allocate NUFFT sub-problems based on chunk specification.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>x_chunks</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[NDArray[int]</span> <span class="pre">|</span> <span class="pre">slice]</span></code>) – (x_idx[0], …, x_idx[A-1]) x-coordinate chunk specifier.
-<code class="code docutils literal notranslate"><span class="pre">x_idx[k]</span></code> contains indices of <code class="code docutils literal notranslate"><span class="pre">x</span></code> which participate in the k-th NUFFT sub-problem.</p></li>
-<li><p><strong>z_chunks</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[NDArray[int]</span> <span class="pre">|</span> <span class="pre">slice]</span></code>) – (z_idx[0], …, z_idx[B-1]) z-coordinate chunk specifier.
-<code class="code docutils literal notranslate"><span class="pre">z_idx[k]</span></code> contains indices of <code class="code docutils literal notranslate"><span class="pre">z</span></code> which participate in the k-th NUFFT sub-problem.</p></li>
-<li><p><strong>direct_eval_threshold</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – <p>If provided: lower bound on <code class="docutils literal notranslate"><span class="pre">len(x)</span> <span class="pre">*</span> <span class="pre">len(z)</span></code> below which an NUFFT sub-problem is replaced with
-direct-evaluation (eps=0) for performance reasons.</p>
-<p>(Defaults to 10k as per the <a class="reference external" href="https://finufft.readthedocs.io/en/latest/#do-i-even-need-a-nufft">FINUFFT guidelines</a>.)</p>
-</p></li>
-</ul>
-</dd>
-</dl>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.NUFFT.auto_chunk" title="pyxu.operator.NUFFT.auto_chunk"><code class="xref py py-meth docutils literal notranslate"><span class="pre">auto_chunk()</span></code></a>, <a class="reference internal" href="#pyxu.operator.NUFFT.diagnostic_plot" title="pyxu.operator.NUFFT.diagnostic_plot"><code class="xref py py-meth docutils literal notranslate"><span class="pre">diagnostic_plot()</span></code></a>, <a class="reference internal" href="#pyxu.operator.NUFFT.stats" title="pyxu.operator.NUFFT.stats"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stats()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.diagnostic_plot">
-<span class="sig-name descname"><span class="pre">diagnostic_plot</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">domain</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.diagnostic_plot"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.diagnostic_plot" title="Link to this definition">#</a></dt>
-<dd><p>(Only applies to chunked type-3 transforms.)</p>
-<p>Plot data + tesselation structure for diagnostic purposes.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>domain</strong> (<code class="docutils literal notranslate"><span class="pre">'x'</span></code>, <code class="docutils literal notranslate"><span class="pre">'z'</span></code>) – Plot x-domain or z-domain data.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>fig</strong> – Diagnostic plot.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://matplotlib.org/stable/api/figure_api.html#matplotlib.figure.Figure" title="(in Matplotlib v3.7.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Figure</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<ul class="simple">
-<li><p>This method can only be called after <a class="reference internal" href="#pyxu.operator.NUFFT.allocate" title="pyxu.operator.NUFFT.allocate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">allocate()</span></code></a>.</p></li>
-<li><p>This method only works for 2D/3D domains.</p></li>
-</ul>
-<p class="rubric">Examples</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-
-<span class="n">rng</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/random/generator.html#numpy.random.default_rng" title="numpy.random.default_rng"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span></a><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
-<span class="n">D</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">N</span> <span class="o">=</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">500</span><span class="p">,</span> <span class="mi">200</span>
-<span class="n">rnd_points</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">_</span><span class="p">:</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">scale</span><span class="o">=</span><span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mf">0.25</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">D</span><span class="p">,)),</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">_</span><span class="p">,</span> <span class="n">D</span><span class="p">))</span>
-<span class="n">rnd_offset</span> <span class="o">=</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">D</span><span class="p">,))</span>
-<span class="n">scale</span> <span class="o">=</span> <span class="mi">20</span>
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.concatenate.html#numpy.concatenate" title="numpy.concatenate"><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span></a><span class="p">(</span>
-    <span class="p">[</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">M</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">M</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">M</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">M</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">M</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-    <span class="p">],</span>
-    <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
-<span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.concatenate.html#numpy.concatenate" title="numpy.concatenate"><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span></a><span class="p">(</span>
-    <span class="p">[</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-        <span class="n">rnd_points</span><span class="p">(</span><span class="n">N</span><span class="p">)</span> <span class="o">+</span> <span class="n">rnd_offset</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">,</span>
-    <span class="p">],</span>
-    <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
-<span class="p">)</span>
-
-<span class="n">kwargs</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#dict" title="dict"><span class="nb">dict</span></a><span class="p">(</span>
-    <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="p">,</span>
-    <span class="n">z</span><span class="o">=</span><span class="n">z</span><span class="p">,</span>
-    <span class="n">isign</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span>
-    <span class="n">eps</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
-<span class="p">)</span>
-<span class="n">A</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">NUFFT</span><span class="o">.</span><span class="n">type3</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">,</span> <span class="n">chunked</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-<span class="n">x_chunks</span><span class="p">,</span> <span class="n">z_chunks</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">auto_chunk</span><span class="p">(</span>
-    <span class="n">max_mem</span><span class="o">=</span><span class="mf">.1</span><span class="p">,</span>
-    <span class="n">max_anisotropy</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
-<span class="p">)</span>
-<span class="n">A</span><span class="o">.</span><span class="n">allocate</span><span class="p">(</span><span class="n">x_chunks</span><span class="p">,</span> <span class="n">z_chunks</span><span class="p">)</span>
-<span class="n">fig</span> <span class="o">=</span> <span class="n">A</span><span class="o">.</span><span class="n">diagnostic_plot</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
-<span class="n">fig</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/9029f349dcba6220309b295a9140982b/operator-2.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/b9ab671fb0a7f18372db2008f8f175b3/operator-2.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/6456824f0a6ba3b0c63ce20c17d96e7d/operator-2.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/1b73e81f624aaa2edc92c239025b33b2/operator-2.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-2.png" class="plot-directive" src="../_images/operator-2.png"/>
-</figure>
-<p class="rubric">Notes</p>
-<p>Requires <a class="reference external" href="https://matplotlib.org/">Matplotlib</a> to be installed.</p>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.NUFFT.stats">
-<span class="sig-name descname"><span class="pre">stats</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.stats"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.stats" title="Link to this definition">#</a></dt>
-<dd><p>(Only applies to chunked type-3 transforms.)</p>
-<p>Gather internal statistics about a chunked type-3 NUFFT.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Returns<span class="colon">:</span></dt>
-<dd class="field-odd"><p><p><strong>p</strong> – Statistics on the NUFFT chunks, with fields:</p>
-<ul class="simple">
-<li><dl class="simple">
-<dt>blk_count: <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Integer</span></code></a></dt><dd><p>Number of NUFFT chunks.</p>
-</dd>
-</dl>
-</li>
-<li><dl class="simple">
-<dt>dEval_count: <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Integer</span></code></a></dt><dd><p>Number of chunks directly evaluated via the NUDFT.</p>
-</dd>
-</dl>
-</li>
-</ul>
-</p>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/collections.html#collections.namedtuple" title="(in Python v3.11)"><code class="xref py py-func docutils literal notranslate"><span class="pre">namedtuple()</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.PartialDerivative">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PartialDerivative</span></span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#PartialDerivative"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.PartialDerivative" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
-<p>Partial derivative operator based on <a class="reference external" href="https://numba.pydata.org/numba-doc/latest/user/stencil.html">Numba stencils</a>.</p>
-<p class="rubric">Notes</p>
-<ul>
-<li><p>This operator approximates the partial derivative of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional signal <span class="math notranslate nohighlight">\(\mathbf{f} \in
-\mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span></p>
-<div class="math notranslate nohighlight">
-\[\frac{\partial^{n} \mathbf{f}}{\partial x_0^{n_0} \cdots \partial x_{D-1}^{n_{D-1}}} \in
-\mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\]</div>
-<p>where <span class="math notranslate nohighlight">\(\frac{\partial^{n_i}}{\partial x_i^{n_i}}\)</span> is the <span class="math notranslate nohighlight">\(n_i\)</span>-th order partial derivative along
-dimension <span class="math notranslate nohighlight">\(i\)</span> and <span class="math notranslate nohighlight">\(n = \prod_{i=0}^{D-1} n_{i}\)</span> is the total derivative order.</p>
-<p>Partial derivatives can be implemented with <a class="reference external" href="https://en.wikipedia.org/wiki/Finite_difference">finite differences</a> via the
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> constructor, or with the <a class="reference external" href="https://www.crisluengo.net/archives/22/">Gaussian
-derivative</a> via the
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a> constructor.</p>
-</li>
-<li><p>When using the <a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> constructor, the adjoint
-of the resulting linear operator will vary depending on the type of finite differences:</p>
-<ul>
-<li><p>For <code class="docutils literal notranslate"><span class="pre">forward</span></code> type, the adjoint corresponds to:</p>
-<p><span class="math notranslate nohighlight">\((\frac{\partial^{\text{fwd}}}{\partial x})^{\ast} = -\frac{\partial^{\text{bwd}}}{\partial x}\)</span></p>
-</li>
-<li><p>For <code class="docutils literal notranslate"><span class="pre">backward</span></code> type, the adjoint corresponds to:</p>
-<p><span class="math notranslate nohighlight">\((\frac{\partial^{\text{bwd}}}{\partial x})^{\ast} = -\frac{\partial^{\text{fwd}}}{\partial x}\)</span></p>
-</li>
-<li><p>For <code class="docutils literal notranslate"><span class="pre">central</span></code> type, and for the <a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>
-constructor, the adjoint corresponds to:</p>
-<p><span class="math notranslate nohighlight">\((\frac{\partial}{\partial x})^{\ast} = -\frac{\partial}{\partial x}\)</span></p>
-</li>
-</ul>
-</li>
-</ul>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>When dealing with high-order partial derivatives, the stencils required to compute them can become large,
-resulting in computationally expensive evaluations.
-In such scenarios, it can be more efficient to construct the partial derivative through a composition of
-lower-order partial derivatives.</p>
-</div>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><code class="xref py py-class docutils literal notranslate"><span class="pre">Gradient</span></code></a>, <a class="reference internal" href="#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><code class="xref py py-class docutils literal notranslate"><span class="pre">Laplacian</span></code></a>, <a class="reference internal" href="#pyxu.operator.Hessian" title="pyxu.operator.Hessian"><code class="xref py py-class docutils literal notranslate"><span class="pre">Hessian</span></code></a></p>
-</div>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.PartialDerivative.finite_difference">
-<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">finite_difference</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">scheme</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'forward'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">accuracy</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#PartialDerivative.finite_difference"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.PartialDerivative.finite_difference" title="Link to this definition">#</a></dt>
-<dd><p>Compute partial derivatives for multi-dimensional signals using finite differences.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>order</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[Integer]</span></code>) – Derivative order for each dimension.
-The total order of the partial derivative is the sum of the elements of the tuple.
-Use zeros to indicate dimensions in which the derivative should not be computed.</p></li>
-<li><p><strong>scheme</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – Type of finite differences: [‘forward, ‘backward, ‘central’].
-Defaults to ‘forward’.
-If a string is provided, the same <code class="code docutils literal notranslate"><span class="pre">scheme</span></code> is assumed for all dimensions.
-If a tuple is provided, it should have as many elements as <code class="code docutils literal notranslate"><span class="pre">order</span></code>.</p></li>
-<li><p><strong>accuracy</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Integer]</span></code>) – Determines the number of points used to approximate the derivative with finite differences (see <code class="code docutils literal notranslate"><span class="pre">Notes</span></code>).
-Defaults to 1.
-If an int is provided, the same <code class="code docutils literal notranslate"><span class="pre">accuracy</span></code> is assumed for all dimensions.
-If a tuple is provided, it should have as many elements as <code class="code docutils literal notranslate"><span class="pre">arg_shape</span></code>.</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU).
-Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Sampling step (i.e. distance between two consecutive elements of an array).
-Defaults to 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Partial derivative</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>We explain here finite differences for one-dimensional signals; this operator performs finite differences for
-multi-dimensional signals along dimensions specified by <code class="code docutils literal notranslate"><span class="pre">order</span></code>.</p>
-<p>This operator approximates derivatives with <a class="reference external" href="https://en.wikipedia.org/wiki/Finite_difference">finite differences</a>.
-It is inspired by the <a class="reference external" href="https://web.media.mit.edu/~crtaylor/calculator.html">Finite Difference Coefficients Calculator</a> to construct finite-difference approximations for the
-desired <em>(i)</em> derivative order, <em>(ii)</em> approximation accuracy, and <em>(iii)</em> finite difference type.
-Three basic types of finite differences are supported, which lead to the following first-order (<code class="docutils literal notranslate"><span class="pre">order</span> <span class="pre">=</span> <span class="pre">1</span></code>)
-operators with <code class="docutils literal notranslate"><span class="pre">accuracy</span> <span class="pre">=</span> <span class="pre">1</span></code> and sampling step <code class="docutils literal notranslate"><span class="pre">sampling</span> <span class="pre">=</span> <span class="pre">h</span></code> for one-dimensional signals:</p>
-<ul>
-<li><p><strong>Forward difference</strong>:
-Approximates the continuous operator <span class="math notranslate nohighlight">\(D_{F}f(x) = \frac{f(x+h) - f(x)}{h}\)</span> with the discrete operator</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{D}_{F} f [n] = \frac{f[n+1] - f[n]}{h},\]</div>
-<p>whose kernel is <span class="math notranslate nohighlight">\(d = \frac{1}{h}[-1, 1]\)</span> and center is (0, ).</p>
-</li>
-<li><p><strong>Backward difference</strong>:
-Approximates the continuous operator <span class="math notranslate nohighlight">\(D_{B}f(x) = \frac{f(x) - f(x-h)}{h}\)</span> with the discrete operator</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{D}_{B} f [n] = \frac{f[n] - f[n-1]}{h},\]</div>
-<p>whose kernel is <span class="math notranslate nohighlight">\(d = \frac{1}{h}[-1, 1]\)</span> and center is (1, ).</p>
-</li>
-<li><p><strong>Central difference</strong>:
-Approximates the continuous operator <span class="math notranslate nohighlight">\(D_{C}f(x) = \frac{f(x+h) - f(x-h)}{2h}\)</span> with the discrete operator</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{D}_{C} f [n] = \frac{f[n+1] - f[n-1]}{2h},\]</div>
-<p>whose kernel is <span class="math notranslate nohighlight">\(d = \frac{1}{h}[-\frac12, 0, \frac12]\)</span> and center is (1, ).</p>
-</li>
-</ul>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>For forward and backward differences, higher-order operators correspond to the composition of first-order
-operators.
-This is not the case for central differences: the second-order continuous operator is given by
-<span class="math notranslate nohighlight">\(D^2_{C}f(x) = \frac{f(x+h) - 2 f(x) + f(x-h)}{h}\)</span>, hence <span class="math notranslate nohighlight">\(D^2_{C} \neq D_{C} \circ D_{C}\)</span>.
-The corresponding discrete operator is given by <span class="math notranslate nohighlight">\(\mathbf{D}^2_{C} f [n] = \frac{f[n+1] - 2 f[n] +
-f[n-1]}{h}\)</span>, whose kernel is <span class="math notranslate nohighlight">\(d = \frac{1}{h}[1, -2, 1]\)</span> and center is (1, ).
-We refer to <a class="reference external" href="https://www.ams.org/journals/mcom/1988-51-184/S0025-5718-1988-0935077-0/S0025-5718-1988-0935077-0.pdf">this paper</a> for
-more details.</p>
-</div>
-<p>For a given derivative order <span class="math notranslate nohighlight">\(N\in\mathbb{Z}^{+}\)</span> and accuracy <span class="math notranslate nohighlight">\(a\in\mathbb{Z}^{+}\)</span>, the size
-<span class="math notranslate nohighlight">\(N_s\)</span> of the stencil kernel <span class="math notranslate nohighlight">\(d\)</span> used for finite differences is given by:</p>
-<ul class="simple">
-<li><p>For central differences: <span class="math notranslate nohighlight">\(N_s = 2 \lfloor\frac{N + 1}{2}\rfloor - 1 + a\)</span></p></li>
-<li><p>For forward and backward differences: <span class="math notranslate nohighlight">\(N_s = N + a\)</span></p></li>
-</ul>
-<p>For <span class="math notranslate nohighlight">\(N_s\)</span> given support indices <span class="math notranslate nohighlight">\(\{s_1, \ldots , s_{N_s} \} \subset \mathbb{Z}\)</span> and a derivative
-order <span class="math notranslate nohighlight">\(N&lt;N_s\)</span>, the stencil kernel <span class="math notranslate nohighlight">\(d = [d_1, \ldots, d_{N_s}]\)</span> of the finite-difference
-approximation of the derivative is obtained by solving the following system of linear equations (see the <a class="reference external" href="https://web.media.mit.edu/~crtaylor/calculator.html">Finite
-Difference Coefficients Calculator</a> documentation):</p>
-<div class="admonition-remark admonition">
-<p class="admonition-title">Remark</p>
-<p>The number of coefficients of the finite-difference kernel is chosen to guarantee the requested accuracy, but
-might be larger than requested accuracy.
-For example, if choosing <code class="code docutils literal notranslate"><span class="pre">scheme='central'</span></code> with <code class="code docutils literal notranslate"><span class="pre">accuracy=1</span></code>, it will create a kernel corresponding to
-<code class="code docutils literal notranslate"><span class="pre">accuracy=2</span></code>, as it is the minimum accuracy possible for such scheme (see the <a class="reference external" href="https://en.wikipedia.org/wiki/Finite_difference_coefficient">finite difference coefficient
-table</a>).</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\left(\begin{array}{ccc}
-s_{1}^{0} &amp; \cdots &amp; s_{N_s}^{0} \\
-\vdots &amp; \ddots &amp; \vdots \\
-s_{1}^{N_s-1} &amp; \cdots &amp; s_{N_s}^{N_s-1}
-\end{array}\right)\left(\begin{array}{c}
-d_{1} \\
-\vdots \\
-d_{N_s}
-\end{array}\right)= \frac{1}{h^{N}}\left(\begin{array}{c}
-\delta_{0, N} \\
-\vdots \\
-\delta_{i, N} \\
-\vdots \\
-\delta_{N_s-1, N}
-\end{array}\right),\end{split}\]</div>
-<p>where <span class="math notranslate nohighlight">\(\delta_{i, j}\)</span> is the Kronecker delta.</p>
-</div>
-<p>This class inherits its methods from <a class="reference internal" href="#pyxu.operator.Stencil" title="pyxu.operator.Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stencil</span></code></a>.</p>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.PartialDerivative" title="pyxu.operator.linop.diff.PartialDerivative"><span class="n">PartialDerivative</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># Shape of our image</span>
-<span class="c1"># Specify derivative order at each direction</span>
-<span class="n">df_dx</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>  <span class="c1"># Compute derivative of order 1 in first dimension</span>
-<span class="n">d2f_dy2</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>  <span class="c1"># Compute derivative of order 2 in second dimension</span>
-<span class="n">d3f_dxdy2</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>  <span class="c1"># Compute derivative of order 1 in first dimension and der. of order 2 in second dimension</span>
-<span class="c1"># Instantiate derivative operators</span>
-<span class="n">sigma</span> <span class="o">=</span> <span class="mf">2.0</span>
-<span class="n">diff1</span> <span class="o">=</span> <span class="n">PartialDerivative</span><span class="o">.</span><span class="n">gaussian_derivative</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="n">df_dx</span><span class="p">,</span> <span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span> <span class="o">/</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><span class="mi">2</span><span class="p">))</span>
-<span class="n">diff2</span> <span class="o">=</span> <span class="n">PartialDerivative</span><span class="o">.</span><span class="n">gaussian_derivative</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="n">d2f_dy2</span><span class="p">,</span> <span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span> <span class="o">/</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><span class="mi">2</span><span class="p">))</span>
-<span class="n">diff</span> <span class="o">=</span> <span class="n">PartialDerivative</span><span class="o">.</span><span class="n">gaussian_derivative</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="n">d3f_dxdy2</span><span class="p">,</span> <span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span><span class="p">)</span>
-<span class="c1"># Compute derivatives</span>
-<span class="n">out1</span> <span class="o">=</span> <span class="p">(</span><span class="n">diff1</span> <span class="o">*</span> <span class="n">diff2</span><span class="p">)(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">out2</span> <span class="o">=</span> <span class="n">diff</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="c1"># Plot derivatives</span>
-<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"f(x,y)"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">out1</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\frac{\partial^</span><span class="si">{3}</span><span class="s2"> f(x,y)}{\partial x\partial y^</span><span class="si">{2}</span><span class="s2">}$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-
-<span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">out2</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\frac{\partial^</span><span class="si">{3}</span><span class="s2"> f(x,y)}{\partial x\partial y^</span><span class="si">{2}</span><span class="s2">}$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
-
-<span class="c1"># Test approximation error</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#abs" title="abs"><span class="nb">abs</span></a><span class="p">(</span><span class="n">out1</span> <span class="o">-</span> <span class="n">out2</span><span class="p">)</span> <span class="o">/</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#abs" title="abs"><span class="nb">abs</span></a><span class="p">(</span><span class="n">out2</span><span class="p">)),</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/557f177f4b474935fc904081afacebf3/operator-3.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>)</p>
-<figure class="align-default" id="id32">
-<img alt="../_images/operator-3_00.png" class="plot-directive" src="../_images/operator-3_00.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/e0edab28ffa8a7b21d2c5383d9cb8c12/operator-3_00.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/5c238fb268b33a8da224f181740013f5/operator-3_00.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ec62b0e358ee5c0b4fe48a7f14c93a09/operator-3_00.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id32" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id33">
-<img alt="../_images/operator-3_01.png" class="plot-directive" src="../_images/operator-3_01.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/64198f23c5f65d9a6e63da1e1c3364d8/operator-3_01.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/2df7baa26b1216d90e237608efc19755/operator-3_01.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/fb2a08c73290a1f099ce4f662f384ba8/operator-3_01.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id33" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-</dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.PartialDerivative.gaussian_derivative">
-<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">gaussian_derivative</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">truncate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#PartialDerivative.gaussian_derivative"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="Link to this definition">#</a></dt>
-<dd><p>Compute partial derivatives for multi-dimensional signals using gaussian derivatives.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>order</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[Integer]</span></code>) – Derivative order for each dimension.
-The total order of the partial derivative is the sum of the elements of the tuple.
-Use zeros to indicate dimensions in which the derivative should not be computed.</p></li>
-<li><p><strong>sigma</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Standard deviation for the Gaussian kernel.
-Defaults to 1.0.
-If a float is provided, the same <code class="code docutils literal notranslate"><span class="pre">sigma</span></code> is assumed for all dimensions.
-If a tuple is provided, it should have as many elements as <code class="code docutils literal notranslate"><span class="pre">order</span></code>.</p></li>
-<li><p><strong>truncate</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Truncate the filter at this many standard deviations (at each side from the origin).
-Defaults to 3.0.
-If a float is provided, the same <code class="code docutils literal notranslate"><span class="pre">truncate</span></code> is assumed for all dimensions.
-If a tuple is provided, it should have as many elements as <code class="code docutils literal notranslate"><span class="pre">order</span></code>.</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU).
-Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Sampling step (i.e., the distance between two consecutive elements of an array).
-Defaults to 1.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Partial derivative.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>We explain here Gaussian derivatives for one-dimensional signals; this operator performs partial Gaussian
-derivatives for multi-dimensional signals along dimensions specified by <code class="docutils literal notranslate"><span class="pre">order</span></code>.</p>
-<p>A Gaussian derivative is an approximation of a derivative that consists in convolving the input function with a
-Gaussian function <span class="math notranslate nohighlight">\(g\)</span> before applying a derivative.
-In the continuous domain, the <span class="math notranslate nohighlight">\(N\)</span>-th order Gaussian derivative <span class="math notranslate nohighlight">\(D^N_G\)</span> amounts to a convolution with
-the <span class="math notranslate nohighlight">\(N\)</span>-th order derivative of <span class="math notranslate nohighlight">\(g\)</span>:</p>
-<div class="math notranslate nohighlight">
-\[D^N_G f (x)
-=
-\frac{\mathrm{d}^N (f * g) }{\mathrm{d} x^N} (x)
-=
-f(x) * \frac{\mathrm{d}^N g}{\mathrm{d} x^N} (x).\]</div>
-<p>For discrete signals <span class="math notranslate nohighlight">\(f[n]\)</span>, this operator is approximated by</p>
-<div class="math notranslate nohighlight">
-\[\mathbf{D}^N_G f [n]
-=
-f[n] *\frac{\mathrm{d}^N g}{\mathrm{d} x^N} \left(\frac{n}{h}\right),\]</div>
-<p>where <span class="math notranslate nohighlight">\(h\)</span> is the spacing between samples and the operator <span class="math notranslate nohighlight">\(*\)</span> is now a discrete convolution.</p>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>The operator <span class="math notranslate nohighlight">\(\mathbf{D}_{G} \circ \mathbf{D}_{G}\)</span> is not directly related to
-<span class="math notranslate nohighlight">\(\mathbf{D}_{G}^{2}\)</span>: Gaussian smoothing is performed twice in the case of the former, whereas it is
-performed only once in the case of the latter.</p>
-</div>
-<p>Note that in contrast with finite differences (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a>), Gaussian derivatives compute exact
-derivatives in the continuous domain, since Gaussians can be differentiated analytically.
-This derivative is then sampled in order to perform a discrete convolution.</p>
-<p>This class inherits its methods from <a class="reference internal" href="#pyxu.operator.Stencil" title="pyxu.operator.Stencil"><code class="xref py py-class docutils literal notranslate"><span class="pre">Stencil</span></code></a>.</p>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.PartialDerivative" title="pyxu.operator.linop.diff.PartialDerivative"><span class="n">PartialDerivative</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># Shape of our image</span>
-<span class="c1"># Specify derivative order at each direction</span>
-<span class="n">df_dx</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="c1"># Compute derivative of order 1 in first dimension</span>
-<span class="n">d2f_dy2</span> <span class="o">=</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="c1"># Compute derivative of order 2 in second dimension</span>
-<span class="n">d3f_dxdy2</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="c1"># Compute derivative of order 1 in first dimension and der. of order 2 in second dimension</span>
-<span class="c1"># Instantiate derivative operators</span>
-<span class="n">diff1</span> <span class="o">=</span> <span class="n">PartialDerivative</span><span class="o">.</span><span class="n">gaussian_derivative</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="n">df_dx</span><span class="p">,</span> <span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span>
-<span class="n">diff2</span> <span class="o">=</span> <span class="n">PartialDerivative</span><span class="o">.</span><span class="n">gaussian_derivative</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="n">d2f_dy2</span><span class="p">,</span> <span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span>
-<span class="n">diff</span> <span class="o">=</span> <span class="n">PartialDerivative</span><span class="o">.</span><span class="n">gaussian_derivative</span><span class="p">(</span><span class="n">order</span><span class="o">=</span><span class="n">d3f_dxdy2</span><span class="p">,</span> <span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span>
-<span class="c1"># Compute derivatives</span>
-<span class="n">out1</span> <span class="o">=</span> <span class="p">(</span><span class="n">diff1</span> <span class="o">*</span> <span class="n">diff2</span><span class="p">)(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">out2</span> <span class="o">=</span> <span class="n">diff</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">image</span><span class="p">),</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'f(x,y)'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">out1</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'$\frac{\partial^</span><span class="si">{3}</span><span class="s1"> f(x,y)}{\partial x\partial y^</span><span class="si">{2}</span><span class="s1">}$'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">out2</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'$\frac{\partial^</span><span class="si">{3}</span><span class="s1"> f(x,y)}{\partial x\partial y^</span><span class="si">{2}</span><span class="s1">}$'</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/c6b377da5d37f9a1a7bd869cb238734f/operator-4.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>)</p>
-<figure class="align-default" id="id34">
-<img alt="../_images/operator-4_00.png" class="plot-directive" src="../_images/operator-4_00.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/84c84a6dd5058dc024f4c28e976c67be/operator-4_00.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/0c27d2285c5e9a51cef246afff3163ad/operator-4_00.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/2e608f839a2dd0470c1ea869e20bccde/operator-4_00.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id34" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id35">
-<img alt="../_images/operator-4_01.png" class="plot-directive" src="../_images/operator-4_01.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/8f59a997c178a3e2bb89f1f4ce7dc2b0/operator-4_01.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ebd30b8cac6ffa23638f86e7e0cbfcf8/operator-4_01.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/c287d657992e4ff9fb0cd17bed7a0b5b/operator-4_01.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id35" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id36">
-<img alt="../_images/operator-4_02.png" class="plot-directive" src="../_images/operator-4_02.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/745f48dcf87b63655f3a16dcef7b2961/operator-4_02.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/980507e47f5840458f13ac6f6b9c23a7/operator-4_02.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/b0e4014986a0f5921e51c57c3f1d2893/operator-4_02.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id36" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-</dd></dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Gradient">
-<span class="sig-name descname"><span class="pre">Gradient</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">directions</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'fd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#Gradient"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Gradient" title="Link to this definition">#</a></dt>
-<dd><p>Gradient operator.</p>
-<p class="rubric">Notes</p>
-<p>This operator stacks the first-order partial derivatives of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional signal <span class="math notranslate nohighlight">\(\mathbf{f} \in
-\mathbb{R}^{N_{0} \times \cdots \times N_{D-1}}\)</span> along each dimension:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\boldsymbol{\nabla} \mathbf{f} = \begin{bmatrix}
-\frac{\partial \mathbf{f}}{\partial x_0} \\
-\vdots \\
-\frac{\partial \mathbf{f}}{\partial x_{D-1}}
-\end{bmatrix} \in \mathbb{R}^{D \times N_{0} \times \cdots \times N_{D-1}}\end{split}\]</div>
-<p>The partial derivatives can be approximated by <a class="reference external" href="https://en.wikipedia.org/wiki/Finite_difference">finite differences</a> via the
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> constructor or by the <a class="reference external" href="https://www.crisluengo.net/archives/22/">Gaussian derivative</a> via
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a> constructor.
-The parametrization of the partial derivatives can be done via the keyword arguments <code class="code docutils literal notranslate"><span class="pre">**diff_kwargs</span></code>, which will
-default to the same values as the <a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-class docutils literal notranslate"><span class="pre">PartialDerivative</span></code></a> constructor.</p>
-<p>The gradient operator’s method <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code> allows reshaping the vectorized
-output gradient to <code class="docutils literal notranslate"><span class="pre">[n_dirs,</span> <span class="pre">N0,</span> <span class="pre">...,</span> <span class="pre">ND]</span></code> (see the example below).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>directions</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Integer]</span></code>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Gradient directions.
-Defaults to <code class="code docutils literal notranslate"><span class="pre">None</span></code>, which computes the gradient for all directions.</p></li>
-<li><p><strong>diff_method</strong> (<code class="docutils literal notranslate"><span class="pre">'gd'</span></code>, <code class="docutils literal notranslate"><span class="pre">'fd'</span></code>) – <p>Method used to approximate the derivative.
-Must be one of:</p>
-<ul>
-<li><p>’fd’ (default): finite differences</p></li>
-<li><p>’gd’: Gaussian derivative</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU).
-Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, use Dask to evaluate the different partial derivatives in parallel.</p></li>
-<li><p><strong>diff_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Keyword arguments to parametrize partial derivatives (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> and
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Gradient</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><span class="n">Gradient</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="c1"># Define input image</span>
-<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
-<span class="c1"># Instantiate gradient operator</span>
-<span class="n">grad</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><span class="n">Gradient</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">)</span>
-
-<span class="c1"># Compute gradients</span>
-<span class="n">output</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span> <span class="c1"># shape = (2000000, )</span>
-<span class="n">df_dx</span><span class="p">,</span> <span class="n">df_dy</span> <span class="o">=</span> <span class="n">grad</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">output</span><span class="p">)</span> <span class="c1"># shape = (2, 1000, 1000)</span>
-
-<span class="c1"># Plot image</span>
-<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Image"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-
-<span class="c1"># Plot gradient</span>
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">df_dx</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\partial f/ \partial x$"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">df_dy</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\partial f/ \partial y$"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/c722cabc6093f717e47975d57ffbc907/operator-5.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/36fe774d4b9531a9b7471cccf5df7552/operator-5.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/d1d43d473b0f4368b7c6e91e21b490e0/operator-5.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/758c43883775bf96c999d8249824235e/operator-5.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-5.png" class="plot-directive" src="../_images/operator-5.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">PartialDerivative()</span></code></a>, <a class="reference internal" href="#pyxu.operator.Jacobian" title="pyxu.operator.Jacobian"><code class="xref py py-func docutils literal notranslate"><span class="pre">Jacobian()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Jacobian">
-<span class="sig-name descname"><span class="pre">Jacobian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_channels</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">directions</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'fd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#Jacobian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Jacobian" title="Link to this definition">#</a></dt>
-<dd><p>Jacobian operator.</p>
-<p class="rubric">Notes</p>
-<p>This operator computes the first-order partial derivatives of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional vector-valued signal of
-<span class="math notranslate nohighlight">\(C\)</span> variables or channels <span class="math notranslate nohighlight">\(\mathbf{f} = [\mathbf{f}_{0}, \ldots, \mathbf{f}_{C-1}]\)</span> with
-<span class="math notranslate nohighlight">\(\mathbf{f}_{c} \in \mathbb{R}^{N_{0} \times \cdots \times N_{D-1}}\)</span>.</p>
-<p>The Jacobian of <span class="math notranslate nohighlight">\(\mathbf{f}\)</span> is computed via the gradient as follows:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{J} \mathbf{f} = \begin{bmatrix}
-(\boldsymbol{\nabla} \mathbf{f}_{0})^{\top} \\
-\vdots \\
-(\boldsymbol{\nabla} \mathbf{f}_{C-1})^{\top} \\
-\end{bmatrix} \in \mathbb{R}^{C \times D \times N_0 \times \cdots \times N_{D-1}}\end{split}\]</div>
-<p>The partial derivatives can be approximated by <a class="reference external" href="https://en.wikipedia.org/wiki/Finite_difference">finite differences</a> via the
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> constructor or by the <a class="reference external" href="https://www.crisluengo.net/archives/22/">Gaussian derivative</a> via
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a> constructor.
-The parametrization of the partial derivatives can be done via the keyword arguments <code class="code docutils literal notranslate"><span class="pre">**diff_kwargs</span></code>, which will
-default to the same values as the <a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-class docutils literal notranslate"><span class="pre">PartialDerivative</span></code></a> constructor.</p>
-<p>The Jacobian operator’s method <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code> allows reshaping the vectorized
-output Jacobian to <code class="docutils literal notranslate"><span class="pre">[...,</span> <span class="pre">n_channels,</span> <span class="pre">n_dirs,</span> <span class="pre">N0,</span> <span class="pre">...,</span> <span class="pre">ND]</span></code> (see the example below).</p>
-<p><strong>Remark</strong></p>
-<p>Pyxu’s convention when it comes to field-vectors, is to work with vectorized arrays.  However, the memory order of
-these arrays before raveling should be <code class="code docutils literal notranslate"><span class="pre">[S_0,</span> <span class="pre">...,</span> <span class="pre">S_D,</span> <span class="pre">C,</span> <span class="pre">N]</span></code> shape, with <code class="code docutils literal notranslate"><span class="pre">S_0,</span> <span class="pre">...,</span> <span class="pre">S_D</span></code> being stacking
-dimensions, <code class="code docutils literal notranslate"><span class="pre">C</span></code> being the number of variables or channels, and <code class="code docutils literal notranslate"><span class="pre">N</span></code> being the size of the domain (for example, <code class="code docutils literal notranslate"><span class="pre">N</span> <span class="pre">=</span>
-<span class="pre">npixels_x</span> <span class="pre">*</span> <span class="pre">npixels_y</span></code> for a 2D image).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>n_channels</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Number of channels or variables of the input vector-valued signal.
-The Jacobian with <code class="code docutils literal notranslate"><span class="pre">n_channels==1</span></code> yields the gradient.</p></li>
-<li><p><strong>directions</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Integer]</span></code>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Gradient directions.
-Defaults to <code class="code docutils literal notranslate"><span class="pre">None</span></code>, which computes the gradient for all directions.</p></li>
-<li><p><strong>diff_method</strong> (<code class="docutils literal notranslate"><span class="pre">"gd"</span></code>, <code class="docutils literal notranslate"><span class="pre">"fd"</span></code>) – <p>Method used to approximate the derivative.
-Must be one of:</p>
-<ul>
-<li><p>’fd’ (default): finite differences</p></li>
-<li><p>’gd’: Gaussian derivative</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU).
-Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, use Dask to evaluate the different partial derivatives in parallel.</p></li>
-<li><p><strong>diff_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Keyword arguments to parametrize partial derivatives (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> and
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Jacobian</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Jacobian" title="pyxu.operator.Jacobian"><span class="n">Jacobian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.tile.html#numpy.tile" title="numpy.tile"><span class="n">np</span><span class="o">.</span><span class="n">tile</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
-<span class="n">jac</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Jacobian" title="pyxu.operator.Jacobian"><span class="n">Jacobian</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">image</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="n">n_channels</span><span class="o">=</span><span class="n">image</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">jac</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">jac</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span>
-<span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">15</span><span class="p">))</span>
-<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#range" title="range"><span class="nb">range</span></a><span class="p">(</span><span class="mi">3</span><span class="p">):</span>
-    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#range" title="range"><span class="nb">range</span></a><span class="p">(</span><span class="mi">2</span><span class="p">):</span>
-        <span class="n">axes</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">out</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="p">[</span><span class="s2">"Reds"</span><span class="p">,</span> <span class="s2">"Greens"</span><span class="p">,</span> <span class="s2">"Blues"</span><span class="p">][</span><span class="n">j</span><span class="p">])</span>
-        <span class="n">axes</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s2">"$\partial I_</span><span class="se">{{</span><span class="si">{</span><span class="p">[</span><span class="s1">'R'</span><span class="p">,</span><span class="w"> </span><span class="s1">'G'</span><span class="p">,</span><span class="w"> </span><span class="s1">'B'</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s2">/\partial</span><span class="se">{{</span><span class="si">{</span><span class="p">[</span><span class="s1">'x'</span><span class="p">,</span><span class="w"> </span><span class="s1">'y'</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="si">}</span><span class="se">}}</span><span class="s2">$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.suptitle.html#matplotlib.pyplot.suptitle" title="matplotlib.pyplot.suptitle"><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span></a><span class="p">(</span><span class="s2">"Jacobian"</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/8b75e17542eb060a859009378ccf739e/operator-6.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/51314ba6ee1ae39115d8e0d37bb6ae91/operator-6.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/3a7603daabb4101f49f7a9dd513ab803/operator-6.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/4617a7e816843b4107fe1d29530b7702/operator-6.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-6.png" class="plot-directive" src="../_images/operator-6.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><code class="xref py py-func docutils literal notranslate"><span class="pre">Gradient()</span></code></a>, <a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">PartialDerivative()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Divergence">
-<span class="sig-name descname"><span class="pre">Divergence</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">directions</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'fd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#Divergence"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Divergence" title="Link to this definition">#</a></dt>
-<dd><p>Divergence operator.</p>
-<p class="rubric">Notes</p>
-<p>This operator computes the expansion or outgoingness of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional vector-valued signal of <span class="math notranslate nohighlight">\(C\)</span>
-variables <span class="math notranslate nohighlight">\(\mathbf{f} = [\mathbf{f}_{0}, \ldots, \mathbf{f}_{C-1}]\)</span> with <span class="math notranslate nohighlight">\(\mathbf{f}_{c} \in
-\mathbb{R}^{N_{0} \times \cdots \times N_{D-1}}\)</span>.</p>
-<p>The Divergence of <span class="math notranslate nohighlight">\(\mathbf{f}\)</span> is computed via the adjoint of the gradient as follows:</p>
-<div class="math notranslate nohighlight">
-\[\operatorname{Div} \mathbf{f} = \boldsymbol{\nabla}^{\ast} \mathbf{f}
-= \begin{bmatrix}
-\frac{\partial \mathbf{f}}{\partial x_0} + \cdots + \frac{\partial \mathbf{f}}{\partial x_{D-1}}
-\end{bmatrix} \in \mathbb{R}^{N_{0} \times \cdots \times N_{D-1}}\]</div>
-<p>The partial derivatives can be approximated by <a class="reference external" href="https://en.wikipedia.org/wiki/Finite_difference">finite differences</a> via the
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> constructor or by the <a class="reference external" href="https://www.crisluengo.net/archives/22/">Gaussian derivative</a> via
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a> constructor.
-The parametrization of the partial derivatives can be done via the keyword arguments <code class="code docutils literal notranslate"><span class="pre">**diff_kwargs</span></code>, which will
-default to the same values as the <a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-class docutils literal notranslate"><span class="pre">PartialDerivative</span></code></a> constructor.</p>
-<p>When using finite differences to compute the Divergence (i.e., <code class="docutils literal notranslate"><span class="pre">diff_method</span> <span class="pre">=</span> <span class="pre">"fd"</span></code>), the divergence returns the
-adjoint of the gradient in reversed order:</p>
-<ul class="simple">
-<li><p>For <code class="docutils literal notranslate"><span class="pre">forward</span></code> type divergence, the adjoint of the gradient of “backward” type is used.</p></li>
-<li><p>For <code class="docutils literal notranslate"><span class="pre">backward</span></code> type divergence, the adjoint of the gradient of “forward” type is used.</p></li>
-</ul>
-<p>For <code class="docutils literal notranslate"><span class="pre">central</span></code> type divergence, and for the Gaussian derivative method (i.e., <code class="docutils literal notranslate"><span class="pre">diff_method</span> <span class="pre">=</span> <span class="pre">"gd"</span></code>), the adjoint
-of the gradient of “central” type is used (no reversed order).</p>
-<p>The divergence operator’s method <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code> allows reshaping the
-vectorized output divergence to <code class="docutils literal notranslate"><span class="pre">[...,</span> <span class="pre">N0,</span> <span class="pre">...,</span> <span class="pre">ND]</span></code>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>directions</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Integer]</span></code>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Divergence directions.
-Defaults to <code class="code docutils literal notranslate"><span class="pre">None</span></code>, which computes the divergence for all directions.</p></li>
-<li><p><strong>diff_method</strong> (<code class="docutils literal notranslate"><span class="pre">"gd"</span></code>, <code class="docutils literal notranslate"><span class="pre">"fd"</span></code>) – <p>Method used to approximate the derivative.
-Must be one of:</p>
-<ul>
-<li><p>’fd’ (default): finite differences</p></li>
-<li><p>’gd’: Gaussian derivative</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU).
-Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, use Dask to evaluate the different partial derivatives in parallel.</p></li>
-<li><p><strong>diff_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Keyword arguments to parametrize partial derivatives (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> and
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Divergence</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><span class="n">Gradient</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Divergence" title="pyxu.operator.Divergence"><span class="n">Divergence</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><span class="n">Laplacian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
-<span class="n">grad</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><span class="n">Gradient</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">div</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Divergence" title="pyxu.operator.Divergence"><span class="n">Divergence</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="c1"># Construct Laplacian via composition</span>
-<span class="n">laplacian1</span> <span class="o">=</span> <span class="n">div</span> <span class="o">*</span> <span class="n">grad</span>
-<span class="c1"># Compare to default Laplacian</span>
-<span class="n">laplacian2</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><span class="n">Laplacian</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">output1</span> <span class="o">=</span> <span class="n">laplacian1</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<span class="n">output2</span> <span class="o">=</span> <span class="n">laplacian2</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
-<span class="n">im</span> <span class="o">=</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.log.html#numpy.log" title="numpy.log"><span class="n">np</span><span class="o">.</span><span class="n">log</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#abs" title="abs"><span class="nb">abs</span></a><span class="p">(</span><span class="n">output1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arg_shape</span><span class="p">))</span>
-<span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Laplacian via composition"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="n">im</span> <span class="o">=</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.log.html#numpy.log" title="numpy.log"><span class="n">np</span><span class="o">.</span><span class="n">log</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#abs" title="abs"><span class="nb">abs</span></a><span class="p">(</span><span class="n">output1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arg_shape</span><span class="p">))</span>
-<span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Default Laplacian"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/a30e3ded8c1066a4592a760dd92364c9/operator-7.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/84355f586daab57f0013b1d59aea0d7c/operator-7.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/a38dda46342bca2d4b49ded8ed4e9096/operator-7.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/59deb88b8c72373ae195592f25d7ee24/operator-7.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-7.png" class="plot-directive" src="../_images/operator-7.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><code class="xref py py-func docutils literal notranslate"><span class="pre">Gradient()</span></code></a>, <a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">PartialDerivative()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Hessian">
-<span class="sig-name descname"><span class="pre">Hessian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">directions</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'all'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'fd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#Hessian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Hessian" title="Link to this definition">#</a></dt>
-<dd><p>Hessian operator.</p>
-<p class="rubric">Notes</p>
-<p>The Hessian matrix or Hessian of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional signal <span class="math notranslate nohighlight">\(\mathbf{f} \in \mathbb{R}^{N_0 \times \cdots
-\times N_{D-1}}\)</span> is the square matrix of second-order partial derivatives:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{H} \mathbf{f} = \begin{bmatrix}
-\dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{0}^{2} } &amp;  \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{0}\,\partial x_{1} } &amp; \cdots &amp; \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{0} \, \partial x_{D-1} } \\
-\dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{1} \, \partial x_{0} } &amp; \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{1}^{2} } &amp; \cdots &amp; \dfrac{ \partial^{2}\mathbf{f} }{\partial x_{1} \,\partial x_{D-1}} \\
-\vdots &amp; \vdots &amp; \ddots &amp; \vdots \\
-\dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{D-1} \, \partial x_{0} } &amp; \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{D-1} \, \partial x_{1} } &amp; \cdots &amp; \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{D-1}^{2}}
-\end{bmatrix}\end{split}\]</div>
-<p>The partial derivatives can be approximated by <a class="reference external" href="https://en.wikipedia.org/wiki/Finite_difference">finite differences</a> via the
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> constructor or by the <a class="reference external" href="https://www.crisluengo.net/archives/22/">Gaussian derivative</a> via
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a> constructor.
-The parametrization of the partial derivatives can be done via the keyword arguments <code class="code docutils literal notranslate"><span class="pre">**diff_kwargs</span></code>, which will
-default to the same values as the <a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-class docutils literal notranslate"><span class="pre">PartialDerivative</span></code></a> constructor.</p>
-<p>The Hessian being symmetric, only the upper triangular part at most needs to be computed.
-Due to the (possibly) large size of the full Hessian, 4 different options are handled:</p>
-<ul>
-<li><p>[mode 0] <code class="docutils literal notranslate"><span class="pre">directions</span></code> is an integer, e.g.: <code class="docutils literal notranslate"><span class="pre">directions=0</span></code></p>
-<div class="math notranslate nohighlight">
-\[\partial^{2}\mathbf{f}/\partial x_{0}^{2}.\]</div>
-</li>
-<li><p>[mode 1] <code class="docutils literal notranslate"><span class="pre">directions</span></code> is a tuple of length 2, e.g.: <code class="docutils literal notranslate"><span class="pre">directions=(0,1)</span></code></p>
-<div class="math notranslate nohighlight">
-\[\partial^{2}\mathbf{f}/\partial x_{0}\partial x_{1}.\]</div>
-</li>
-<li><p>[mode 2] <code class="docutils literal notranslate"><span class="pre">directions</span></code> is a tuple of tuples, e.g.: <code class="docutils literal notranslate"><span class="pre">directions=((0,0),</span> <span class="pre">(0,1))</span></code></p>
-<div class="math notranslate nohighlight">
-\[\left(\frac{ \partial^{2}\mathbf{f} }{ \partial x_{0}^{2} }, \frac{ \partial^{2}\mathbf{f} }{ \partial x_{0}\partial x_{1} }\right).\]</div>
-</li>
-<li><p>[mode 3] <code class="docutils literal notranslate"><span class="pre">directions</span> <span class="pre">=</span> <span class="pre">'all'</span></code> (default), computes the Hessian for all directions (only the
-upper triangular part of the Hessian matrix), in row order, i.e.:</p>
-<div class="math notranslate nohighlight">
-\[\left(\frac{ \partial^{2}\mathbf{f} }{ \partial x_{0}^{2} }, \frac{ \partial^{2}\mathbf{f} }
-{ \partial x_{0}\partial x_{1} }, \, \ldots , \, \frac{ \partial^{2}\mathbf{f} }{ \partial x_{D-1}^{2} }\right).\]</div>
-</li>
-</ul>
-<p>The shape of the output <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> depends on the number of computed directions; by
-default (all directions), we have <span class="math notranslate nohighlight">\(\mathbf{H} \mathbf{f} \in \mathbb{R}^{\frac{D(D-1)}{2} \times N_0 \times
-\cdots \times N_{D-1}}\)</span>.</p>
-<p>The Hessian operator’s <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code> method allows reshaping the vectorized
-output Hessian to <code class="code docutils literal notranslate"><span class="pre">[n_dirs,</span> <span class="pre">N0,</span> <span class="pre">...,</span> <span class="pre">ND]</span></code> (see the example below).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>directions</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">(Integer</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">Integer)</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">((Integer</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">Integer)</span></code>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#Ellipsis" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">...</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">(Integer</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">Integer))</span></code>, <code class="docutils literal notranslate"><span class="pre">'all'</span></code>) – Hessian directions.
-Defaults to <code class="code docutils literal notranslate"><span class="pre">all</span></code>, which computes the Hessian for all directions. (See <code class="docutils literal notranslate"><span class="pre">Notes</span></code>.)</p></li>
-<li><p><strong>diff_method</strong> (<code class="docutils literal notranslate"><span class="pre">"gd"</span></code>, <code class="docutils literal notranslate"><span class="pre">"fd"</span></code>) – <p>Method used to approximate the derivative.
-Must be one of:</p>
-<ul>
-<li><p>’fd’ (default): finite differences</p></li>
-<li><p>’gd’: Gaussian derivative</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU).
-Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, use Dask to evaluate the different partial derivatives in parallel.</p></li>
-<li><p><strong>diff_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Keyword arguments to parametrize partial derivatives (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> and
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Hessian</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Hessian" title="pyxu.operator.Hessian"><span class="n">Hessian</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.PartialDerivative" title="pyxu.operator.linop.diff.PartialDerivative"><span class="n">PartialDerivative</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
-
-<span class="c1"># Instantiate Hessian operator</span>
-<span class="n">hessian</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Hessian" title="pyxu.operator.Hessian"><span class="n">Hessian</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">directions</span><span class="o">=</span><span class="s2">"all"</span><span class="p">)</span>
-<span class="c1"># Compute Hessian</span>
-<span class="n">output</span> <span class="o">=</span> <span class="n">hessian</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span> <span class="c1"># shape = (300000,)</span>
-<span class="n">d2f_dx2</span><span class="p">,</span> <span class="n">d2f_dxdy</span><span class="p">,</span> <span class="n">d2f_dy2</span> <span class="o">=</span> <span class="n">hessian</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">output</span><span class="p">)</span>
-
-<span class="c1"># Plot</span>
-<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Image"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">d2f_dx2</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\partial^</span><span class="si">{2}</span><span class="s2"> f/ \partial x^</span><span class="si">{2}</span><span class="s2">$"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">d2f_dxdy</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\partial^</span><span class="si">{2}</span><span class="s2"> f/ \partial x\partial y$"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">d2f_dy2</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\partial^</span><span class="si">{2}</span><span class="s2"> f/ \partial y^</span><span class="si">{2}</span><span class="s2">$"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/cac3dcf5082691d7fec7aafb5a70b646/operator-8.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/cb592e426f343abde6179a6c6c588c24/operator-8.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/298e89895fe824420ba2e49aeb0c3fea/operator-8.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/7e7493ef5be8fe7afc5d4591de150cb7/operator-8.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-8.png" class="plot-directive" src="../_images/operator-8.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-class docutils literal notranslate"><span class="pre">PartialDerivative</span></code></a>, <a class="reference internal" href="#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><code class="xref py py-class docutils literal notranslate"><span class="pre">Gradient</span></code></a>, <a class="reference internal" href="#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><code class="xref py py-class docutils literal notranslate"><span class="pre">Laplacian</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Laplacian">
-<span class="sig-name descname"><span class="pre">Laplacian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">directions</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'fd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#Laplacian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Laplacian" title="Link to this definition">#</a></dt>
-<dd><p>Laplacian operator.</p>
-<p class="rubric">Notes</p>
-<p>The Laplacian of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional signal <span class="math notranslate nohighlight">\(\mathbf{f} \in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span>
-is the sum of second-order partial derivatives across all input directions:</p>
-<div class="math notranslate nohighlight">
-\[\sum_{d = 0}^{D-1} \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{d}^{2} }\]</div>
-<p>The partial derivatives can be approximated by <a class="reference external" href="https://en.wikipedia.org/wiki/Finite_difference">finite differences</a> via the
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> constructor or by the <a class="reference external" href="https://www.crisluengo.net/archives/22/">Gaussian derivative</a> via
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a> constructor.
-The parametrization of the partial derivatives can be done via the keyword arguments <code class="code docutils literal notranslate"><span class="pre">**diff_kwargs</span></code>, which will
-default to <code class="code docutils literal notranslate"><span class="pre">scheme='central'</span></code> and <code class="code docutils literal notranslate"><span class="pre">accuracy=2</span></code> for <code class="code docutils literal notranslate"><span class="pre">diff_method='fd'</span></code> (finite difference), and the same values as
-the <a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-class docutils literal notranslate"><span class="pre">PartialDerivative</span></code></a> constructor for <code class="code docutils literal notranslate"><span class="pre">diff_method='gd'</span></code> (gaussian
-derivative).</p>
-<p>The Laplacian operator’s method <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code> allows reshaping the
-vectorized output Laplacian to <code class="docutils literal notranslate"><span class="pre">[...,</span> <span class="pre">N0,</span> <span class="pre">...,</span> <span class="pre">ND]</span></code> (see the example below).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>directions</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Integer]</span></code>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Laplacian directions. Defaults to <code class="code docutils literal notranslate"><span class="pre">None</span></code>, which computes the Laplacian with all directions.</p></li>
-<li><p><strong>diff_method</strong> (<code class="docutils literal notranslate"><span class="pre">"gd"</span></code>, <code class="docutils literal notranslate"><span class="pre">"fd"</span></code>) – <p>Method used to approximate the derivative.
-Must be one of:</p>
-<ul>
-<li><p>’fd’ (default): finite differences</p></li>
-<li><p>’gd’: Gaussian derivative</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU).
-Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, use Dask to evaluate the different partial derivatives in parallel.</p></li>
-<li><p><strong>diff_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Keyword arguments to parametrize partial derivatives (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> and
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Laplacian</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><span class="n">Laplacian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="c1"># Define input image</span>
-<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
-<span class="c1"># Compute Laplacian</span>
-<span class="n">laplacian</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><span class="n">Laplacian</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">output</span> <span class="o">=</span> <span class="n">laplacian</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<span class="n">output</span> <span class="o">=</span> <span class="n">laplacian</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">output</span><span class="p">)</span> <span class="c1"># shape = (1, 1000, 1000)</span>
-<span class="c1"># Plot</span>
-<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Image"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-
-<span class="n">im</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">output</span><span class="o">.</span><span class="n">squeeze</span><span class="p">())</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\partial^</span><span class="si">{2}</span><span class="s2"> f/ \partial x^</span><span class="si">{2}</span><span class="s2">+\partial^</span><span class="si">{2}</span><span class="s2"> f/ \partial y^</span><span class="si">{2}</span><span class="s2">$"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-
-<span class="n">fig</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/d95682f2902576513757e8747a4f94d8/operator-9.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/fe6968ec011cf22e38035319bd778af2/operator-9.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/4b255f3f357b804c1d553a554aa9a10e/operator-9.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/524c1e2c0e80a155bd2bc9ca41e01180/operator-9.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-9.png" class="plot-directive" src="../_images/operator-9.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-class docutils literal notranslate"><span class="pre">PartialDerivative</span></code></a>, <a class="reference internal" href="#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><code class="xref py py-class docutils literal notranslate"><span class="pre">Gradient</span></code></a>, <a class="reference internal" href="#pyxu.operator.Hessian" title="pyxu.operator.Hessian"><code class="xref py py-class docutils literal notranslate"><span class="pre">Hessian</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.DirectionalDerivative">
-<span class="sig-name descname"><span class="pre">DirectionalDerivative</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">directions</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'fd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#DirectionalDerivative"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.DirectionalDerivative" title="Link to this definition">#</a></dt>
-<dd><p>Directional derivative operator.</p>
-<p class="rubric">Notes</p>
-<p>The <strong>first-order</strong> <code class="docutils literal notranslate"><span class="pre">DirectionalDerivative</span></code> of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional signal <span class="math notranslate nohighlight">\(\mathbf{f} \in
-\mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> applies a derivative along the direction specified by a constant
-unitary vector <span class="math notranslate nohighlight">\(\mathbf{v} \in \mathbb{R}^D\)</span>:</p>
-<div class="math notranslate nohighlight">
-\[\boldsymbol{\nabla}_\mathbf{v} \mathbf{f} = \sum_{i=0}^{D-1} v_i \frac{\partial \mathbf{f}}{\partial x_i} \in
-\mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\]</div>
-<p>or along spatially-varying directions <span class="math notranslate nohighlight">\(\mathbf{v} = [\mathbf{v}_0, \ldots , \mathbf{v}_{D-1}]^\top \in
-\mathbb{R}^{D \times N_0 \times \cdots \times N_{D-1} }\)</span> where each direction <span class="math notranslate nohighlight">\(\mathbf{v}_{\cdot, i_0, \ldots
-, i_{D-1}} \in \mathbb{R}^D\)</span> for any <span class="math notranslate nohighlight">\(0 \leq i_d \leq N_d-1\)</span> with <span class="math notranslate nohighlight">\(0 \leq d \leq D-1\)</span> is a unitary
-vector:</p>
-<div class="math notranslate nohighlight">
-\[\boldsymbol{\nabla}_\mathbf{v} \mathbf{f} = \sum_{i=0}^{D-1} \mathbf{v}_i \odot
-\frac{\partial \mathbf{f}}{\partial x_i} \in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}},\]</div>
-<p>where <span class="math notranslate nohighlight">\(\odot\)</span> denotes the Hadamard (elementwise) product.</p>
-<p>Note that choosing <span class="math notranslate nohighlight">\(\mathbf{v}= \mathbf{e}_d \in \mathbb{R}^D\)</span> (the <span class="math notranslate nohighlight">\(d\)</span>-th canonical basis vector)
-amounts to the first-order <a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">PartialDerivative()</span></code></a> operator applied along axis
-<span class="math notranslate nohighlight">\(d\)</span>.</p>
-<p>The <strong>second-order</strong> <code class="docutils literal notranslate"><span class="pre">DirectionalDerivative</span></code> <span class="math notranslate nohighlight">\(\boldsymbol{\nabla}^2_{\mathbf{v}_{1, 2}}\)</span> is obtained by
-composing the first-order directional derivatives <span class="math notranslate nohighlight">\(\boldsymbol{\nabla}_{\mathbf{v}_{1}}\)</span> and
-<span class="math notranslate nohighlight">\(\boldsymbol{\nabla}_{\mathbf{v}_{2}}\)</span>:</p>
-<div class="math notranslate nohighlight">
-\[\boldsymbol{\nabla}_{\mathbf{v}_{1}} (\boldsymbol{\nabla}_{\mathbf{v}_{2}} \mathbf{f}) =
-\boldsymbol{\nabla}_{\mathbf{v}_{1}} (\sum_{i=0}^{D-1} {v_{2}}_{i} \frac{\partial \mathbf{f}}{\partial x_i}) =
-\sum_{j=0}^{D-1} {v_{1}}_{j} \frac{\partial}{\partial x_j} (\sum_{i=0}^{D-1} {v_{2}}_{i} \frac{\partial \mathbf{f}}{\partial x_i}) =
-\sum_{i, j=0}^{D-1} {v_{1}}_{j} {v_{2}}_{i} \frac{\partial}{\partial x_j} \frac{\partial}{\partial x_i}\mathbf{f} =
-\mathbf{v}_{1}^{\top}\mathbf{H}\mathbf{f}\mathbf{v}_{2},\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathbf{H}\)</span> is the discrete Hessian operator, implemented via
-<a class="reference internal" href="#pyxu.operator.Hessian" title="pyxu.operator.Hessian"><code class="xref py py-class docutils literal notranslate"><span class="pre">Hessian</span></code></a>.</p>
-<p>Higher-order <code class="docutils literal notranslate"><span class="pre">DirectionalDerivative</span></code> <span class="math notranslate nohighlight">\(\boldsymbol{\nabla}^{N}_\mathbf{v}\)</span> can be obtained by composing the
-first-order directional derivative <span class="math notranslate nohighlight">\(\boldsymbol{\nabla}_\mathbf{v}\)</span> <span class="math notranslate nohighlight">\(N\)</span> times.</p>
-<p>The directional derivative operator’s method <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code>
-allows reshaping the vectorized output directional derivative to <code class="docutils literal notranslate"><span class="pre">[...,</span> <span class="pre">N0,</span> <span class="pre">...,</span> <span class="pre">ND]</span></code> (see the example below).</p>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<ul class="simple">
-<li><p><a class="reference internal" href="#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">DirectionalDerivative()</span></code></a> instances are <strong>not array module-agnostic</strong>: they
-will only work with NDArrays belonging to the same array module as <code class="docutils literal notranslate"><span class="pre">directions</span></code>. Inner
-computations may recast input arrays when the precision of <code class="docutils literal notranslate"><span class="pre">directions</span></code> does not match the user-requested
-precision.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">directions</span></code> are always normalized to be unit vectors.</p></li>
-</ul>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>order</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Which directional derivative (restricted to 1: First or 2: Second, see <code class="docutils literal notranslate"><span class="pre">Notes</span></code>).</p></li>
-<li><p><strong>directions</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – <p>For <code class="docutils literal notranslate"><span class="pre">order=1</span></code>, it can be a single direction (array of size <span class="math notranslate nohighlight">\((D,)\)</span>, where <span class="math notranslate nohighlight">\(D\)</span> is the number of
-axes) or spatially-varying directions:</p>
-<ul>
-<li><p>array of size <span class="math notranslate nohighlight">\((D, N_0 \times \ldots \times N_{D-1})\)</span> for <code class="docutils literal notranslate"><span class="pre">order=1</span></code>, i.e., one direction per element
-in the gradient, and,</p></li>
-<li><p>array of size <span class="math notranslate nohighlight">\((D * (D + 1) / 2, N_0 \times \ldots \times N_{D-1})\)</span> for <code class="docutils literal notranslate"><span class="pre">order=2</span></code>, i.e., one direction
-per element in the Hessian.</p></li>
-</ul>
-<p>For <code class="docutils literal notranslate"><span class="pre">order=2</span></code>, it can be a tuple/list of two single directions or spatially-varying dimensions of the same
-shape, which will compute <span class="math notranslate nohighlight">\(\mathbf{v}_{1}^{\top}\mathbf{H}\mathbf{f}\mathbf{v}_{2}\)</span> or a single direction,
-as for <code class="docutils literal notranslate"><span class="pre">order=1</span></code>, which will compute <span class="math notranslate nohighlight">\(\mathbf{v}_{1}^{\top}\mathbf{H}\mathbf{f}\mathbf{v}_{1}\)</span>. Note
-that for <code class="docutils literal notranslate"><span class="pre">order=2</span></code>, even though directions are spatially-varying, no differentiation is performed for this
-parameter.</p>
-</p></li>
-<li><p><strong>diff_method</strong> (<code class="docutils literal notranslate"><span class="pre">"gd"</span></code>, <code class="docutils literal notranslate"><span class="pre">"fd"</span></code>) – <p>Method used to approximate the derivative. Must be one of:</p>
-<ul>
-<li><p>’fd’ (default): finite differences</p></li>
-<li><p>’gd’: Gaussian derivative</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, use Dask to evaluate the different partial derivatives in parallel.</p></li>
-<li><p><strong>diff_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Keyword arguments to parametrize partial derivatives (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> and
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Directional derivative</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><span class="n">DirectionalDerivative</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">directions</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
-<span class="n">directions</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">directions</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">dop</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><span class="n">DirectionalDerivative</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">z</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">directions</span><span class="o">=</span><span class="n">directions</span><span class="p">)</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">dop</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">dop</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span>
-<span class="n">dop2</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><span class="n">DirectionalDerivative</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">z</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">directions</span><span class="o">=</span><span class="n">directions</span><span class="p">)</span>
-<span class="n">out2</span> <span class="o">=</span> <span class="n">dop2</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">dop2</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span>
-<span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
-<span class="n">axs</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.ravel.html#numpy.ravel" title="numpy.ravel"><span class="n">np</span><span class="o">.</span><span class="n">ravel</span></a><span class="p">(</span><span class="n">axs</span><span class="p">)</span>
-<span class="n">h</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">shading</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">)</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">quiver</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">directions</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="n">directions</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Signal and directions of first derivatives"</span><span class="p">)</span>
-
-<span class="n">h</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(),</span> <span class="n">shading</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"First-order directional derivatives"</span><span class="p">)</span>
-
-<span class="n">h</span> <span class="o">=</span> <span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">pcolormesh</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">out2</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(),</span> <span class="n">shading</span><span class="o">=</span><span class="s2">"auto"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
-<span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Second-order directional derivative"</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/f54ac688c85e54a5c4e01ac51d047db1/operator-10.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/027b1d95119170b929f57668d02810ce/operator-10.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/86e69c2455bde978da9d846de7a188a9/operator-10.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/e8ddacc83821817f83af535a3fdc0c3d/operator-10.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-10.png" class="plot-directive" src="../_images/operator-10.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><code class="xref py py-func docutils literal notranslate"><span class="pre">Gradient()</span></code></a>, <a class="reference internal" href="#pyxu.operator.DirectionalGradient" title="pyxu.operator.DirectionalGradient"><code class="xref py py-func docutils literal notranslate"><span class="pre">DirectionalGradient()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.DirectionalGradient">
-<span class="sig-name descname"><span class="pre">DirectionalGradient</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">directions</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'fd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#DirectionalGradient"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.DirectionalGradient" title="Link to this definition">#</a></dt>
-<dd><p>Directional gradient operator.</p>
-<p class="rubric">Notes</p>
-<p>The <code class="docutils literal notranslate"><span class="pre">DirectionalGradient</span></code> of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional signal <span class="math notranslate nohighlight">\(\mathbf{f} \in \mathbb{R}^{N_0 \times \cdots
-\times N_{D-1}}\)</span> stacks the directional derivatives of <span class="math notranslate nohighlight">\(\mathbf{f}\)</span> along a list of <span class="math notranslate nohighlight">\(m\)</span> directions
-<span class="math notranslate nohighlight">\(\mathbf{v}_i\)</span> for <span class="math notranslate nohighlight">\(1 \leq i \leq m\)</span>:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\boldsymbol{\nabla}_{\mathbf{v}_1, \ldots ,\mathbf{v}_m} \mathbf{f} = \begin{bmatrix}
-     \boldsymbol{\nabla}_{\mathbf{v}_1} \\
-     \vdots\\
-     \boldsymbol{\nabla}_{\mathbf{v}_m}\\
-    \end{bmatrix} \mathbf{f} \in \mathbb{R}^{m \times N_0 \times \cdots \times N_{D-1}},\end{split}\]</div>
-<p>where <span class="math notranslate nohighlight">\(\boldsymbol{\nabla}_{\mathbf{v}_i}\)</span> is the first-order directional derivative along
-<span class="math notranslate nohighlight">\(\mathbf{v}_i\)</span> implemented with <a class="reference internal" href="#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">DirectionalDerivative()</span></code></a>, with
-<span class="math notranslate nohighlight">\(\mathbf{v}_i \in \mathbb{R}^D\)</span> or <span class="math notranslate nohighlight">\(\mathbf{v}_i \in \mathbb{R}^{D \times N_0 \times \cdots \times
-N_{D-1}}\)</span>.</p>
-<p>Note that choosing <span class="math notranslate nohighlight">\(m=D\)</span> and <span class="math notranslate nohighlight">\(\mathbf{v}_i = \mathbf{e}_i \in \mathbb{R}^D\)</span> (the <span class="math notranslate nohighlight">\(i\)</span>-th canonical
-basis vector) amounts to the <a class="reference internal" href="#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><code class="xref py py-func docutils literal notranslate"><span class="pre">Gradient()</span></code></a> operator.</p>
-<p>The directional gradient operator’s method <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code> allows
-reshaping the vectorized output directional derivative to <code class="docutils literal notranslate"><span class="pre">[...,</span> <span class="pre">n_dirs,</span> <span class="pre">N0,</span> <span class="pre">...,</span> <span class="pre">ND]</span></code> (see the example below).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>directions</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[NDArray]</span></code>) – List of directions, either constant (array of size <span class="math notranslate nohighlight">\((D,)\)</span>) or spatially-varying (array of size <span class="math notranslate nohighlight">\((D,
-N_0, \ldots, N_{D-1})\)</span>)</p></li>
-<li><p><strong>diff_method</strong> (<code class="docutils literal notranslate"><span class="pre">"gd"</span></code>, <code class="docutils literal notranslate"><span class="pre">"fd"</span></code>) – <p>Method used to approximate the derivative. Must be one of:</p>
-<ul>
-<li><p>’fd’ (default): finite differences</p></li>
-<li><p>’gd’: Gaussian derivative</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, use Dask to evaluate the different partial derivatives in parallel.</p></li>
-<li><p><strong>diff_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Keyword arguments to parametrize partial derivatives (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> and
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Directional gradient</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DirectionalGradient" title="pyxu.operator.DirectionalGradient"><span class="n">DirectionalGradient</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">directions1</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
-<span class="n">directions1</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">directions1</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">directions2</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
-<span class="n">directions2</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
-<span class="n">directions2</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">z</span><span class="o">.</span><span class="n">shape</span>
-<span class="n">dop</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DirectionalGradient" title="pyxu.operator.DirectionalGradient"><span class="n">DirectionalGradient</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">directions</span><span class="o">=</span><span class="p">[</span><span class="n">directions1</span><span class="p">,</span> <span class="n">directions2</span><span class="p">])</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">dop</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">dop</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<span class="n">h</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">shading</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.quiver.html#matplotlib.pyplot.quiver" title="matplotlib.pyplot.quiver"><span class="n">plt</span><span class="o">.</span><span class="n">quiver</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">directions1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">),</span> <span class="n">directions1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.quiver.html#matplotlib.pyplot.quiver" title="matplotlib.pyplot.quiver"><span class="n">plt</span><span class="o">.</span><span class="n">quiver</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">directions2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">),</span> <span class="n">directions2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'red'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'Signal $\mathbf</span><span class="si">{f}</span><span class="s1">$ and directions of derivatives'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<span class="n">h</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">out</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">shading</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'$\nabla_{\mathbf</span><span class="si">{v}</span><span class="s1">_0} \mathbf</span><span class="si">{f}</span><span class="s1">$'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<span class="n">h</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">out</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">shading</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'$\nabla_{\mathbf</span><span class="si">{v}</span><span class="s1">_1} \mathbf</span><span class="si">{f}</span><span class="s1">$'</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/eff18b5fef44d9c0d77331121a291e8f/operator-11.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>)</p>
-<figure class="align-default" id="id37">
-<img alt="../_images/operator-11_00.png" class="plot-directive" src="../_images/operator-11_00.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/507c4e7f83f78bf820d3fcff11186a24/operator-11_00.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/a55a7abe3d36074d183a6c2f04c216f0/operator-11_00.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/80e8d2262c83f8aa3286c318c355a06b/operator-11_00.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id37" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id38">
-<img alt="../_images/operator-11_01.png" class="plot-directive" src="../_images/operator-11_01.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/d334da298262f6838cd851168625d306/operator-11_01.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/c6cc146e09111e224dd32387b5f48af9/operator-11_01.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/fa1e9c492a3642cd6b2e4edb05885d27/operator-11_01.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id38" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id39">
-<img alt="../_images/operator-11_02.png" class="plot-directive" src="../_images/operator-11_02.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/c69c5719c815b1c976384c957f6e9777/operator-11_02.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/5acb9b748c14cdfa52f2de300f4722e9/operator-11_02.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/b5b8151ee0b479d40092a5e2c7ba8055/operator-11_02.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id39" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><code class="xref py py-func docutils literal notranslate"><span class="pre">Gradient()</span></code></a>, <a class="reference internal" href="#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">DirectionalDerivative()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.DirectionalLaplacian">
-<span class="sig-name descname"><span class="pre">DirectionalLaplacian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">directions</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'fd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#DirectionalLaplacian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.DirectionalLaplacian" title="Link to this definition">#</a></dt>
-<dd><p>Directional Laplacian operator.</p>
-<p>Sum of the second directional derivatives of a multi-dimensional array (at least two dimensions are required) along
-multiple <code class="docutils literal notranslate"><span class="pre">directions</span></code> for each entry of the array.</p>
-<p class="rubric">Notes</p>
-<p>The <code class="docutils literal notranslate"><span class="pre">DirectionalLaplacian</span></code> of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional signal <span class="math notranslate nohighlight">\(\mathbf{f} \in \mathbb{R}^{N_0 \times \cdots
-\times N_{D-1}}\)</span> sums the second-order directional derivatives of <span class="math notranslate nohighlight">\(\mathbf{f}\)</span> along a list of <span class="math notranslate nohighlight">\(m\)</span>
-directions <span class="math notranslate nohighlight">\(\mathbf{v}_i\)</span> for <span class="math notranslate nohighlight">\(1 \leq i \leq m\)</span>:</p>
-<div class="math notranslate nohighlight">
-\[\boldsymbol{\Delta}_{\mathbf{v}_1, \ldots ,\mathbf{v}_m} \mathbf{f} = \sum_{i=1}^m
-\boldsymbol{\nabla}^2_{\mathbf{v}_i} \mathbf{f} \in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}},\]</div>
-<p>where <span class="math notranslate nohighlight">\(\boldsymbol{\nabla}^2_{\mathbf{v}_i}\)</span> is the second-order directional derivative along
-<span class="math notranslate nohighlight">\(\mathbf{v}_i\)</span> implemented with <a class="reference internal" href="#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">DirectionalDerivative()</span></code></a>.</p>
-<p>Note that choosing <span class="math notranslate nohighlight">\(m=D\)</span> and <span class="math notranslate nohighlight">\(\mathbf{v}_i = \mathbf{e}_i \in \mathbb{R}^D\)</span> (the <span class="math notranslate nohighlight">\(i\)</span>-th canonical
-basis vector) amounts to the <a class="reference internal" href="#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><code class="xref py py-func docutils literal notranslate"><span class="pre">Laplacian()</span></code></a> operator.</p>
-<p>The directional Laplacian operator’s method <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code> allows
-reshaping the vectorized output directional Laplacian to <code class="docutils literal notranslate"><span class="pre">[...,</span> <span class="pre">N0,</span> <span class="pre">...,</span> <span class="pre">ND]</span></code> (see the example below).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>directions</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[NDArray]</span></code>) – List of directions, either constant (array of size <span class="math notranslate nohighlight">\((D,)\)</span>) or spatially-varying (array of size
-<span class="math notranslate nohighlight">\((D, N_0, \ldots, N_{D-1})\)</span>)</p></li>
-<li><p><strong>weights</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – List of optional positive weights with which each second directional derivative operator is multiplied.</p></li>
-<li><p><strong>diff_method</strong> (<code class="docutils literal notranslate"><span class="pre">"gd"</span></code>, <code class="docutils literal notranslate"><span class="pre">"fd"</span></code>) – <p>Method used to approximate the derivative. Must be one of:</p>
-<ul>
-<li><p>’fd’ (default): finite differences</p></li>
-<li><p>’gd’: Gaussian derivative</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, use Dask to evaluate the different partial derivatives in parallel.</p></li>
-<li><p><strong>diff_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Keyword arguments to parametrize partial derivatives (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> and
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Directional Laplacian</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DirectionalLaplacian" title="pyxu.operator.DirectionalLaplacian"><span class="n">DirectionalLaplacian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">directions1</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
-<span class="n">directions1</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">directions1</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">directions2</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
-<span class="n">directions2</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
-<span class="n">directions2</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">z</span><span class="o">.</span><span class="n">shape</span>
-<span class="n">dop</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DirectionalLaplacian" title="pyxu.operator.DirectionalLaplacian"><span class="n">DirectionalLaplacian</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">directions</span><span class="o">=</span><span class="p">[</span><span class="n">directions1</span><span class="p">,</span> <span class="n">directions2</span><span class="p">])</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">dop</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">dop</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<span class="n">h</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">shading</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.quiver.html#matplotlib.pyplot.quiver" title="matplotlib.pyplot.quiver"><span class="n">plt</span><span class="o">.</span><span class="n">quiver</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">directions1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">),</span> <span class="n">directions1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.quiver.html#matplotlib.pyplot.quiver" title="matplotlib.pyplot.quiver"><span class="n">plt</span><span class="o">.</span><span class="n">quiver</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">directions2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">),</span> <span class="n">directions2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'red'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Signal and directions of derivatives'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<span class="n">h</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(),</span> <span class="n">shading</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s1">'Directional Laplacian'</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/176694d4afd8c703e2f166119010b4a5/operator-12.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>)</p>
-<figure class="align-default" id="id40">
-<img alt="../_images/operator-12_00.png" class="plot-directive" src="../_images/operator-12_00.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/390b0bd8774742dfe7b58970af28e8c4/operator-12_00.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/00a03ca7daa38b33580314c7f5f51dcb/operator-12_00.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ddb65118b9c2654fdc8b8c39e75cc610/operator-12_00.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id40" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id41">
-<img alt="../_images/operator-12_01.png" class="plot-directive" src="../_images/operator-12_01.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/a91dd135849d728226e425b0ff0e1bd6/operator-12_01.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/43864c0e1201a6ed908d58fc3d598b00/operator-12_01.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/59794358488e15e2bf1ca40d5f99cb9e/operator-12_01.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id41" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><code class="xref py py-func docutils literal notranslate"><span class="pre">Laplacian()</span></code></a>, <a class="reference internal" href="#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">DirectionalDerivative()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.DirectionalHessian">
-<span class="sig-name descname"><span class="pre">DirectionalHessian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">directions</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'gd'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/diff.html#DirectionalHessian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.DirectionalHessian" title="Link to this definition">#</a></dt>
-<dd><p>Directional Hessian operator.</p>
-<p class="rubric">Notes</p>
-<p>The <code class="docutils literal notranslate"><span class="pre">DirectionalHessian</span></code> of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional signal <span class="math notranslate nohighlight">\(\mathbf{f} \in \mathbb{R}^{N_0 \times \cdots
-\times N_{D-1}}\)</span> stacks the second-order directional derivatives of <span class="math notranslate nohighlight">\(\mathbf{f}\)</span> along a list of <span class="math notranslate nohighlight">\(m\)</span>
-directions <span class="math notranslate nohighlight">\(\mathbf{v}_i\)</span> for <span class="math notranslate nohighlight">\(1 \leq i \leq m\)</span>:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{H}_{\mathbf{v}_1, \ldots ,\mathbf{v}_m} \mathbf{f} = \begin{bmatrix}
-\boldsymbol{\nabla}^2_{\mathbf{v}_0} &amp; \cdots &amp; \boldsymbol{\nabla}_{\mathbf{v}_0} \boldsymbol{\nabla}_{\mathbf{v}_{m-1}} \\
-\vdots &amp; \ddots &amp; \vdots \\
-\boldsymbol{\nabla}_{\mathbf{v}_{m-1}} \boldsymbol{\nabla}_{\mathbf{v}_0} &amp; \cdots &amp; \boldsymbol{\nabla}^2_{\mathbf{v}_{m-1}}
-\end{bmatrix} \mathbf{f},\end{split}\]</div>
-<p>where <span class="math notranslate nohighlight">\(\boldsymbol{\nabla}_{\mathbf{v}_i}\)</span> is the first-order directional derivative along
-<span class="math notranslate nohighlight">\(\mathbf{v}_i\)</span> implemented with <a class="reference internal" href="#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">DirectionalDerivative()</span></code></a>.</p>
-<p>However, due to the symmetry of the Hessian, only the upper triangular part is computed in practice:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{H}_{\mathbf{v}_1, \ldots ,\mathbf{v}_m} \mathbf{f} = \begin{bmatrix}
-\boldsymbol{\nabla}^2_{\mathbf{v}_0}\\
-\boldsymbol{\nabla}_{\mathbf{v}_0} \boldsymbol{\nabla}_{\mathbf{v}_{1}} \\
-\vdots \\
-\boldsymbol{\nabla}^2_{\mathbf{v}_{m-1}}
-\end{bmatrix} \mathbf{f} \in \mathbb{R}^{\frac{m (m-1)}{2} \times N_0 \times \cdots \times N_{D-1}}\end{split}\]</div>
-<p>Note that choosing <span class="math notranslate nohighlight">\(m=D\)</span> and <span class="math notranslate nohighlight">\(\mathbf{v}_i = \mathbf{e}_i \in \mathbb{R}^D\)</span> (the <span class="math notranslate nohighlight">\(i\)</span>-th canonical
-basis vector) amounts to the <a class="reference internal" href="#pyxu.operator.Hessian" title="pyxu.operator.Hessian"><code class="xref py py-func docutils literal notranslate"><span class="pre">Hessian()</span></code></a> operator.</p>
-<p>The directional Hessian operator’s method <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code> allows
-reshaping the vectorized output directional Hessian to <code class="docutils literal notranslate"><span class="pre">[...,</span> <span class="pre">n_dirs,</span> <span class="pre">N0,</span> <span class="pre">...,</span> <span class="pre">ND]</span></code> (see the example below).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>directions</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">list[NDArray]</span></code>) – List of directions, either constant (array of size <span class="math notranslate nohighlight">\((D,)\)</span>) or spatially-varying (array of size <span class="math notranslate nohighlight">\((D,
-N_0, \ldots, N_{D-1})\)</span>)</p></li>
-<li><p><strong>diff_method</strong> (<code class="docutils literal notranslate"><span class="pre">"gd"</span></code>, <code class="docutils literal notranslate"><span class="pre">"fd"</span></code>) – <p>Method used to approximate the derivative. Must be one of:</p>
-<ul>
-<li><p>’fd’ (default): finite differences</p></li>
-<li><p>’gd’: Gaussian derivative</p></li>
-</ul>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, use Dask to evaluate the different partial derivatives in parallel.</p></li>
-<li><p><strong>diff_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Keyword arguments to parametrize partial derivatives (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.finite_difference" title="pyxu.operator.PartialDerivative.finite_difference"><code class="xref py py-meth docutils literal notranslate"><span class="pre">finite_difference()</span></code></a> and
-<a class="reference internal" href="#pyxu.operator.PartialDerivative.gaussian_derivative" title="pyxu.operator.PartialDerivative.gaussian_derivative"><code class="xref py py-meth docutils literal notranslate"><span class="pre">gaussian_derivative()</span></code></a>)</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Directional Hessian</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DirectionalHessian" title="pyxu.operator.DirectionalHessian"><span class="n">DirectionalHessian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">directions1</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
-<span class="n">directions1</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">directions1</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">directions2</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
-<span class="n">directions2</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
-<span class="n">directions2</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">z</span><span class="o">.</span><span class="n">shape</span>
-<span class="n">d_hess</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DirectionalHessian" title="pyxu.operator.DirectionalHessian"><span class="n">DirectionalHessian</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">directions</span><span class="o">=</span><span class="p">[</span><span class="n">directions1</span><span class="p">,</span> <span class="n">directions2</span><span class="p">])</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">d_hess</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">d_hess</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<span class="n">h</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">shading</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.quiver.html#matplotlib.pyplot.quiver" title="matplotlib.pyplot.quiver"><span class="n">plt</span><span class="o">.</span><span class="n">quiver</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">directions1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">),</span> <span class="n">directions1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.quiver.html#matplotlib.pyplot.quiver" title="matplotlib.pyplot.quiver"><span class="n">plt</span><span class="o">.</span><span class="n">quiver</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">directions2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">),</span> <span class="n">directions2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="n">color</span><span class="o">=</span><span class="s1">'red'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'Signal $\mathbf</span><span class="si">{f}</span><span class="s1">$ and directions of derivatives'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<span class="n">h</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">out</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">shading</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'$\nabla^2_{\mathbf</span><span class="si">{v}</span><span class="s1">_0} \mathbf</span><span class="si">{f}</span><span class="s1">$'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<span class="n">h</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">out</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">shading</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'$\nabla_{\mathbf</span><span class="si">{v}</span><span class="s1">_0} \nabla_{\mathbf</span><span class="si">{v}</span><span class="s1">_</span><span class="si">{1}</span><span class="s1">} \mathbf</span><span class="si">{f}</span><span class="s1">$'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<span class="n">h</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.pcolormesh.html#matplotlib.pyplot.pcolormesh" title="matplotlib.pyplot.pcolormesh"><span class="n">plt</span><span class="o">.</span><span class="n">pcolormesh</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">out</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">shading</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">h</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s1">'$\nabla^2_{\mathbf</span><span class="si">{v}</span><span class="s1">_1} \mathbf</span><span class="si">{f}</span><span class="s1">$'</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/5bc77603e37ab6857e35a64c763b0285/operator-13.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>)</p>
-<figure class="align-default" id="id42">
-<img alt="../_images/operator-13_00.png" class="plot-directive" src="../_images/operator-13_00.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/ac2d8e4fa5ab3cfce5066292ea2e5ee4/operator-13_00.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/c5a9926c064600f986df1e9b30229987/operator-13_00.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/90b6ede7cd0b624bf04b02a069518152/operator-13_00.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id42" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id43">
-<img alt="../_images/operator-13_01.png" class="plot-directive" src="../_images/operator-13_01.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/ee39cd6f03890e23e667a22fcfb0878d/operator-13_01.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ecac7b967e6cb984424af14d8b946bce/operator-13_01.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ee22dc0a66baaeda24d579f4dd50f185/operator-13_01.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id43" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id44">
-<img alt="../_images/operator-13_02.png" class="plot-directive" src="../_images/operator-13_02.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/191962a7e06446281208e5b3542ba6d8/operator-13_02.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/74d1d3b6135054cbe9fd1fe59d6f8bad/operator-13_02.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/d0179760969d96a450497e7728d72b0c/operator-13_02.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id44" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id45">
-<img alt="../_images/operator-13_03.png" class="plot-directive" src="../_images/operator-13_03.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/2567cfd1b90b151e14d7b845b313e372/operator-13_03.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/29a19a1fb21ffd45345b62d68053b614/operator-13_03.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/2a27831b457a8e11354eed9aa36db333/operator-13_03.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id45" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Hessian" title="pyxu.operator.Hessian"><code class="xref py py-func docutils literal notranslate"><span class="pre">Hessian()</span></code></a>, <a class="reference internal" href="#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><code class="xref py py-func docutils literal notranslate"><span class="pre">DirectionalDerivative()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.MovingAverage">
-<span class="sig-name descname"><span class="pre">MovingAverage</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">center</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#MovingAverage"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.MovingAverage" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional moving average or uniform filter.</p>
-<p class="rubric">Notes</p>
-<p>This operator performs a convolution between the input <span class="math notranslate nohighlight">\(D\)</span>-dimensional NDArray <span class="math notranslate nohighlight">\(\mathbf{x} \in
-\mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> and a uniform <span class="math notranslate nohighlight">\(D\)</span>-dimensional filter <span class="math notranslate nohighlight">\(\mathbf{h} \in
-\mathbb{R}^{\text{size} \times \cdots \times \text{size}}\)</span> that computes the <code class="code docutils literal notranslate"><span class="pre">size</span></code>-point local mean values using
-separable kernels for improved performance.</p>
-<div class="math notranslate nohighlight">
-\[y_{i} = \frac{1}{|\mathcal{N}_{i}|}\sum_{j \in \mathcal{N}_{i}} x_{j}\]</div>
-<p>Where <span class="math notranslate nohighlight">\(\mathcal{N}_{i}\)</span> is the set of elements neighbouring the <span class="math notranslate nohighlight">\(i\)</span>-th element of the input array, and
-<span class="math notranslate nohighlight">\(\mathcal{N}_{i}\)</span> denotes its cardinality, i.e. the total number of neighbors.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – <p>Size of the moving average kernel.</p>
-<p>If a single integer value is provided, then the moving average filter will have as many dimensions as the input
-array.  If a tuple is provided, it should contain as many elements as <code class="code docutils literal notranslate"><span class="pre">arg_shape</span></code>.  For example, the <code class="docutils literal notranslate"><span class="pre">size=(1,</span>
-<span class="pre">3)</span></code> will convolve the input image with the filter <code class="docutils literal notranslate"><span class="pre">[[1,</span> <span class="pre">1,</span> <span class="pre">1]]</span> <span class="pre">/</span> <span class="pre">3</span></code>.</p>
-</p></li>
-<li><p><strong>center</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">IndexSpec</span></code>) – <p>(i_1, …, i_D) index of the kernel’s center.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">center</span></code> defines how a kernel is overlaid on inputs to produce outputs.
-For odd <code class="code docutils literal notranslate"><span class="pre">size</span></code>, it defaults to the central element (<code class="docutils literal notranslate"><span class="pre">center=size//2</span></code>).
-For even <code class="code docutils literal notranslate"><span class="pre">size</span></code> the desired center indices must be provided.</p>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="code docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU). Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – MovingAverage</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.MovingAverage" title="pyxu.operator.MovingAverage"><span class="n">MovingAverage</span></a>
-
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">11</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">image</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</span>
-
-<span class="n">ma</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.MovingAverage" title="pyxu.operator.MovingAverage"><span class="n">MovingAverage</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">ma</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">out</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/feb0d965c7c0bb35ac098ec3ef67df61/operator-14.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/c391db68b8dc3c5e9af1e480d97b4c31/operator-14.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/224d8e48ea022f3ad8e02331df42dace/operator-14.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/57fe8e40f534fdcff0e15bffe502c8fe/operator-14.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-14.png" class="plot-directive" src="../_images/operator-14.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Gaussian" title="pyxu.operator.Gaussian"><code class="xref py py-class docutils literal notranslate"><span class="pre">Gaussian</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Gaussian">
-<span class="sig-name descname"><span class="pre">Gaussian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">truncate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">order</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#Gaussian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Gaussian" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional Gaussian filter.</p>
-<p class="rubric">Notes</p>
-<p>This operator performs a convolution between the input <span class="math notranslate nohighlight">\(D\)</span>-dimensional NDArray <span class="math notranslate nohighlight">\(\mathbf{x} \in
-\mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> and a Gaussian <span class="math notranslate nohighlight">\(D\)</span>-dimensional filter <span class="math notranslate nohighlight">\(\mathbf{h} \in
-\mathbb{R}^{\text{size} \times \cdots \times \text{size}}\)</span> using separable kernels for improved performance.</p>
-<div class="math notranslate nohighlight">
-\[y_{i} = \sum_{j \in \mathcal{N}_{i}} a_{j} x_{j} \exp(\frac{d_{ij}^{2}}{\sigma^{2}})\]</div>
-<p>Where <span class="math notranslate nohighlight">\(\mathcal{N}_{i}\)</span> is the set of elements neighbouring the <span class="math notranslate nohighlight">\(i\)</span>-th element of the input array, and
-<span class="math notranslate nohighlight">\(a_{j} = \sum_{j \in \mathcal{N}_{i}} a_{j} \exp(\frac{d_{ij}^{2}}{\sigma^{2}})\)</span> normalizes the kernel to sum
-to one.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>sigma</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – <p>Standard deviation of the Gaussian kernel.</p>
-<p>If a scalar value is provided, then the Gaussian filter will have as many dimensions as the input array.
-If a tuple is provided, it should contain as many elements as <code class="code docutils literal notranslate"><span class="pre">arg_shape</span></code>.
-Use <code class="docutils literal notranslate"><span class="pre">0</span></code> to prevent filtering in a given dimension.
-For example, the <code class="docutils literal notranslate"><span class="pre">sigma=(0,</span> <span class="pre">3)</span></code> will convolve the input image in its last dimension.</p>
-</p></li>
-<li><p><strong>truncate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – Truncate the filter at this many standard deviations.
-Defaults to 3.0.</p></li>
-<li><p><strong>order</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – <p>Gaussian derivative order.</p>
-<p>Use <code class="docutils literal notranslate"><span class="pre">0</span></code> for the standard Gaussian kernel.</p>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="code docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Sampling step (i.e. distance between two consecutive elements of an array).
-Defaults to 1.</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU).
-Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Gaussian</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Gaussian" title="pyxu.operator.Gaussian"><span class="n">Gaussian</span></a>
-
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">11</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">image</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</span>
-
-<span class="n">gaussian</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Gaussian" title="pyxu.operator.Gaussian"><span class="n">Gaussian</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">gaussian</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">out</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/5822ec21ae4dcb79a8910f34bb426b2a/operator-15.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/427c29d9fe06f23074682a0c3cb7f952/operator-15.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/55854ad41c5a3d5cbee9b24ef1577582/operator-15.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/830c6cf1ca9ddce08ef358693dbce351/operator-15.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-15.png" class="plot-directive" src="../_images/operator-15.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.MovingAverage" title="pyxu.operator.MovingAverage"><code class="xref py py-class docutils literal notranslate"><span class="pre">MovingAverage</span></code></a>, <a class="reference internal" href="#pyxu.operator.DifferenceOfGaussians" title="pyxu.operator.DifferenceOfGaussians"><code class="xref py py-class docutils literal notranslate"><span class="pre">DifferenceOfGaussians</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.DifferenceOfGaussians">
-<span class="sig-name descname"><span class="pre">DifferenceOfGaussians</span></span><span class="sig-paren">(</span>
-<dl>
-<dd><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">low_sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">high_sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">low_truncate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3.0</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">high_truncate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3.0</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>,</dd>
-</dl>
-<span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#DifferenceOfGaussians"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.DifferenceOfGaussians" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional Difference of Gaussians filter.</p>
-<p class="rubric">Notes</p>
-<p>This operator uses the Difference of Gaussians (DoG) method to a <span class="math notranslate nohighlight">\(D\)</span>-dimensional NDArray <span class="math notranslate nohighlight">\(\mathbf{x} \in
-\mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> using separable kernels for improved performance.
-The DoG method blurs the input image with two Gaussian kernels with different sigma, and subtracts the more-blurred
-signal from the less-blurred image.
-This creates an output signal containing only the information from the original signal at the spatial scale
-indicated by the two sigmas.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>low_sigma</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – <p>Standard deviation of the Gaussian kernel with smaller sigmas across all axes.</p>
-<p>If a scalar value is provided, then the Gaussian filter will have as many dimensions as the input array.
-If a tuple is provided, it should contain as many elements as <code class="code docutils literal notranslate"><span class="pre">arg_shape</span></code>.
-Use <code class="docutils literal notranslate"><span class="pre">0</span></code> to prevent filtering in a given dimension.
-For example, the <code class="docutils literal notranslate"><span class="pre">low_sigma=(0,</span> <span class="pre">3)</span></code> will convolve the input image in its last dimension.</p>
-</p></li>
-<li><p><strong>high_sigma</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Standard deviation of the Gaussian kernel with larger sigmas across all axes.
-If <code class="docutils literal notranslate"><span class="pre">None</span></code> is given (default), sigmas for all axes are calculated as <code class="docutils literal notranslate"><span class="pre">1.6</span> <span class="pre">*</span> <span class="pre">low_sigma</span></code>.</p></li>
-<li><p><strong>low_truncate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – Truncate the filter at this many standard deviations.
-Defaults to 3.0.</p></li>
-<li><p><strong>high_truncate</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – Truncate the filter at this many standard deviations.
-Defaults to 3.0.</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="code docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Sampling step (i.e. distance between two consecutive elements of an array).
-Defaults to 1.</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU). Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – DifferenceOfGaussians</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DoG" title="pyxu.operator.DoG"><span class="n">DoG</span></a>
-
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">11</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">image</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</span>
-
-<span class="n">dog</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.DoG" title="pyxu.operator.DoG"><span class="n">DoG</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">,</span> <span class="n">low_sigma</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">dog</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">out</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/b720f3f70e5d870af630b0311b862bdc/operator-16.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/001882fa6559d942c582faa9cb948f03/operator-16.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/92c55fbba0661a785247389e08ad5597/operator-16.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/3350197cf4a2d8503d4a5460eee1fd3b/operator-16.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-16.png" class="plot-directive" src="../_images/operator-16.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Gaussian" title="pyxu.operator.Gaussian"><code class="xref py py-class docutils literal notranslate"><span class="pre">Gaussian</span></code></a>, <a class="reference internal" href="#pyxu.operator.Sobel" title="pyxu.operator.Sobel"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sobel</span></code></a>, <a class="reference internal" href="#pyxu.operator.Prewitt" title="pyxu.operator.Prewitt"><code class="xref py py-class docutils literal notranslate"><span class="pre">Prewitt</span></code></a>, <a class="reference internal" href="#pyxu.operator.Scharr" title="pyxu.operator.Scharr"><code class="xref py py-class docutils literal notranslate"><span class="pre">Scharr</span></code></a>, <a class="reference internal" href="#pyxu.operator.StructureTensor" title="pyxu.operator.StructureTensor"><code class="xref py py-class docutils literal notranslate"><span class="pre">StructureTensor</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.DoG">
-<span class="sig-name descname"><span class="pre">DoG</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">low_sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">high_sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">low_truncate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">high_truncate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pyxu.operator.DoG" title="Link to this definition">#</a></dt>
-<dd><p>Alias of <a class="reference internal" href="#pyxu.operator.DifferenceOfGaussians" title="pyxu.operator.DifferenceOfGaussians"><code class="xref py py-func docutils literal notranslate"><span class="pre">DifferenceOfGaussians()</span></code></a>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-<li><p><strong>dtype</strong> (<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><em>dtype</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>None</em><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><em>Type</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>_SupportsDType</em><em>[</em><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><em>dtype</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>]</em><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><em>int</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><em>SupportsIndex</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><em>SupportsIndex</em></a><em>]</em><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.11)"><em>List</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>_DTypeDict</em><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>]</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Laplace">
-<span class="sig-name descname"><span class="pre">Laplace</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#Laplace"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Laplace" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional Laplace filter.</p>
-<p>The implementation is based on second derivatives approximated via finite differences.</p>
-<p class="rubric">Notes</p>
-<p>This operator uses the applies the Laplace kernel <span class="math notranslate nohighlight">\([1 -2 1]\)</span> to a <span class="math notranslate nohighlight">\(D\)</span>-dimensional NDArray
-<span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> using separable kernels for improved
-performance.  The Laplace filter is commonly used to find high-frequency components in the signal, such as for
-example, the edges in an image.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="code docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Sampling step (i.e. distance between two consecutive elements of an array).
-Defaults to 1.</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU). Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – DifferenceOfGaussians</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Laplace" title="pyxu.operator.Laplace"><span class="n">Laplace</span></a>
-
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">11</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">image</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</span>
-
-<span class="n">laplace</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Laplace" title="pyxu.operator.Laplace"><span class="n">Laplace</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">laplace</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">out</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/67094c89382ad81380a52906901bb725/operator-17.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ea065ef29eb66de1c45bbe0702cc77be/operator-17.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/08c11a4f54d6a5f6b338299631747747/operator-17.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/73bedc7b7248ca036824dc8463b36828/operator-17.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-17.png" class="plot-directive" src="../_images/operator-17.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Sobel" title="pyxu.operator.Sobel"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sobel</span></code></a>, <a class="reference internal" href="#pyxu.operator.Prewitt" title="pyxu.operator.Prewitt"><code class="xref py py-class docutils literal notranslate"><span class="pre">Prewitt</span></code></a>, <a class="reference internal" href="#pyxu.operator.Scharr" title="pyxu.operator.Scharr"><code class="xref py py-class docutils literal notranslate"><span class="pre">Scharr</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Sobel">
-<span class="sig-name descname"><span class="pre">Sobel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#Sobel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Sobel" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional Sobel filter.</p>
-<p class="rubric">Notes</p>
-<p>This operator uses the applies the multi-dimensional Sobel filter to a <span class="math notranslate nohighlight">\(D\)</span>-dimensional NDArray
-<span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> using separable kernels for improved
-performance.  The Sobel filter applies the following edge filter in the dimensions of interest: <code class="docutils literal notranslate"><span class="pre">[1,</span> <span class="pre">0,</span> <span class="pre">-1]</span></code> and
-the smoothing filter on the rest of dimensions: <code class="docutils literal notranslate"><span class="pre">[1,</span> <span class="pre">2,</span> <span class="pre">1]</span> <span class="pre">/</span> <span class="pre">4</span></code>.  The Sobel filter is commonly used to find
-high-frequency components in the signal, such as for example, the edges in an image.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>axis</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – <p>Compute the edge filter along this axis. If not provided, the edge magnitude is computed.</p>
-<p>This is defined as: <code class="docutils literal notranslate"><span class="pre">np.sqrt(sum([sobel(array,</span> <span class="pre">axis=i)**2</span> <span class="pre">for</span> <span class="pre">i</span> <span class="pre">in</span> <span class="pre">range(array.ndim)])</span> <span class="pre">/</span> <span class="pre">array.ndim)</span></code> The
-magnitude is also computed if axis is a sequence.</p>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="code docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Sampling step (i.e. distance between two consecutive elements of an array).
-Defaults to 1.</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU). Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Sobel</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Sobel" title="pyxu.operator.Sobel"><span class="n">Sobel</span></a>
-
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">11</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">image</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</span>
-
-<span class="n">sobel</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Sobel" title="pyxu.operator.Sobel"><span class="n">Sobel</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">sobel</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">out</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/40fedab1780635b89af691e5c4ea11fb/operator-18.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/cde91f0a039a2f1ff6788278b2648951/operator-18.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/210cb0deb2ac8363471ad2f714bf5985/operator-18.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/2fc8c1957a4c7f9f2fe757e5469a31e4/operator-18.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-18.png" class="plot-directive" src="../_images/operator-18.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Prewitt" title="pyxu.operator.Prewitt"><code class="xref py py-class docutils literal notranslate"><span class="pre">Prewitt</span></code></a>, <a class="reference internal" href="#pyxu.operator.Scharr" title="pyxu.operator.Scharr"><code class="xref py py-class docutils literal notranslate"><span class="pre">Scharr</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Prewitt">
-<span class="sig-name descname"><span class="pre">Prewitt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#Prewitt"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Prewitt" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional Prewitt filter.</p>
-<p class="rubric">Notes</p>
-<p>This operator uses the applies the multi-dimensional Prewitt filter to a <span class="math notranslate nohighlight">\(D\)</span>-dimensional NDArray
-<span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> using separable kernels for improved
-performance.  The Prewitt filter applies the following edge filter in the dimensions of interest: <code class="docutils literal notranslate"><span class="pre">[1,</span> <span class="pre">0,</span> <span class="pre">-1]</span></code>,
-and the smoothing filter on the rest of dimensions: <code class="docutils literal notranslate"><span class="pre">[1,</span> <span class="pre">1,</span> <span class="pre">1]</span> <span class="pre">/</span> <span class="pre">3</span></code>.  The Prewitt filter is commonly used to find
-high-frequency components in the signal, such as for example, the edges in an image.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>axis</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – <p>Compute the edge filter along this axis. If not provided, the edge magnitude is computed. This is defined as:</p>
-<p><code class="docutils literal notranslate"><span class="pre">np.sqrt(sum([prewitt(array,</span> <span class="pre">axis=i)**2</span> <span class="pre">for</span> <span class="pre">i</span> <span class="pre">in</span> <span class="pre">range(array.ndim)])</span> <span class="pre">/</span> <span class="pre">array.ndim)</span></code> The magnitude is also
-computed if axis is a sequence.</p>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="code docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Sampling step (i.e. distance between two consecutive elements of an array).
-Defaults to 1.</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU). Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Prewitt</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Prewitt" title="pyxu.operator.Prewitt"><span class="n">Prewitt</span></a>
-
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">11</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">image</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</span>
-
-<span class="n">prewitt</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Prewitt" title="pyxu.operator.Prewitt"><span class="n">Prewitt</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">prewitt</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">out</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/821591bde9f2c4bb83a1dbdf85716dce/operator-19.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/3d5a83560b1cd58d557e6254a9784261/operator-19.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/8aaa0ff216ce48a45f853f1ad1ff4869/operator-19.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/501c0d344ad2b1378a6ffc9e3b3f1ab0/operator-19.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-19.png" class="plot-directive" src="../_images/operator-19.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Sobel" title="pyxu.operator.Sobel"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sobel</span></code></a>, <a class="reference internal" href="#pyxu.operator.Scharr" title="pyxu.operator.Scharr"><code class="xref py py-class docutils literal notranslate"><span class="pre">Scharr</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.Scharr">
-<span class="sig-name descname"><span class="pre">Scharr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#Scharr"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Scharr" title="Link to this definition">#</a></dt>
-<dd><p>Multi-dimensional Scharr filter.</p>
-<p class="rubric">Notes</p>
-<p>This operator uses the applies the multi-dimensional Scharr filter to a <span class="math notranslate nohighlight">\(D\)</span>-dimensional NDArray
-<span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> using separable kernels for improved
-performance.  The Scharr filter applies the following edge filter in the dimensions of interest: <code class="docutils literal notranslate"><span class="pre">[1,</span> <span class="pre">0,</span> <span class="pre">-1]</span></code>, and
-the smoothing filter on the rest of dimensions: <code class="docutils literal notranslate"><span class="pre">[3,</span> <span class="pre">10,</span> <span class="pre">3]</span> <span class="pre">/</span> <span class="pre">16</span></code>.  The Scharr filter is commonly used to find
-high-frequency components in the signal, such as for example, the edges in an image.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – Shape of the input array.</p></li>
-<li><p><strong>axis</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></a>) – <p>Compute the edge filter along this axis. If not provided, the edge magnitude is computed. This is defined as:</p>
-<p><code class="docutils literal notranslate"><span class="pre">np.sqrt(sum([scharr(array,</span> <span class="pre">axis=i)**2</span> <span class="pre">for</span> <span class="pre">i</span> <span class="pre">in</span> <span class="pre">range(array.ndim)])</span> <span class="pre">/</span> <span class="pre">array.ndim)</span></code> The magnitude is also
-computed if axis is a sequence.</p>
-</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[str]</span></code>) – <p>Boundary conditions.
-Multiple forms are accepted:</p>
-<ul>
-<li><p>str: unique mode shared amongst dimensions.
-Must be one of:</p>
-<ul>
-<li><p>’constant’ (default): zero-padding</p></li>
-<li><p>’wrap’</p></li>
-<li><p>’reflect’</p></li>
-<li><p>’symmetric’</p></li>
-<li><p>’edge’</p></li>
-</ul>
-</li>
-<li><p>tuple[str, …]: the <code class="code docutils literal notranslate"><span class="pre">d</span></code>-th dimension uses <code class="code docutils literal notranslate"><span class="pre">mode[d]</span></code> as boundary condition.</p></li>
-</ul>
-<p>(See <a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.pad.html#numpy.pad" title="(in NumPy v1.25)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.pad()</span></code></a> for details.)</p>
-</p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">list[Real]</span></code>) – Sampling step (i.e. distance between two consecutive elements of an array).
-Defaults to 1.</p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Input NDArray type (<code class="code docutils literal notranslate"><span class="pre">True</span></code> for GPU, <code class="code docutils literal notranslate"><span class="pre">False</span></code> for CPU). Defaults to <code class="code docutils literal notranslate"><span class="pre">False</span></code>.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Working precision of the linear operator.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – Scharr</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Scharr" title="pyxu.operator.Scharr"><span class="n">Scharr</span></a>
-
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="p">(</span><span class="mi">11</span><span class="p">,</span> <span class="mi">11</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">image</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.</span>
-
-<span class="n">scharr</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.Scharr" title="pyxu.operator.Scharr"><span class="n">Scharr</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
-<span class="n">out</span> <span class="o">=</span> <span class="n">scharr</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">image</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">out</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">*</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/d033201855f1ac9d7e8eb509601ad103/operator-20.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/80a3b5b858569587ccf5e93587163d10/operator-20.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/609e087aab0132654c29d1c90c1481a0/operator-20.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/5aff9c364459ff6030f38559ad70a41d/operator-20.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/operator-20.png" class="plot-directive" src="../_images/operator-20.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.Sobel" title="pyxu.operator.Sobel"><code class="xref py py-class docutils literal notranslate"><span class="pre">Sobel</span></code></a>, <a class="reference internal" href="#pyxu.operator.Prewitt" title="pyxu.operator.Prewitt"><code class="xref py py-class docutils literal notranslate"><span class="pre">Prewitt</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.operator.StructureTensor">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">StructureTensor</span></span><span class="sig-paren">(</span>
-<dl>
-<dd><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">diff_method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'fd'</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">smooth_sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">smooth_truncate</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">3.0</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">sampling</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">gpu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">parallel</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em>,</dd>
-</dl>
-<span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#StructureTensor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.StructureTensor" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a></p>
-<p>Structure tensor operator.</p>
-<p class="rubric">Notes</p>
-<p>The Structure Tensor, also known as the second-order moment tensor or the inertia tensor, is a matrix derived from
-the gradient of a function. It describes the distribution of the gradient (i.e., its prominent directions) in a
-specified neighbourhood around a point, and the degree to which those directions are coherent.  The structure tensor
-of a <span class="math notranslate nohighlight">\(D\)</span>-dimensional signal <span class="math notranslate nohighlight">\(\mathbf{f} \in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> can be
-written as:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{S}_\sigma \mathbf{f} = \mathbf{g}_{\sigma} * \nabla\mathbf{f} (\nabla\mathbf{f})^{\top} = \mathbf{g}_{\sigma} *
-\begin{bmatrix}
-\left( \dfrac{ \partial\mathbf{f} }{ \partial x_{0} } \right)^2 &amp;  \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{0}\,\partial x_{1} } &amp; \cdots &amp; \dfrac{ \partial\mathbf{f} }{ \partial x_{0} } \dfrac{ \partial\mathbf{f} }{ \partial x_{D-1} } \\
-\dfrac{ \partial\mathbf{f} }{ \partial x_{1} } \dfrac{ \partial\mathbf{f} }{ \partial x_{0} } &amp; \left( \dfrac{ \partial\mathbf{f} }{ \partial x_{1} }\right)^2 &amp; \cdots &amp; \dfrac{ \partial\mathbf{f} }{ \partial x_{1} } \dfrac{ \partial\mathbf{f} }{ \partial x_{D-1} } \\
-\vdots &amp; \vdots &amp; \ddots &amp; \vdots \\
-\dfrac{ \partial\mathbf{f} }{ \partial x_{D-1} } \dfrac{ \partial\mathbf{f} }{ \partial x_{0} } &amp; \dfrac{ \partial\mathbf{f} }{ \partial x_{D-1} } \dfrac{ \partial\mathbf{f} }{ \partial x_{1} } &amp; \cdots &amp; \left( \dfrac{ \partial\mathbf{f} }{ \partial x_{D-1}} \right)^2
-\end{bmatrix},\end{split}\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathbf{g}_{\sigma} \in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\)</span> is a discrete Gaussian filter
-with standard variation <span class="math notranslate nohighlight">\(\sigma\)</span> with which a convolution is performed elementwise.</p>
-<p>However, due to the symmetry of the structure tensor, only the upper triangular part is computed in practice:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{H}_{\mathbf{v}_1, \ldots ,\mathbf{v}_m} \mathbf{f} = \mathbf{g}_{\sigma} * \begin{bmatrix}
-\left( \dfrac{ \partial\mathbf{f} }{ \partial x_{0} } \right)^2 \\
-\dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{0}\,\partial x_{1} } \\
-\vdots \\
-\left( \dfrac{ \partial\mathbf{f} }{ \partial x_{D-1}} \right)^2
-\end{bmatrix} \mathbf{f} \in \mathbb{R}^{\frac{D (D-1)}{2} \times N_0 \times \cdots \times N_{D-1}}\end{split}\]</div>
-<section id="remark">
-<h2>Remark<a class="headerlink" href="#remark" title="Link to this heading">#</a></h2>
-<p>In case of using the finite differences (<code class="code docutils literal notranslate"><span class="pre">diff_type="fd"</span></code>), the finite difference scheme defaults to <code class="code docutils literal notranslate"><span class="pre">central</span></code> (see
-<a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-class docutils literal notranslate"><span class="pre">PartialDerivative</span></code></a>).</p>
-<p class="rubric">Example</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.StructureTensor" title="pyxu.operator.linop.filter.StructureTensor"><span class="n">StructureTensor</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="c1"># Define input image</span>
-<span class="n">n</span> <span class="o">=</span> <span class="mi">1000</span>
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<span class="n">nsamples</span> <span class="o">=</span> <span class="mi">2</span>
-<span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
-<span class="n">images</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.tile.html#numpy.tile" title="numpy.tile"><span class="n">np</span><span class="o">.</span><span class="n">tile</span></a><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="p">(</span><span class="n">nsamples</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">nsamples</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#print" title="print"><span class="nb">print</span></a><span class="p">(</span><span class="n">images</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>  <span class="c1"># (2, 1000000)</span>
-<span class="c1"># Instantiate structure tensor operator</span>
-<a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.StructureTensor" title="pyxu.operator.linop.filter.StructureTensor"><span class="n">structure_tensor</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.StructureTensor" title="pyxu.operator.linop.filter.StructureTensor"><span class="n">StructureTensor</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">)</span>
-
-<span class="n">outputs</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.html#pyxu.operator.StructureTensor" title="pyxu.operator.linop.filter.StructureTensor"><span class="n">structure_tensor</span></a><span class="p">(</span><span class="n">images</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#print" title="print"><span class="nb">print</span></a><span class="p">(</span><span class="n">outputs</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>  <span class="c1"># (2, 3000000)</span>
-<span class="c1"># Plot</span>
-<span class="n">outputs</span> <span class="o">=</span> <span class="n">structure_tensor</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">outputs</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#print" title="print"><span class="nb">print</span></a><span class="p">(</span><span class="n">outputs</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>  <span class="c1"># (2, 3, 1000, 1000)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">images</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Image"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">outputs</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s2">"$\hat</span><span class="si">{S}</span><span class="s2">_</span><span class="si">{xx}</span><span class="s2">$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">outputs</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s2">"$\hat</span><span class="si">{S}</span><span class="s2">_</span><span class="si">{xy}</span><span class="s2">$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">outputs</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="sa">r</span><span class="s2">"$\hat</span><span class="si">{S}</span><span class="s2">_</span><span class="si">{yy}</span><span class="s2">$"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html#matplotlib.pyplot.axis" title="matplotlib.pyplot.axis"><span class="n">plt</span><span class="o">.</span><span class="n">axis</span></a><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/7a311f51d351b440032a25d77b6b0f15/operator-21.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>)</p>
-<figure class="align-default" id="id46">
-<img alt="../_images/operator-21_00.png" class="plot-directive" src="../_images/operator-21_00.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/ecb8cc6e01fafd628c1f3f5476756590/operator-21_00.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/9fb2ea53b64737bdcfba96217fef5782/operator-21_00.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/673d72fb29625abae78650b04ff992cf/operator-21_00.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id46" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id47">
-<img alt="../_images/operator-21_01.png" class="plot-directive" src="../_images/operator-21_01.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/dbd13b2660ccf8ff01353b1a063aaa1c/operator-21_01.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/7fade2ac152b694790a10dace2a8fb9d/operator-21_01.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/129c00df1a520657bba17d5d67553f10/operator-21_01.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id47" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id48">
-<img alt="../_images/operator-21_02.png" class="plot-directive" src="../_images/operator-21_02.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/a8991112e97556caf0e2fd5883613b0a/operator-21_02.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/4ba5c9eaac728e0995605bd6a8c46c0b/operator-21_02.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/346e1717be7da8fa867cbbe2294f196a/operator-21_02.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id48" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<figure class="align-default" id="id49">
-<img alt="../_images/operator-21_03.png" class="plot-directive" src="../_images/operator-21_03.png"/>
-<figcaption>
-<p><span class="caption-text">(<a class="reference download internal" download="" href="../_downloads/e739c7c86eb1e91d889c2ba6a4a6af52/operator-21_03.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/c4dc0f0fa9d2ce5348b916d5ee685aba/operator-21_03.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/ebda9c8427d0061add5c36d23ac72518/operator-21_03.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</span><a class="headerlink" href="#id49" title="Link to this image">#</a></p>
-</figcaption>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.operator.PartialDerivative" title="pyxu.operator.PartialDerivative"><code class="xref py py-class docutils literal notranslate"><span class="pre">PartialDerivative</span></code></a>, <a class="reference internal" href="#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><code class="xref py py-class docutils literal notranslate"><span class="pre">Gradient</span></code></a>, <a class="reference internal" href="#pyxu.operator.Hessian" title="pyxu.operator.Hessian"><code class="xref py py-class docutils literal notranslate"><span class="pre">Hessian</span></code></a></p>
-</div>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.StructureTensor.unravel">
-<span class="sig-name descname"><span class="pre">unravel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#StructureTensor.unravel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.StructureTensor.unravel" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.StructureTensor.ravel">
-<span class="sig-name descname"><span class="pre">ravel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#StructureTensor.ravel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.StructureTensor.ravel" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.operator.StructureTensor.apply">
-<span class="sig-name descname"><span class="pre">apply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/linop/filter.html#StructureTensor.apply"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.StructureTensor.apply" title="Link to this definition">#</a></dt>
-<dd><p>Evaluate operator at specified point(s).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>arr</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, M) input points.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>out</strong> – (…, N) output points.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>smooth_sigma</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>smooth_truncate</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-<li><p><strong>dtype</strong> (<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><em>dtype</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>None</em><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><em>Type</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>_SupportsDType</em><em>[</em><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><em>dtype</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>]</em><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><em>int</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><em>SupportsIndex</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><em>SupportsIndex</em></a><em>]</em><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.11)"><em>List</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>_DTypeDict</em><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>]</em>) – </p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
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-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.ConstantValued"><code class="docutils literal notranslate"><span class="pre">ConstantValued()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.L1Norm"><code class="docutils literal notranslate"><span class="pre">L1Norm</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.L2Norm"><code class="docutils literal notranslate"><span class="pre">L2Norm</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.SquaredL2Norm"><code class="docutils literal notranslate"><span class="pre">SquaredL2Norm</span></code></a></li>
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-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.L1Ball"><code class="docutils literal notranslate"><span class="pre">L1Ball()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.L2Ball"><code class="docutils literal notranslate"><span class="pre">L2Ball()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.LInfinityBall"><code class="docutils literal notranslate"><span class="pre">LInfinityBall()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.PositiveOrthant"><code class="docutils literal notranslate"><span class="pre">PositiveOrthant</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.HyperSlab"><code class="docutils literal notranslate"><span class="pre">HyperSlab</span></code></a><ul class="visible nav section-nav flex-column">
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-</ul>
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-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.RangeSet.__init__"><code class="docutils literal notranslate"><span class="pre">RangeSet.__init__()</span></code></a></li>
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-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.AffineSet"><code class="docutils literal notranslate"><span class="pre">AffineSet</span></code></a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.operator.AffineSet.__init__"><code class="docutils literal notranslate"><span class="pre">AffineSet.__init__()</span></code></a></li>
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diff --git a/api/operator.interop.html b/api/operator.interop.html
index fda99a90..205aa2c5 100644
--- a/api/operator.interop.html
+++ b/api/operator.interop.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
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     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -408,16 +408,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="operator/blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
@@ -429,13 +424,7 @@
 <li class="toctree-l1"><a class="reference internal" href="opt.stop.html">pyxu.opt.stop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="runtime.html">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="util/array_module.html">pyxu.util.array_module</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../references.html"><strong>References</strong></a></li>
 </ul>
@@ -511,32 +500,32 @@ <h2><a class="toc-backref" href="#id1" role="doc-backlink">General</a><a class="
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.operator.interop.from_source">
 <span class="sig-name descname"><span class="pre">from_source</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cls</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">embed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vectorize</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vmethod</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enforce_precision</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/interop/source.html#from_source"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.from_source" title="Link to this definition">#</a></dt>
-<dd><p>Define an <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from low-level constructs.</p>
+<dd><p>Define an <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from low-level constructs.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>cls</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpC" title="pyxu.info.ptype.OpC"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpC</span></code></a>) – Operator sub-class to instantiate.</p></li>
 <li><p><strong>shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpShape" title="pyxu.info.ptype.OpShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpShape</span></code></a>) – (N, M) operator shape.</p></li>
 <li><p><strong>embed</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>(k[str], v[value]) pairs to embed into the created operator.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">embed</span></code> is useful to attach extra information to synthesized <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> used by arithmetic
+<p><code class="code docutils literal notranslate"><span class="pre">embed</span></code> is useful to attach extra information to synthesized <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> used by arithmetic
 methods.</p>
 </p></li>
 <li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>(k[str], v[callable]) pairs to use as arithmetic methods.</p>
-<p>Keys must be entries from <a class="reference internal" href="abc/operator.html#pyxu.abc.Property.arithmetic_methods" title="pyxu.abc.Property.arithmetic_methods"><code class="xref py py-meth docutils literal notranslate"><span class="pre">arithmetic_methods()</span></code></a>.</p>
+<p>Keys must be entries from <a class="reference internal" href="abc.html#pyxu.abc.Property.arithmetic_methods" title="pyxu.abc.Property.arithmetic_methods"><code class="xref py py-meth docutils literal notranslate"><span class="pre">arithmetic_methods()</span></code></a>.</p>
 <p>Omitted arithmetic attributes/methods default to those provided by <code class="code docutils literal notranslate"><span class="pre">cls</span></code>.</p>
 </p></li>
 <li><p><strong>vectorize</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – <p>Arithmetic methods to vectorize.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">vectorize</span></code> is useful if an arithmetic method provided to <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> (ex: <a class="reference internal" href="abc/operator.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>):</p>
+<p><code class="code docutils literal notranslate"><span class="pre">vectorize</span></code> is useful if an arithmetic method provided to <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> (ex: <a class="reference internal" href="abc.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>):</p>
 <ul>
 <li><p>does not support stacking dimensions; OR</p></li>
 <li><p>does not support DASK inputs.</p></li>
 </ul>
 </p></li>
-<li><p><strong>vmethod</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>Vectorization strategy. (See <a class="reference internal" href="util/operator.html#pyxu.util.vectorize" title="pyxu.util.vectorize"><code class="xref py py-class docutils literal notranslate"><span class="pre">vectorize</span></code></a>.)</p>
+<li><p><strong>vmethod</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>Vectorization strategy. (See <a class="reference internal" href="util.html#pyxu.util.vectorize" title="pyxu.util.vectorize"><code class="xref py py-class docutils literal notranslate"><span class="pre">vectorize</span></code></a>.)</p>
 <p>Different strategies can be applied per arithmetic method via a dictionary.</p>
 </p></li>
 <li><p><strong>enforce_precision</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – <p>Arithmetic methods to make compliant with Pyxu’s runtime FP-precision.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">enforce_precision</span></code> is useful if an arithmetic method provided to <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> (ex: <a class="reference internal" href="abc/operator.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>)
+<p><code class="code docutils literal notranslate"><span class="pre">enforce_precision</span></code> is useful if an arithmetic method provided to <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> (ex: <a class="reference internal" href="abc.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>)
 is unaware of Pyxu’s runtime FP context.</p>
 </p></li>
 </ul>
@@ -563,7 +552,7 @@ <h2><a class="toc-backref" href="#id1" role="doc-backlink">General</a><a class="
 consider populating <code class="code docutils literal notranslate"><span class="pre">vectorize</span></code>.</p>
 </li>
 <li><p>Auto-vectorization consists in decorating <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code>-specified arithmetic methods with
-<a class="reference internal" href="util/operator.html#pyxu.util.vectorize" title="pyxu.util.vectorize"><code class="xref py py-func docutils literal notranslate"><span class="pre">vectorize()</span></code></a>.  Auto-vectorization may be less efficient than explicitly providing a vectorized
+<a class="reference internal" href="util.html#pyxu.util.vectorize" title="pyxu.util.vectorize"><code class="xref py py-func docutils literal notranslate"><span class="pre">vectorize()</span></code></a>.  Auto-vectorization may be less efficient than explicitly providing a vectorized
 implementation.</p></li>
 <li><p>Enforcing precision consists in decorating <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code>-specified arithmetic methods with
 <a class="reference internal" href="runtime.html#pyxu.runtime.enforce_precision" title="pyxu.runtime.enforce_precision"><code class="xref py py-func docutils literal notranslate"><span class="pre">enforce_precision()</span></code></a>.  Not all arithmetic methods can be made runtime FP-precision
@@ -606,7 +595,7 @@ <h2><a class="toc-backref" href="#id2" role="doc-backlink">SciPy</a><a class="he
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.operator.interop.from_sciop">
 <span class="sig-name descname"><span class="pre">from_sciop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cls</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sp_op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/interop/sciop.html#from_sciop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.from_sciop" title="Link to this definition">#</a></dt>
-<dd><p>Wrap a <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html#scipy.sparse.linalg.LinearOperator" title="(in SciPy v1.11.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinearOperator</span></code></a> as a <a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> (or sub-class thereof).</p>
+<dd><p>Wrap a <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html#scipy.sparse.linalg.LinearOperator" title="(in SciPy v1.11.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinearOperator</span></code></a> as a <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> (or sub-class thereof).</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
@@ -629,7 +618,7 @@ <h2><a class="toc-backref" href="#id3" role="doc-backlink">JAX</a><a class="head
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.operator.interop.from_jax">
 <span class="sig-name descname"><span class="pre">from_jax</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cls</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vectorize</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">jit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/interop/jax.html#from_jax"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.from_jax" title="Link to this definition">#</a></dt>
-<dd><p>Define an <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from JAX functions.</p>
+<dd><p>Define an <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from JAX functions.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
@@ -679,7 +668,7 @@ <h2><a class="toc-backref" href="#id3" role="doc-backlink">JAX</a><a class="head
 precision/copy-related warnings can be silenced via the <code class="code docutils literal notranslate"><span class="pre">enable_warnings</span></code> option of
 <a class="reference internal" href="#pyxu.operator.interop.from_jax" title="pyxu.operator.interop.from_jax"><code class="xref py py-func docutils literal notranslate"><span class="pre">from_jax()</span></code></a>.</p></li>
 <li><p>Inferred arithmetic methods are not JIT-ed by default since the operation is error-prone depending on how
-<a class="reference internal" href="abc/operator.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> is defined.  If <a class="reference internal" href="abc/operator.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> supplied to
+<a class="reference internal" href="abc.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> is defined.  If <a class="reference internal" href="abc.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> supplied to
 <a class="reference internal" href="#pyxu.operator.interop.from_jax" title="pyxu.operator.interop.from_jax"><code class="xref py py-func docutils literal notranslate"><span class="pre">from_jax()</span></code></a> is JIT-friendly, then consider enabling <code class="code docutils literal notranslate"><span class="pre">jit</span></code>.</p></li>
 </ul>
 <p class="rubric">Examples</p>
@@ -739,7 +728,7 @@ <h2><a class="toc-backref" href="#id3" role="doc-backlink">JAX</a><a class="head
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>x</strong> (<em>JaxArray</em>) – </p></li>
+<li><p><strong>x</strong> (<a class="reference external" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="(in JAX)"><em>Array</em></a>) – </p></li>
 <li><p><strong>xp</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><em>ArrayModule</em></a>) – </p></li>
 </ul>
 </dd>
@@ -763,7 +752,7 @@ <h2><a class="toc-backref" href="#id3" role="doc-backlink">JAX</a><a class="head
 </ul>
 </dd>
 <dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><em>JaxArray</em></p>
+<dd class="field-even"><p><a class="reference external" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="(in JAX)"><em>Array</em></a></p>
 </dd>
 </dl>
 </dd></dl>
@@ -790,11 +779,11 @@ <h2><a class="toc-backref" href="#id4" role="doc-backlink">PyTorch</a><a class="
 </dl>
 
 <span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/operator/interop/torch.html#from_torch"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.from_torch" title="Link to this definition">#</a></dt>
-<dd><p>Define an <a class="reference internal" href="abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from PyTorch functions.</p>
+<dd><p>Define an <a class="reference internal" href="abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from PyTorch functions.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>apply</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Callable</span></code></a>) – A Python function with single-element Tensor input/output. Defines the <a class="reference internal" href="abc/operator.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> method of
+<li><p><strong>apply</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Callable</span></code></a>) – A Python function with single-element Tensor input/output. Defines the <a class="reference internal" href="abc.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> method of
 the operator: <code class="docutils literal notranslate"><span class="pre">apply(x)==op.apply(x)</span></code>.</p></li>
 <li><p><strong>shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.OpShape" title="pyxu.info.ptype.OpShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpShape</span></code></a>) – (N,M) shape of the operator, where N and M are the sizes of the output and input Tensors of <code class="docutils literal notranslate"><span class="pre">apply</span></code>
 respectively.</p></li>
@@ -855,8 +844,8 @@ <h2><a class="toc-backref" href="#id4" role="doc-backlink">PyTorch</a><a class="
 <li><p>Arithmetic methods are <strong>not currently JIT-ed</strong> even if <code class="code docutils literal notranslate"><span class="pre">jit</span></code> is set to <code class="docutils literal notranslate"><span class="pre">True</span></code>.  This is because of the
 undocumented and currently poor interaction between <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.0)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> transforms and <a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.compile.html#torch.compile" title="(in PyTorch v2.0)"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.compile()</span></code></a>.
 See <a class="reference external" href="https://github.com/pytorch/pytorch/issues/98822">this issue</a> for additional details.</p></li>
-<li><p>For <a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a> (or subclasses thereof), the methods <a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap.jacobian" title="pyxu.abc.DiffMap.jacobian"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jacobian()</span></code></a>,
-<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc.grad" title="pyxu.abc.DiffFunc.grad"><code class="xref py py-meth docutils literal notranslate"><span class="pre">grad()</span></code></a> and <a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp.adjoint" title="pyxu.abc.LinOp.adjoint"><code class="xref py py-meth docutils literal notranslate"><span class="pre">adjoint()</span></code></a> are defined implicitly if not provided
+<li><p>For <a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a> (or subclasses thereof), the methods <a class="reference internal" href="abc.html#pyxu.abc.DiffMap.jacobian" title="pyxu.abc.DiffMap.jacobian"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jacobian()</span></code></a>,
+<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc.grad" title="pyxu.abc.DiffFunc.grad"><code class="xref py py-meth docutils literal notranslate"><span class="pre">grad()</span></code></a> and <a class="reference internal" href="abc.html#pyxu.abc.LinOp.adjoint" title="pyxu.abc.LinOp.adjoint"><code class="xref py py-meth docutils literal notranslate"><span class="pre">adjoint()</span></code></a> are defined implicitly if not provided
 using the auto-differentiation transforms from <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.0)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a>.  As detailed <a class="reference external" href="https://pytorch.org/docs/stable/func.ux_limitations.html">on this page</a>, such transforms work well on pure functions (that
 is, functions where the output is completely determined by the input and that do not involve side effects like
 mutation), but may fail on more complex functions.  Moreover, <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.0)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> does not yet have full coverage
diff --git a/api/operator/blocks.html b/api/operator/blocks.html
index 6d442a50..32f55618 100644
--- a/api/operator/blocks.html
+++ b/api/operator/blocks.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -408,16 +408,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="../abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="../abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="../abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">pyxu.operator</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">pyxu.operator</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2 current active"><a class="current reference internal" href="#">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="linop.html">pyxu.operator.linop</a></li>
@@ -429,13 +424,7 @@
 <li class="toctree-l1"><a class="reference internal" href="../opt.stop.html">pyxu.opt.stop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../runtime.html">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="../util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="../util/array_module.html">pyxu.util.array_module</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="../util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../references.html"><strong>References</strong></a></li>
 </ul>
diff --git a/api/operator/func.html b/api/operator/func.html
index a9ee00f3..d8abfba0 100644
--- a/api/operator/func.html
+++ b/api/operator/func.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -408,16 +408,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="../abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="../abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="../abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">pyxu.operator</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">pyxu.operator</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2 current active"><a class="current reference internal" href="#">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="linop.html">pyxu.operator.linop</a></li>
@@ -429,13 +424,7 @@
 <li class="toctree-l1"><a class="reference internal" href="../opt.stop.html">pyxu.opt.stop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../runtime.html">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="../util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="../util/array_module.html">pyxu.util.array_module</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="../util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../references.html"><strong>References</strong></a></li>
 </ul>
@@ -512,7 +501,7 @@ <h2><a class="toc-backref" href="#id5" role="doc-backlink">Norms &amp; Loss Func
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.L1Norm">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">L1Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/norm.html#L1Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.L1Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
 <p><span class="math notranslate nohighlight">\(\ell_{1}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert_{1} := \sum_{i=1}^{N} |x_{i}|\)</span>.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -524,7 +513,7 @@ <h2><a class="toc-backref" href="#id5" role="doc-backlink">Norms &amp; Loss Func
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.L2Norm">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">L2Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/norm.html#L2Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.L2Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
 <p><span class="math notranslate nohighlight">\(\ell_{2}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert_{2} := \sqrt{\sum_{i=1}^{N} |x_{i}|^{2}}\)</span>.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -536,7 +525,7 @@ <h2><a class="toc-backref" href="#id5" role="doc-backlink">Norms &amp; Loss Func
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.SquaredL2Norm">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SquaredL2Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/norm.html#SquaredL2Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SquaredL2Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.QuadraticFunc" title="pyxu.abc.operator.QuadraticFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">QuadraticFunc</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.QuadraticFunc" title="pyxu.abc.operator.QuadraticFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">QuadraticFunc</span></code></a></p>
 <p><span class="math notranslate nohighlight">\(\ell^{2}_{2}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert^{2}_{2} := \sum_{i=1}^{N} |x_{i}|^{2}\)</span>.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -548,7 +537,7 @@ <h2><a class="toc-backref" href="#id5" role="doc-backlink">Norms &amp; Loss Func
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.SquaredL1Norm">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SquaredL1Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">prox_algo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'sort'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/norm.html#SquaredL1Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SquaredL1Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
 <p><span class="math notranslate nohighlight">\(\ell^{2}_{1}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert^{2}_{1} := (\sum_{i=1}^{N} |x_{i}|)^{2}\)</span>.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -635,7 +624,7 @@ <h2><a class="toc-backref" href="#id5" role="doc-backlink">Norms &amp; Loss Func
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.KLDivergence">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">KLDivergence</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">data</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/loss.html#KLDivergence"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.KLDivergence" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
 <p>Generalised Kullback-Leibler divergence <span class="math notranslate nohighlight">\(D_{KL}(\mathbf{y}||\mathbf{x}):=\sum_{i=1}^N y_i\log(y_i/x_i) -y_i
 +x_i\)</span>.</p>
 <dl class="field-list simple">
@@ -686,7 +675,7 @@ <h2><a class="toc-backref" href="#id5" role="doc-backlink">Norms &amp; Loss Func
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.LInfinityNorm">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">LInfinityNorm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/norm.html#LInfinityNorm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.LInfinityNorm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
 <p><span class="math notranslate nohighlight">\(\ell_{\infty}\)</span>-norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert_{\infty} := \max_{i=1,\ldots,N} |x_{i}|\)</span>.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -698,7 +687,7 @@ <h2><a class="toc-backref" href="#id5" role="doc-backlink">Norms &amp; Loss Func
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.L21Norm">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">L21Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">l2_axis</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(0,)</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/norm.html#L21Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.L21Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
 <p>Mixed <span class="math notranslate nohighlight">\(\ell_{2}-\ell_{1}\)</span> norm, <span class="math notranslate nohighlight">\(\Vert\mathbf{x}\Vert_{2, 1} := \sum_{i=1}^{N} \sqrt{\sum_{j=1}^{M}
 x_{i, j}^{2}}\)</span>.</p>
 <div class="admonition note">
@@ -732,7 +721,7 @@ <h2><a class="toc-backref" href="#id5" role="doc-backlink">Norms &amp; Loss Func
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.PositiveL1Norm">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PositiveL1Norm</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/norm.html#PositiveL1Norm"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.PositiveL1Norm" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_ShiftLossMixin</span></code>, <a class="reference internal" href="../abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a></p>
 <p><span class="math notranslate nohighlight">\(\ell_{1}\)</span>-norm, with a positivity constraint.</p>
 <div class="math notranslate nohighlight">
 \[f(\mathbf{x})
@@ -895,9 +884,9 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">Indicator Functions</
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>a</strong> (<a class="reference internal" href="../abc/operator.html#pyxu.abc.LinFunc" title="pyxu.abc.operator.LinFunc"><em>LinFunc</em></a>) – </p></li>
-<li><p><strong>lb</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-<li><p><strong>ub</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
+<li><p><strong>a</strong> (<a class="reference internal" href="../abc.html#pyxu.abc.LinFunc" title="pyxu.abc.operator.LinFunc"><em>LinFunc</em></a>) – </p></li>
+<li><p><strong>lb</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
+<li><p><strong>ub</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -907,10 +896,10 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">Indicator Functions</
 <dd><dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="../abc/operator.html#pyxu.abc.LinFunc" title="pyxu.abc.operator.LinFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinFunc</span></code></a>) – (N,) operator</p></li>
+<li><p><strong>A</strong> (<a class="reference internal" href="../abc.html#pyxu.abc.LinFunc" title="pyxu.abc.operator.LinFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinFunc</span></code></a>) – (N,) operator</p></li>
 <li><p><strong>lb</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Lower bound</p></li>
 <li><p><strong>ub</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Upper bound</p></li>
-<li><p><strong>a</strong> (<a class="reference internal" href="../abc/operator.html#pyxu.abc.LinFunc" title="pyxu.abc.operator.LinFunc"><em>LinFunc</em></a>) – </p></li>
+<li><p><strong>a</strong> (<a class="reference internal" href="../abc.html#pyxu.abc.LinFunc" title="pyxu.abc.operator.LinFunc"><em>LinFunc</em></a>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -936,7 +925,7 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">Indicator Functions</
 \mathbf{A} (\mathbf{A}^{T} \mathbf{A})^{-1} \mathbf{A}^{T} \mathbf{x}.\]</div>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>A</strong> (<a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><em>LinOp</em></a>) – </p>
+<dd class="field-odd"><p><strong>A</strong> (<a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><em>LinOp</em></a>) – </p>
 </dd>
 </dl>
 <dl class="py method">
@@ -944,7 +933,7 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">Indicator Functions</
 <span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/indicator.html#RangeSet.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.RangeSet.__init__" title="Link to this definition">#</a></dt>
 <dd><dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>A</strong> (<a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>) – (M, N) operator</p>
+<dd class="field-odd"><p><strong>A</strong> (<a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>) – (M, N) operator</p>
 </dd>
 </dl>
 </dd></dl>
@@ -981,7 +970,7 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">Indicator Functions</
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><em>LinOp</em></a>) – </p></li>
+<li><p><strong>A</strong> (<a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><em>LinOp</em></a>) – </p></li>
 <li><p><strong>b</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>) – </p></li>
 </ul>
 </dd>
@@ -992,7 +981,7 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">Indicator Functions</
 <dd><dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>) – (M, N) operator</p></li>
+<li><p><strong>A</strong> (<a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>) – (M, N) operator</p></li>
 <li><p><strong>b</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (M,)</p></li>
 </ul>
 </dd>
@@ -1036,7 +1025,7 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">Indicator Functions</
 </div>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>args</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference internal" href="../abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em>]</em>) – </p>
+<dd class="field-odd"><p><strong>args</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference internal" href="../abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em>]</em>) – </p>
 </dd>
 </dl>
 <dl class="py method">
@@ -1044,7 +1033,7 @@ <h2><a class="toc-backref" href="#id6" role="doc-backlink">Indicator Functions</
 <span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/func/indicator.html#ConvexSetIntersection.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.ConvexSetIntersection.__init__" title="Link to this definition">#</a></dt>
 <dd><dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>args</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a> ( <a class="reference internal" href="../abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a> )) – Sequence of indicator functions encoding convex domains.</p>
+<dd class="field-odd"><p><strong>args</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a> ( <a class="reference internal" href="../abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a> )) – Sequence of indicator functions encoding convex domains.</p>
 </dd>
 </dl>
 </dd></dl>
diff --git a/api/operator/index.html b/api/operator/index.html
index 1ed07952..f87fb003 100644
--- a/api/operator/index.html
+++ b/api/operator/index.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -406,16 +406,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="../abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="../abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="../abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1 current active has-children"><a class="current reference internal" href="#">pyxu.operator</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l1 current active has-children"><a class="current reference internal" href="#">pyxu.operator</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="linop.html">pyxu.operator.linop</a></li>
@@ -427,13 +422,7 @@
 <li class="toctree-l1"><a class="reference internal" href="../opt.stop.html">pyxu.opt.stop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../runtime.html">pyxu.runtime</a></li>
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-  <section id="pyxu-operator-interop">
-<h1>pyxu.operator.interop<a class="headerlink" href="#pyxu-operator-interop" title="Link to this heading">#</a></h1>
-<nav class="contents local" id="table-of-contents">
-<p class="topic-title">Table of Contents</p>
-<ul class="simple">
-<li><p><a class="reference internal" href="#generic-constructor" id="id1">Generic Constructor</a></p></li>
-<li><p><a class="reference internal" href="#scipy-interoperability" id="id2">SciPy Interoperability</a></p></li>
-<li><p><a class="reference internal" href="#jax-interoperability" id="id3">JAX Interoperability</a></p></li>
-<li><p><a class="reference internal" href="#pytorch-interoperability" id="id4">PyTorch Interoperability</a></p></li>
-</ul>
-</nav>
-<section id="generic-constructor">
-<h2><a class="toc-backref" href="#id1" role="doc-backlink">Generic Constructor</a><a class="headerlink" href="#generic-constructor" title="Link to this heading">#</a></h2>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.interop.source.from_source">
-<span class="sig-name descname"><span class="pre">from_source</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cls</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">embed</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vectorize</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vmethod</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enforce_precision</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/interop/source.html#from_source"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.source.from_source" title="Link to this definition">#</a></dt>
-<dd><p>Define an <a class="reference internal" href="../abc.html#pyxu.abc.operator.Operator" title="pyxu.abc.operator.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from low-level constructs.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>cls</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.OpC" title="pyxu.info.ptype.OpC"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpC</span></code></a>) – Operator sub-class to instantiate.</p></li>
-<li><p><strong>shape</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.OpShape" title="pyxu.info.ptype.OpShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpShape</span></code></a>) – (N, M) operator shape.</p></li>
-<li><p><strong>embed</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>(k[str], v[value]) pairs to embed into the created operator.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">embed</span></code> is useful to attach extra information to synthesized
-<a class="reference internal" href="../abc.html#pyxu.abc.operator.Operator" title="pyxu.abc.operator.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> used by arithmetic methods.</p>
-</p></li>
-<li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>(k[str], v[callable]) pairs to use as arithmetic methods.</p>
-<p>Keys must be entries from <a class="reference internal" href="../abc.html#pyxu.abc.operator.Property.arithmetic_methods" title="pyxu.abc.operator.Property.arithmetic_methods"><code class="xref py py-meth docutils literal notranslate"><span class="pre">arithmetic_methods()</span></code></a>.</p>
-<p>Omitted arithmetic attributes/methods default to those provided by <code class="code docutils literal notranslate"><span class="pre">cls</span></code>.</p>
-</p></li>
-<li><p><strong>vectorize</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – <p>Arithmetic methods to vectorize.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">vectorize</span></code> is useful if an arithmetic method provided to <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> (ex:
-<a class="reference internal" href="../abc.html#pyxu.abc.operator.Map.apply" title="pyxu.abc.operator.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>):</p>
-<ul>
-<li><p>does not support stacking dimensions; OR</p></li>
-<li><p>does not support DASK inputs.</p></li>
-</ul>
-</p></li>
-<li><p><strong>vmethod</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>Vectorization strategy. (See <a class="reference internal" href="../util.html#pyxu.util.operator.vectorize" title="pyxu.util.operator.vectorize"><code class="xref py py-class docutils literal notranslate"><span class="pre">vectorize</span></code></a>.)</p>
-<p>Different strategies can be applied per arithmetic method via a dictionary.</p>
-</p></li>
-<li><p><strong>enforce_precision</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – <p>Arithmetic methods to make compliant with Pyxu’s runtime FP-precision.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">enforce_precision</span></code> is useful if an arithmetic method provided to <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> (ex:
-<a class="reference internal" href="../abc.html#pyxu.abc.operator.Map.apply" title="pyxu.abc.operator.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>) is unaware of Pyxu’s runtime FP context.</p>
-</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (N, M) Pyxu-compliant operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="../info.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<ul>
-<li><p>If provided, arithmetic methods must abide exactly to the Pyxu interface.
-In particular, the following arithmetic methods, if supplied, <strong>must</strong> have
-the following interface:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span>
-<span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span>
-<span class="k">def</span> <span class="nf">adjoint</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span>
-<span class="k">def</span> <span class="nf">prox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">tau</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span>
-<span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">damp</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pxt</span><span class="o">.</span><span class="n">NDArray</span>
-</pre></div>
-</div>
-<p>Moreover, the methods above <strong>must</strong> accept <code class="docutils literal notranslate"><span class="pre">(...,</span> <span class="pre">M)</span></code>-shaped inputs for <code class="docutils literal notranslate"><span class="pre">arr</span></code>.
-If this does not hold, consider populating <code class="code docutils literal notranslate"><span class="pre">vectorize</span></code>.</p>
-</li>
-<li><p>Auto-vectorization consists in decorating <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code>-specified arithmetic methods with
-<a class="reference internal" href="../util.html#pyxu.util.operator.vectorize" title="pyxu.util.operator.vectorize"><code class="xref py py-func docutils literal notranslate"><span class="pre">vectorize()</span></code></a>.
-Auto-vectorization may be less efficient than explicitly providing a vectorized implementation.</p></li>
-<li><p>Enforcing precision consists in decorating <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code>-specified arithmetic methods with
-<a class="reference internal" href="../runtime.html#pyxu.runtime.enforce_precision" title="pyxu.runtime.enforce_precision"><code class="xref py py-func docutils literal notranslate"><span class="pre">enforce_precision()</span></code></a>.
-Not all arithmetic methods can be made runtime FP-precision compliant.
-It is thus recommended to make arithmetic methods precision-compliant manually.</p></li>
-</ul>
-<p class="rubric">Examples</p>
-<p>Creation of the custom element-wise differential operator <span class="math notranslate nohighlight">\(f(\mathbf{x}) = \mathbf{x}^{2}\)</span>.</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">N</span> <span class="o">=</span> <span class="mi">5</span>
-<span class="n">f</span> <span class="o">=</span> <span class="n">from_source</span><span class="p">(</span>
-    <span class="bp">cls</span><span class="o">=</span><span class="n">pyxu</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">DiffMap</span><span class="p">,</span>
-    <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span>
-    <span class="n">apply</span><span class="o">=</span><span class="k">lambda</span> <span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">arr</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span>
-<span class="p">)</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># [0, 1, 4, 9, 16]</span>
-<span class="n">dL</span> <span class="o">=</span> <span class="n">f</span><span class="o">.</span><span class="n">diff_lipschitz</span>  <span class="c1"># inf (default value provided by DiffMap class.)</span>
-</pre></div>
-</div>
-<p>In practice we know that <span class="math notranslate nohighlight">\(f\)</span> has a finite-valued diff-Lipschitz constant.
-It is thus recommended to set it too when instantiating via <code class="docutils literal notranslate"><span class="pre">from_source</span></code>:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">N</span> <span class="o">=</span> <span class="mi">5</span>
-<span class="n">f</span> <span class="o">=</span> <span class="n">from_source</span><span class="p">(</span>
-    <span class="bp">cls</span><span class="o">=</span><span class="n">pyxu</span><span class="o">.</span><span class="n">abc</span><span class="o">.</span><span class="n">DiffMap</span><span class="p">,</span>
-    <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">N</span><span class="p">),</span>
-    <span class="n">embed</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span>  <span class="c1"># special form to set (diff-)Lipschitz attributes via from_source()</span>
-        <span class="n">_diff_lipschitz</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
-    <span class="p">),</span>
-    <span class="n">apply</span><span class="o">=</span><span class="k">lambda</span> <span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">arr</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span>
-<span class="p">)</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># [0, 1, 4, 9, 16]</span>
-<span class="n">dL</span> <span class="o">=</span> <span class="n">f</span><span class="o">.</span><span class="n">diff_lipschitz</span>  <span class="c1"># 2  &lt;- instead of inf</span>
-</pre></div>
-</div>
-</dd></dl>
-
-</section>
-<section id="scipy-interoperability">
-<h2><a class="toc-backref" href="#id2" role="doc-backlink">SciPy Interoperability</a><a class="headerlink" href="#scipy-interoperability" title="Link to this heading">#</a></h2>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.interop.sciop.from_sciop">
-<span class="sig-name descname"><span class="pre">from_sciop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cls</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sp_op</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/interop/sciop.html#from_sciop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.sciop.from_sciop" title="Link to this definition">#</a></dt>
-<dd><p>Wrap a <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html#scipy.sparse.linalg.LinearOperator" title="(in SciPy v1.11.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">scipy.sparse.linalg.LinearOperator</span></code></a> as a
-<a class="reference internal" href="../abc.html#pyxu.abc.operator.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> (or sub-classes thereof).</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>sp_op</strong> (<a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.LinearOperator.html#scipy.sparse.linalg.LinearOperator" title="(in SciPy v1.11.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinearOperator</span></code></a>) – (N, M) Linear CPU/GPU operator compliant with SciPy’s interface.</p></li>
-<li><p><strong>cls</strong> (<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><em>Type</em></a><em>[</em><a class="reference internal" href="../info.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><em>OpT</em></a><em>]</em>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (N, M) Pyxu-compliant linear operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="../info.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-
-</section>
-<section id="jax-interoperability">
-<h2><a class="toc-backref" href="#id3" role="doc-backlink">JAX Interoperability</a><a class="headerlink" href="#jax-interoperability" title="Link to this heading">#</a></h2>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.interop.jax.from_jax">
-<span class="sig-name descname"><span class="pre">from_jax</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cls</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vectorize</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">frozenset({})</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">jit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/interop/jax.html#from_jax"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.jax.from_jax" title="Link to this definition">#</a></dt>
-<dd><p>Define an <a class="reference internal" href="../abc.html#pyxu.abc.operator.Operator" title="pyxu.abc.operator.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from low-level constructs.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>cls</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.OpC" title="pyxu.info.ptype.OpC"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpC</span></code></a>) – Operator sub-class to instantiate.</p></li>
-<li><p><strong>shape</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.OpShape" title="pyxu.info.ptype.OpShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpShape</span></code></a>) – (N, M) operator shape.</p></li>
-<li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>(k[str], v[callable]) pairs to use as arithmetic methods.</p>
-<p>Keys are restricted to the following arithmetic methods:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">apply</span><span class="p">(),</span> <span class="n">grad</span><span class="p">(),</span> <span class="n">prox</span><span class="p">(),</span> <span class="n">pinv</span><span class="p">(),</span> <span class="n">adjoint</span><span class="p">()</span>
-</pre></div>
-</div>
-<p>Omitted arithmetic methods default to those provided by <code class="code docutils literal notranslate"><span class="pre">cls</span></code>, or are
-auto-inferred via auto-diff rules.</p>
-</p></li>
-<li><p><strong>vectorize</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – <p>Arithmetic methods to vectorize.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">vectorize</span></code> is useful if an arithmetic method provided to <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> does not support stacking
-dimensions.</p>
-</p></li>
-<li><p><strong>jit</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, JIT-compile JAX-backed arithmetic methods for better performance.</p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit warnings in case of precision/zero-copy issues.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (N, M) Pyxu-compliant operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="../info.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<ul>
-<li><p>If provided, arithmetic methods must abide exactly to the interface below:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span>
-<span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span>
-<span class="k">def</span> <span class="nf">adjoint</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span>
-<span class="k">def</span> <span class="nf">prox</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span><span class="p">,</span> <span class="n">tau</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span>
-<span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span><span class="p">,</span> <span class="n">damp</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span>
-</pre></div>
-</div>
-<p>Moreover, the methods above <strong>must</strong> accept <code class="docutils literal notranslate"><span class="pre">(...,</span> <span class="pre">M)</span></code>-shaped inputs for <code class="docutils literal notranslate"><span class="pre">arr</span></code>.
-If this does not hold, consider populating <code class="code docutils literal notranslate"><span class="pre">vectorize</span></code>.</p>
-</li>
-<li><p>Auto-vectorization consists in decorating <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code>-specified arithmetic methods with
-<a class="reference external" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.vectorize.html#jax.numpy.vectorize" title="(in JAX)"><code class="xref py py-func docutils literal notranslate"><span class="pre">jax.numpy.vectorize()</span></code></a>.</p></li>
-<li><p>All arithmetic methods provided in <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> are decorated using
-<a class="reference internal" href="../runtime.html#pyxu.runtime.enforce_precision" title="pyxu.runtime.enforce_precision"><code class="xref py py-func docutils literal notranslate"><span class="pre">enforce_precision()</span></code></a> to abide by Pyxu’s FP-runtime semantics.
-Note however that JAX enforces <a class="reference external" href="https://jax.readthedocs.io/en/latest/notebooks/Common_Gotchas_in_JAX.html#double-64bit-precision">32-bit arithmetic</a>
-by default, and this constraint cannot be changed at runtime.
-As such, to allow zero-copy transfers between JAX and NUMPY/CUPY arrays, it is advised to
-perform computations in single-precision mode.
-This can be achieved locally using the <a class="reference internal" href="../runtime.html#pyxu.runtime.Precision" title="pyxu.runtime.Precision"><code class="xref py py-class docutils literal notranslate"><span class="pre">Precision</span></code></a> context manager.
-(See example.)
-Alternatively, precision/copy-related warnings can be silenced via the <code class="code docutils literal notranslate"><span class="pre">enable_warnings</span></code>
-option of <a class="reference internal" href="#pyxu.operator.interop.jax.from_jax" title="pyxu.operator.interop.jax.from_jax"><code class="xref py py-func docutils literal notranslate"><span class="pre">from_jax()</span></code></a>.</p></li>
-<li><p>Inferred arithmetic methods are not JIT-ed by default since the operation is error-prone
-depending on how <a class="reference internal" href="../abc.html#pyxu.abc.operator.Map.apply" title="pyxu.abc.operator.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> is defined.
-If <a class="reference internal" href="../abc.html#pyxu.abc.operator.Map.apply" title="pyxu.abc.operator.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a> supplied to
-<a class="reference internal" href="#pyxu.operator.interop.jax.from_jax" title="pyxu.operator.interop.jax.from_jax"><code class="xref py py-func docutils literal notranslate"><span class="pre">from_jax()</span></code></a> is JIT-friendly, then consider enabling <code class="code docutils literal notranslate"><span class="pre">jit</span></code>.</p></li>
-</ul>
-<p class="rubric">Examples</p>
-<p>Create the custom differential map <span class="math notranslate nohighlight">\(f: \mathbb{R}^{2} \to \mathbb{R}^{3}\)</span>:</p>
-<div class="math notranslate nohighlight">
-\[f(x, y) =
-\left[
-    \sin(x) + \cos(y),
-    \cos(x) - \sin(y),
-    \sin(x) + \cos(x)
-\right]\]</div>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pyxu.abc</span> <span class="k">as</span> <span class="nn">pxa</span>
-<span class="kn">import</span> <span class="nn">pyxu.runtime</span> <span class="k">as</span> <span class="nn">pxrt</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator.interop</span> <span class="k">as</span> <span class="nn">pxi</span>
-<span class="kn">import</span> <span class="nn">jax</span><span class="o">,</span> <span class="nn">jax.numpy</span> <span class="k">as</span> <span class="nn">jnp</span>
-<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-
-<span class="nd">@jax</span><span class="o">.</span><span class="n">jit</span>
-<span class="k">def</span> <span class="nf">j_apply</span><span class="p">(</span><span class="n">arr</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">jax</span><span class="o">.</span><span class="n">Array</span><span class="p">:</span>
-    <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">arr</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">arr</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
-    <span class="n">o1</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="n">jnp</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
-    <span class="n">o2</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">-</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
-    <span class="n">o3</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="n">jnp</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-    <span class="n">out</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="n">o1</span><span class="p">,</span> <span class="n">o2</span><span class="p">,</span> <span class="n">o3</span><span class="p">]</span>
-    <span class="k">return</span> <span class="n">out</span>
-
-<span class="n">op</span> <span class="o">=</span> <span class="n">pxi</span><span class="o">.</span><span class="n">from_jax</span><span class="p">(</span>
-    <span class="bp">cls</span><span class="o">=</span><span class="n">pxa</span><span class="o">.</span><span class="n">DiffMap</span><span class="p">,</span>
-    <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span>
-    <span class="n">vectorize</span><span class="o">=</span><span class="s2">&quot;apply&quot;</span><span class="p">,</span>  <span class="c1"># j_apply() does not work on stacked inputs</span>
-                        <span class="c1"># --&gt; let JAX figure it out automatically.</span>
-    <span class="n">apply</span><span class="o">=</span><span class="n">j_apply</span><span class="p">,</span>
-<span class="p">)</span>
-<span class="k">with</span> <span class="n">pxrt</span><span class="o">.</span><span class="n">Precision</span><span class="p">(</span><span class="n">pxrt</span><span class="o">.</span><span class="n">Width</span><span class="o">.</span><span class="n">SINGLE</span><span class="p">):</span>
-    <span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
-    <span class="n">x</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
-    <span class="n">y1</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># (5,3,4,3)</span>
-
-    <span class="n">x</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,))</span>
-    <span class="n">opJ</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">jacobian</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># JAX auto-infers the Jacobian for you.</span>
-
-    <span class="n">v</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
-    <span class="n">w</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">))</span>
-    <span class="n">y2</span> <span class="o">=</span> <span class="n">opJ</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>  <span class="c1"># (5,3)</span>
-    <span class="n">y3</span> <span class="o">=</span> <span class="n">opJ</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>  <span class="c1"># (4,2)</span>
-</pre></div>
-</div>
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.interop.jax._from_jax">
-<span class="sig-name descname"><span class="pre">_from_jax</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">xp</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/interop/jax.html#_from_jax"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.jax._from_jax" title="Link to this definition">#</a></dt>
-<dd><p>JAX -&gt; NUMPY/CUPY conversion.</p>
-<p>The transform is always zero-copy, but it is not easy to check this condition for all array
-types (contiguous, views, etc.) and backends (NUMPY, CUPY).</p>
-<p>[More info] <a class="github reference external" href="https://github.com/google/jax/issues/1961#issuecomment-875773326">google/jax#1961</a></p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>x</strong> (<em>JaxArray</em>) – </p></li>
-<li><p><strong>xp</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><em>ArrayModule</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference internal" href="../info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a></p>
-</dd>
-</dl>
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.interop.jax._to_jax">
-<span class="sig-name descname"><span class="pre">_to_jax</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/interop/jax.html#_to_jax"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.jax._to_jax" title="Link to this definition">#</a></dt>
-<dd><p>NUMPY/CUPY -&gt; JAX conversion.</p>
-<p>Conversion is zero-copy when possible, i.e. 16-byte alignment, on the right device, etc.</p>
-<p>[More info] <a class="github reference external" href="https://github.com/google/jax/issues/4486#issuecomment-735842976">google/jax#4486</a></p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>x</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a>) – </p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
-</dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><em>JaxArray</em></p>
-</dd>
-</dl>
-</dd></dl>
-
-</section>
-<section id="pytorch-interoperability">
-<h2><a class="toc-backref" href="#id4" role="doc-backlink">PyTorch Interoperability</a><a class="headerlink" href="#pytorch-interoperability" title="Link to this heading">#</a></h2>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.interop.torch.from_torch">
-<span class="sig-name descname"><span class="pre">from_torch</span></span><span class="sig-paren">(</span>
-
-<dl>
-<dd><em class="sig-param"><span class="n"><span class="pre">apply</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">cls=&lt;class</span> <span class="pre">'pyxu.abc.operator.Map'&gt;</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">vectorize=frozenset({})</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">batch_size=None</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">jit=False</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">dtype=None</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">enable_warnings=True</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">name='TorchOp'</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">meta=None</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">**kwargs</span></span></em>,</dd>
-</dl>
-
-<span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/interop/torch.html#from_torch"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.torch.from_torch" title="Link to this definition">#</a></dt>
-<dd><p>Define an <a class="reference internal" href="../abc.html#pyxu.abc.operator.Operator" title="pyxu.abc.operator.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> from Torch-based callables.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>apply</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Callable</span></code></a>) – A Python function with single-element Tensor input/output. Defines the <a class="reference internal" href="../abc.html#pyxu.abc.operator.Map.apply" title="pyxu.abc.operator.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>
-method of the operator: <code class="docutils literal notranslate"><span class="pre">apply(x)==op.apply(x)</span></code>.</p></li>
-<li><p><strong>shape</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.OpShape" title="pyxu.info.ptype.OpShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpShape</span></code></a>) – (N,M) shape of the operator, where N and M are the sizes of the output and input Tensors of <code class="docutils literal notranslate"><span class="pre">apply</span></code> respectively.</p></li>
-<li><p><strong>cls</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a>) – Pyxu abstract base class to instantiate from.</p></li>
-<li><p><strong>vectorize</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">pxt.VarName</span></code>) – <p>Arithmetic methods to vectorize.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">vectorize</span></code> is useful if an arithmetic method provided to <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> does not support stacking
-dimensions.</p>
-</p></li>
-<li><p><strong>batch_size</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>) – If None (default), vectorized methods are applied as a single map over all inputs.
-If not None, then compute the vectorized methods <code class="code docutils literal notranslate"><span class="pre">batch_size</span></code> samples at a time.
-Note that <code class="docutils literal notranslate"><span class="pre">batch_size=1</span></code> is equivalent to computing the vectorization with a for-loop.
-If you run into memory issues applying your vectorized methods over stacked inputs, try a non-None <code class="code docutils literal notranslate"><span class="pre">batch_size</span></code>.</p></li>
-<li><p><strong>jit</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – Currently has no effect (for future-compatibility only). In the future, if <code class="docutils literal notranslate"><span class="pre">True</span></code>, then Torch-backed arithmetic methods
-will be JIT-compiled for better performance.</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – Assumed <code class="code docutils literal notranslate"><span class="pre">dtype</span></code> of the Torch-defined arithmetic methods. If <code class="code docutils literal notranslate"><span class="pre">None</span></code> the arithmetic methods are assumed precision-agnostic.</p></li>
-<li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit warnings in case of precision/zero-copy issues.</p></li>
-<li><p><strong>name</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>) – Name of the operator.</p></li>
-<li><p><strong>meta</strong> (<code class="xref py py-class docutils literal notranslate"><span class="pre">Any</span></code>) – Meta information to be provided as tail to <code class="xref py py-class docutils literal notranslate"><span class="pre">_expr</span></code>.</p></li>
-<li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – <p>Optional   (k[str], v[value | callable]) pairs to use as arithmetic methods.</p>
-<p>Keys are restricted to the following arithmetic methods:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">grad</span><span class="p">(),</span> <span class="n">prox</span><span class="p">(),</span> <span class="n">pinv</span><span class="p">(),</span> <span class="n">adjoint</span><span class="p">()</span>  <span class="c1"># methods</span>
-</pre></div>
-</div>
-<p>Omitted arithmetic methods default to those provided by <code class="code docutils literal notranslate"><span class="pre">cls</span></code>, or are
-auto-inferred via auto-diff rules.</p>
-</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>op</strong> – (N, M) Pyxu-compliant operator.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="../info.html#pyxu.info.ptype.OpT" title="pyxu.info.ptype.OpT"><code class="xref py py-class docutils literal notranslate"><span class="pre">OpT</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<ul>
-<li><p>If provided, arithmetic methods must abide exactly to the interface below:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="n">tensor</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span>
-<span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="n">tensor</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span>
-<span class="k">def</span> <span class="nf">adjoint</span><span class="p">(</span><span class="n">tensor</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span>
-<span class="k">def</span> <span class="nf">prox</span><span class="p">(</span><span class="n">tensor</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">tau</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span>
-<span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span><span class="n">tensor</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">damp</span><span class="p">:</span> <span class="n">pxt</span><span class="o">.</span><span class="n">Real</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span>
-</pre></div>
-</div>
-<p>The arithmetic methods <code class="code docutils literal notranslate"><span class="pre">apply</span></code>, <code class="code docutils literal notranslate"><span class="pre">grad</span></code>, <code class="code docutils literal notranslate"><span class="pre">prox</span></code> <strong>must</strong> accept <code class="docutils literal notranslate"><span class="pre">(-1,</span> <span class="pre">M)</span></code>-shaped inputs for <code class="docutils literal notranslate"><span class="pre">tensor</span></code>, that is a
-core dimension of size <code class="code docutils literal notranslate"><span class="pre">M</span></code> and an optional stacking/batching dimension of arbitrary size.
-The arithmetic methods <code class="code docutils literal notranslate"><span class="pre">adjoint</span></code>, <code class="code docutils literal notranslate"><span class="pre">pinv</span></code> <strong>must</strong> accept <code class="docutils literal notranslate"><span class="pre">(-1,</span> <span class="pre">N)</span></code>-shaped inputs for <code class="docutils literal notranslate"><span class="pre">tensor</span></code>, that is a core
-dimension of size <code class="code docutils literal notranslate"><span class="pre">N</span></code> and an optional stacking/batching dimension of arbitrary size.
-If stacking/batching dimensions are not supported for some methods, consider populating <code class="code docutils literal notranslate"><span class="pre">vectorize</span></code> accordingly.</p>
-</li>
-<li><p>Auto-vectorization consists in decorating <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code>-specified arithmetic methods with <a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.vmap.html#torch.vmap" title="(in PyTorch v2.0)"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.vmap()</span></code></a>.
-See the <a class="reference external" href="https://pytorch.org/docs/stable/func.ux_limitations.html#vmap-limitations">PyTorch documentation</a> for
-known limitations.</p></li>
-<li><p>All arithmetic methods provided in <code class="code docutils literal notranslate"><span class="pre">kwargs</span></code> are decorated using <a class="reference internal" href="../runtime.html#pyxu.runtime.enforce_precision" title="pyxu.runtime.enforce_precision"><code class="xref py py-func docutils literal notranslate"><span class="pre">enforce_precision()</span></code></a> to
-abide by Pyxu’s FP-runtime semantics.
-Note however that Torch does not allow mixed-precision computation, so this wrapper will coerce the input if its
-precision does not comply with the specified <code class="code docutils literal notranslate"><span class="pre">dtype</span></code>.
-This triggers a warning by default, which can be silenced via the <code class="code docutils literal notranslate"><span class="pre">enable_warnings</span></code>.</p></li>
-<li><p>Arithmetic methods are <strong>not currently JIT-ed</strong> even if <code class="code docutils literal notranslate"><span class="pre">jit</span></code> is set to <code class="docutils literal notranslate"><span class="pre">True</span></code>.
-This is because of the undocumented and currently poor interaction between <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.0)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> transforms and
-<a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.compile.html#torch.compile" title="(in PyTorch v2.0)"><code class="xref py py-func docutils literal notranslate"><span class="pre">torch.compile()</span></code></a>.
-See <a class="reference external" href="https://github.com/pytorch/pytorch/issues/98822">this issue</a> for additional details.</p></li>
-<li><p>For <a class="reference internal" href="../abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a> (or subclasses thereof), the methods
-<a class="reference internal" href="../abc.html#pyxu.abc.operator.DiffMap.jacobian" title="pyxu.abc.operator.DiffMap.jacobian"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jacobian()</span></code></a>, <a class="reference internal" href="../abc.html#pyxu.abc.operator.DiffFunc.grad" title="pyxu.abc.operator.DiffFunc.grad"><code class="xref py py-meth docutils literal notranslate"><span class="pre">grad()</span></code></a> and
-<a class="reference internal" href="../abc.html#pyxu.abc.operator.LinOp.adjoint" title="pyxu.abc.operator.LinOp.adjoint"><code class="xref py py-meth docutils literal notranslate"><span class="pre">adjoint()</span></code></a> are defined implicitly if not provided using the
-auto-differentiation transforms from <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.0)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a>.
-As detailed <a class="reference external" href="https://pytorch.org/docs/stable/func.ux_limitations.html">on this page</a>, such transforms work well
-on pure functions (that is, functions where the output is completely determined by the input and that do not
-involve side effects like mutation), but may fail on more complex functions.
-Moreover, <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#module-torch.func" title="(in PyTorch v2.0)"><code class="xref py py-mod docutils literal notranslate"><span class="pre">torch.func</span></code></a> does not yet have full coverage over PyTorch operations.
-For functions that call a <a class="reference external" href="https://pytorch.org/docs/stable/generated/torch.nn.Module.html#torch.nn.Module" title="(in PyTorch v2.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.Module</span></code></a>, see <a class="reference external" href="https://pytorch.org/docs/stable/func.api.html#utilities-for-working-with-torch-nn-modules">here</a> for some utilities.</p></li>
-</ul>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>Operators created with this wrapper do not support Dask inputs for now.</p>
-</div>
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.interop.torch.astensor">
-<span class="sig-name descname"><span class="pre">astensor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">requires_grad</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/interop/torch.html#astensor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.torch.astensor" title="Link to this definition">#</a></dt>
-<dd><p>Convert a Numpy-like array into a PyTorch tensor, sharing data, dtype and device.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>arr</strong> (<a class="reference internal" href="../info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – Input array.</p></li>
-<li><p><strong>requires_grad</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If autograd should record operations on the returned tensor.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>tensor</strong> – Output tensor.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="(in PyTorch v2.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.Tensor</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>The returned tensor and input array share the same memory.
-Modifications to the tensor will be reflected in the ndarray and vice versa.
-The returned tensor is not resizable.</p>
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.operator.interop.torch.asarray">
-<span class="sig-name descname"><span class="pre">asarray</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">tensor</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/interop/torch.html#asarray"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.interop.torch.asarray" title="Link to this definition">#</a></dt>
-<dd><p>Convert a PyTorch tensor into a Numpy-like array, sharing data, dtype and device.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>tensor</strong> (<a class="reference external" href="https://pytorch.org/docs/stable/tensors.html#torch.Tensor" title="(in PyTorch v2.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.Tensor</span></code></a>) – Input tensor.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>arr</strong> – Output array.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="../info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>The returned array and input tensor share the same memory.
-Modifications to the tensor will be reflected in the ndarray and vice versa.</p>
-</dd></dl>
-
-</section>
-</section>
-
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diff --git a/api/operator/linop.html b/api/operator/linop.html
index 96f252e9..537cf78e 100644
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 <li class="toctree-l2"><a class="reference internal" href="blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2 current active"><a class="current reference internal" href="#">pyxu.operator.linop</a></li>
@@ -246,13 +241,7 @@
 <li class="toctree-l1"><a class="reference internal" href="../opt.stop.html">pyxu.opt.stop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../runtime.html">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="../util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="../util/array_module.html">pyxu.util.array_module</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="../util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="../util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../references.html"><strong>References</strong></a></li>
 </ul>
@@ -306,7 +295,7 @@ <h2><a class="toc-backref" href="#id46" role="doc-backlink">Basic Operators</a><
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.SubSample">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">SubSample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">indices</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/select.html#SubSample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.SubSample" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
 <p>Multi-dimensional sub-sampling operator.</p>
 <p>This operator extracts a subset of the input matching the provided subset specifier.
 Its Lipschitz constant is 1.</p>
@@ -484,7 +473,7 @@ <h2><a class="toc-backref" href="#id46" role="doc-backlink">Basic Operators</a><
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.IdentityOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">IdentityOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dim</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/base.html#IdentityOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.IdentityOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.OrthProjOp" title="pyxu.abc.operator.OrthProjOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">OrthProjOp</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.OrthProjOp" title="pyxu.abc.operator.OrthProjOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">OrthProjOp</span></code></a></p>
 <p>Identity operator.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -495,7 +484,7 @@ <h2><a class="toc-backref" href="#id46" role="doc-backlink">Basic Operators</a><
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.NullOp">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NullOp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/base.html#NullOp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NullOp" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
 <p>Null operator.</p>
 <p>This operator maps any input vector on the null vector.</p>
 <dl class="field-list simple">
@@ -567,7 +556,7 @@ <h2><a class="toc-backref" href="#id46" role="doc-backlink">Basic Operators</a><
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.Pad">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Pad</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pad_width</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/pad.html#Pad"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Pad" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
 <p>Multi-dimensional padding operator.</p>
 <p>This operator pads the input array in each dimension according to specified widths.</p>
 <p class="rubric">Notes</p>
@@ -723,7 +712,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.FFT">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">FFT</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">axes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/fft/fft.html#FFT"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.FFT" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
 <p>Multi-dimensional Discrete Fourier Transform (DFT) <span class="math notranslate nohighlight">\(A: \mathbb{C}^{N_{1} \times \cdots \times N_{D}} \to
 \mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span>.</p>
 <p>The FFT is defined as follows:</p>
@@ -899,13 +888,13 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <li><p>(…,  N.prod()) inputs <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_{1} \times \cdots \times N_{D}}\)</span>
 (<code class="docutils literal notranslate"><span class="pre">real=True</span></code>.)</p></li>
 <li><p>(…, 2N.prod()) inputs <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span> viewed as a
-real array. (See <a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
+real array. (See <a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
 </ul>
 </p>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
 <dd class="field-even"><p><strong>out</strong> – (…, 2N.prod()) outputs <span class="math notranslate nohighlight">\(\hat{\mathbf{x}} \in \mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span> viewed
-as a real array. (See <a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
+as a real array. (See <a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
 <dd class="field-odd"><p><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
@@ -918,7 +907,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <dd><dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>arr</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, 2N.prod()) outputs <span class="math notranslate nohighlight">\(\hat{\mathbf{x}} \in \mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span> viewed
-as a real array. (See <a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
+as a real array. (See <a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
 <dd class="field-even"><p><p><strong>out</strong> –</p>
@@ -926,7 +915,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <li><p>(…,  N.prod()) inputs <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{R}^{N_{1} \times \cdots \times N_{D}}\)</span>
 (<code class="docutils literal notranslate"><span class="pre">real=True</span></code>.)</p></li>
 <li><p>(…, 2N.prod()) inputs <span class="math notranslate nohighlight">\(\mathbf{x} \in \mathbb{C}^{N_{1} \times \cdots \times N_{D}}\)</span> viewed as a
-real array. (See <a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
+real array. (See <a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
 </ul>
 </p>
 </dd>
@@ -939,7 +928,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.NUFFT">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NUFFT</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">shape</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a></p>
 <p>Non-Uniform Fast Fourier Transform (NUFFT) of Type 1/2/3 (for <span class="math notranslate nohighlight">\(d=\{1,2,3\}\)</span>).</p>
 <p>The <em>Non-Uniform Fast Fourier Transform (NUFFT)</em> generalizes the FFT to off-grid data.  There are three types of
 NUFFTs proposed in the literature:</p>
@@ -993,7 +982,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <li><p><strong>Lipschitz Constants.</strong>
 We bound the Lipschitz constant by the Frobenius norm of the operators, which yields <span class="math notranslate nohighlight">\(L \leq \sqrt{NM}\)</span>.
 Note that these Lipschitz constants are cheap to compute but may be pessimistic.  Tighter Lipschitz constants can
-be computed by calling <a class="reference internal" href="../abc/operator.html#pyxu.abc.Map.estimate_lipschitz" title="pyxu.abc.Map.estimate_lipschitz"><code class="xref py py-meth docutils literal notranslate"><span class="pre">estimate_lipschitz()</span></code></a>.</p></li>
+be computed by calling <a class="reference internal" href="../abc.html#pyxu.abc.Map.estimate_lipschitz" title="pyxu.abc.Map.estimate_lipschitz"><code class="xref py py-meth docutils literal notranslate"><span class="pre">estimate_lipschitz()</span></code></a>.</p></li>
 <li><p><strong>Error Analysis.</strong>
 Let <span class="math notranslate nohighlight">\(\tilde{\mathbf{u}}\in\mathbb{C}^{\mathcal{I}_{N_1,\ldots, N_d}}\)</span> and
 <span class="math notranslate nohighlight">\(\tilde{\mathbf{w}}\in\mathbb{C}^{M}\)</span> be the outputs of the type-1 and type-2 NUFFT algorithms which
@@ -1153,7 +1142,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 vectors viewed as bijections with <span class="math notranslate nohighlight">\(\mathbb{R}^{2M}\)</span>.</p>
 </p></li>
 <li><p><strong>plan_fw/bw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, allocate FINUFFT resources to do the forward (fw) and/or backward (bw) transform.  These are
-advanced options: use them with care.  Some public methods in the <a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> interface may
+advanced options: use them with care.  Some public methods in the <a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> interface may
 not work if fw/bw transforms are disabled.  These options only take effect if <code class="docutils literal notranslate"><span class="pre">eps</span> <span class="pre">&gt;</span> <span class="pre">0</span></code>.</p></li>
 <li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
 <li><p><strong>**kwargs</strong> – <p>Extra kwargs to <a class="reference external" href="https://finufft.readthedocs.io/en/latest/python.html#finufft.Plan">finufft.Plan</a>.
@@ -1223,7 +1212,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <span class="math notranslate nohighlight">\(\mathbb{C}^{N}\)</span> vectors viewed as bijections with <span class="math notranslate nohighlight">\(\mathbb{R}^{2N}\)</span>.</p>
 </p></li>
 <li><p><strong>plan_fw/bw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, allocate FINUFFT resources to do the forward (fw) and/or backward (bw) transform.  These are
-advanced options: use them with care.  Some public methods in the <a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> interface may
+advanced options: use them with care.  Some public methods in the <a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> interface may
 not work if fw/bw transforms are disabled.  These options only take effect if <code class="docutils literal notranslate"><span class="pre">eps</span> <span class="pre">&gt;</span> <span class="pre">0</span></code>.</p></li>
 <li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
 <li><p><strong>**kwargs</strong> – <p>Extra kwargs to <a class="reference external" href="https://finufft.readthedocs.io/en/latest/python.html#finufft.Plan">finufft.Plan</a>.
@@ -1308,7 +1297,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 vectors viewed as bijections with <span class="math notranslate nohighlight">\(\mathbb{R}^{2M}\)</span>.</p>
 </p></li>
 <li><p><strong>plan_fw/bw</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, allocate FINUFFT resources to do the forward (fw) and/or backward (bw) transform.  These are
-advanced options: use them with care.  Some public methods in the <a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> interface may
+advanced options: use them with care.  Some public methods in the <a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> interface may
 not work if fw/bw transforms are disabled.  These options only take effect if <code class="docutils literal notranslate"><span class="pre">eps</span> <span class="pre">&gt;</span> <span class="pre">0</span></code>.</p></li>
 <li><p><strong>enable_warnings</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, emit a warning in case of precision mis-match issues.</p></li>
 <li><p><strong>chunked</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If <code class="docutils literal notranslate"><span class="pre">True</span></code>, the transform is performed in small chunks. (See Notes for details.)</p></li>
@@ -1427,7 +1416,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <dt><strong>Type 1 and 3:</strong></dt><dd><ul>
 <li><p>(…,  M) input weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{R}^{M}\)</span> (real transform).</p></li>
 <li><p>(…, 2M) input weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{C}^{M}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
+<a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
 </ul>
 </dd>
 </dl>
@@ -1437,7 +1426,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <li><p>(…,  N.prod()) input weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{R}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
 (real transform).</p></li>
 <li><p>(…, 2N.prod()) input weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{C}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-viewed as a real array.  (See <a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
+viewed as a real array.  (See <a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
 </ul>
 </dd>
 </dl>
@@ -1450,19 +1439,19 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <ul class="simple">
 <li><dl class="simple">
 <dt><strong>Type 1:</strong></dt><dd><p>(…, 2N.prod()) output weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{C}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-viewed as a real array.  (See <a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
+viewed as a real array.  (See <a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
 </dd>
 </dl>
 </li>
 <li><dl class="simple">
 <dt><strong>Type 2:</strong></dt><dd><p>(…, 2M) output weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{C}^{M}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
+<a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
 </dd>
 </dl>
 </li>
 <li><dl class="simple">
 <dt><strong>Type 3:</strong></dt><dd><p>(…, 2N) output weights <span class="math notranslate nohighlight">\(\mathbf{v} \in \mathbb{C}^{N}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
+<a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
 </dd>
 </dl>
 </li>
@@ -1482,19 +1471,19 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <dd class="field-odd"><p><strong>arr</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – <ul class="simple">
 <li><dl class="simple">
 <dt><strong>Type 1:</strong></dt><dd><p>(…, 2N.prod()) output weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{C}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-viewed as a real array.  (See <a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
+viewed as a real array.  (See <a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
 </dd>
 </dl>
 </li>
 <li><dl class="simple">
 <dt><strong>Type 2:</strong></dt><dd><p>(…, 2M) output weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{C}^{M}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
+<a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
 </dd>
 </dl>
 </li>
 <li><dl class="simple">
 <dt><strong>Type 3:</strong></dt><dd><p>(…, 2N) output weights <span class="math notranslate nohighlight">\(\mathbf{v} \in \mathbb{C}^{N}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
+<a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
 </dd>
 </dl>
 </li>
@@ -1508,7 +1497,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <dt><strong>Type 1 and 3:</strong></dt><dd><ul>
 <li><p>(…,  M) input weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{R}^{M}\)</span> (real transform).</p></li>
 <li><p>(…, 2M) input weights <span class="math notranslate nohighlight">\(\mathbf{w} \in \mathbb{C}^{M}\)</span> viewed as a real array.  (See
-<a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
+<a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
 </ul>
 </dd>
 </dl>
@@ -1518,7 +1507,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <li><p>(…,  N.prod()) input weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{R}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
 (real transform).</p></li>
 <li><p>(…, 2N.prod()) input weights <span class="math notranslate nohighlight">\(\mathbf{u} \in \mathbb{C}^{\mathcal{I}_{N_1, \ldots, N_d}}\)</span>
-viewed as a real array.  (See <a class="reference internal" href="../util/complex.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
+viewed as a real array.  (See <a class="reference internal" href="../util.html#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p></li>
 </ul>
 </dd>
 </dl>
@@ -1533,12 +1522,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 </dd></dl>
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.operator.NUFFT.ascomplexarray">
-<span class="sig-name descname"><span class="pre">ascomplexarray</span></span><span class="sig-paren">(</span>
-<dl>
-<dd><em class="sig-param"><span class="n"><span class="pre">xp=&lt;module</span> <span class="pre">'numpy'</span> <span class="pre">from</span> <span class="pre">'/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/numpy/__init__.py'&gt;</span></span></em>,</dd>
-<dd><em class="sig-param"><span class="n"><span class="pre">dtype=None</span></span></em>,</dd>
-</dl>
-<span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.ascomplexarray"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.ascomplexarray" title="Link to this definition">#</a></dt>
+<span class="sig-name descname"><span class="pre">ascomplexarray</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">xp=&lt;module</span> <span class="pre">'numpy'</span> <span class="pre">from</span> <span class="pre">'/home/sep/miniconda3/envs/pyxu/lib/python3.11/site-packages/numpy/__init__.py'&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype=None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/fft/nufft.html#NUFFT.ascomplexarray"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.NUFFT.ascomplexarray" title="Link to this definition">#</a></dt>
 <dd><p>Matrix representation (complex-valued) of the linear operator.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -1565,7 +1549,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <dt class="sig sig-object py" id="pyxu.operator.NUFFT.mesh">
 <span class="sig-name descname"><span class="pre">mesh</span></span><span class="sig-paren">(</span>
 <dl>
-<dd><em class="sig-param"><span class="n"><span class="pre">xp=&lt;module</span> <span class="pre">'numpy'</span> <span class="pre">from</span> <span class="pre">'/Users/mmjasime/miniconda3/envs/pyxu/lib/python3.11/site-packages/numpy/__init__.py'&gt;</span></span></em>,</dd>
+<dd><em class="sig-param"><span class="n"><span class="pre">xp=&lt;module</span> <span class="pre">'numpy'</span> <span class="pre">from</span> <span class="pre">'/home/sep/miniconda3/envs/pyxu/lib/python3.11/site-packages/numpy/__init__.py'&gt;</span></span></em>,</dd>
 <dd><em class="sig-param"><span class="n"><span class="pre">dtype=None</span></span></em>,</dd>
 <dd><em class="sig-param"><span class="n"><span class="pre">scale='unit'</span></span></em>,</dd>
 <dd><em class="sig-param"><span class="n"><span class="pre">upsampled=False</span></span></em>,</dd>
@@ -1637,15 +1621,15 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>ax</strong> (<a class="reference external" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="(in Matplotlib v3.7.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Axes</span></code></a>) – Axes to draw on.  If <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>, a new axes is used.</p></li>
-<li><p><strong>**kwargs</strong> – Keyword arguments forwarded to <a class="reference external" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="(in Matplotlib v3.7.2)"><code class="xref py py-meth docutils literal notranslate"><span class="pre">matplotlib.axes.Axes.plot()</span></code></a>.</p></li>
+<li><p><strong>ax</strong> (<a class="reference external" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="(in Matplotlib v3.8.0rc1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Axes</span></code></a>) – Axes to draw on.  If <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>, a new axes is used.</p></li>
+<li><p><strong>**kwargs</strong> – Keyword arguments forwarded to <a class="reference external" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.plot.html#matplotlib.axes.Axes.plot" title="(in Matplotlib v3.8.0rc1)"><code class="xref py py-meth docutils literal notranslate"><span class="pre">matplotlib.axes.Axes.plot()</span></code></a>.</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
 <dd class="field-even"><p><strong>ax</strong></p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="(in Matplotlib v3.7.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Axes</span></code></a></p>
+<dd class="field-odd"><p><a class="reference external" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes" title="(in Matplotlib v3.8.0rc1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Axes</span></code></a></p>
 </dd>
 </dl>
 <p class="rubric">Examples</p>
@@ -1860,7 +1844,7 @@ <h2><a class="toc-backref" href="#id47" role="doc-backlink">Transforms</a><a cla
 <dd class="field-even"><p><strong>fig</strong> – Diagnostic plot.</p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://matplotlib.org/stable/api/figure_api.html#matplotlib.figure.Figure" title="(in Matplotlib v3.7.2)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Figure</span></code></a></p>
+<dd class="field-odd"><p><a class="reference external" href="https://matplotlib.org/stable/api/figure_api.html#matplotlib.figure.Figure" title="(in Matplotlib v3.8.0rc1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Figure</span></code></a></p>
 </dd>
 </dl>
 <p class="rubric">Notes</p>
@@ -2062,7 +2046,7 @@ <h2><a class="toc-backref" href="#id48" role="doc-backlink">Stencils &amp; Convo
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.operator.Stencil">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Stencil</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kernel</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">center</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'constant'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">enable_warnings</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/stencil/stencil.html#Stencil"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.Stencil" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.SquareOp" title="pyxu.abc.operator.SquareOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareOp</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.SquareOp" title="pyxu.abc.operator.SquareOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">SquareOp</span></code></a></p>
 <p>Multi-dimensional JIT-compiled stencil.</p>
 <p>Stencils are a common computational pattern in which array elements are updated according to some fixed pattern
 called the <em>stencil kernel</em>.  Notable examples include multi-dimensional convolutions, correlations and finite
@@ -2865,7 +2849,7 @@ <h2><a class="toc-backref" href="#id49" role="doc-backlink">Filters</a><a class=
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
 <li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
+<li><p><strong>sampling</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
 <li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
 <li><p><strong>dtype</strong> (<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><em>dtype</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>None</em><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><em>Type</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>_SupportsDType</em><em>[</em><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><em>dtype</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>]</em><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><em>int</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><em>SupportsIndex</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><em>SupportsIndex</em></a><em>]</em><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.11)"><em>List</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>_DTypeDict</em><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>]</em>) – </p></li>
 </ul>
@@ -3188,7 +3172,7 @@ <h2><a class="toc-backref" href="#id49" role="doc-backlink">Filters</a><a class=
 <dd><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">diff_kwargs</span></span></em>,</dd>
 </dl>
 <span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/operator/linop/filter.html#StructureTensor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.operator.StructureTensor" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="../abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="../abc.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a></p>
 <p>Structure tensor operator.</p>
 <p class="rubric">Notes</p>
 <p>The Structure Tensor, also known as the second-order moment tensor or the inertia tensor, is a matrix derived from
@@ -3222,13 +3206,13 @@ <h3>Remark<a class="headerlink" href="#remark" title="Link to this heading">#</a
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.StructureTensor" title="pyxu.operator.linop.filter.StructureTensor"><span class="n">StructureTensor</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="c1"># Define input image</span>
 <span class="n">n</span> <span class="o">=</span> <span class="mi">1000</span>
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">nsamples</span> <span class="o">=</span> <span class="mi">2</span>
 <span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
 <span class="n">images</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.tile.html#numpy.tile" title="numpy.tile"><span class="n">np</span><span class="o">.</span><span class="n">tile</span></a><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="p">(</span><span class="n">nsamples</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">nsamples</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
@@ -3324,10 +3308,10 @@ <h3>Remark<a class="headerlink" href="#remark" title="Link to this heading">#</a
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>arg_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>smooth_sigma</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
-<li><p><strong>smooth_truncate</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
+<li><p><strong>smooth_sigma</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
+<li><p><strong>smooth_truncate</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
 <li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>sampling</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
+<li><p><strong>sampling</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em>, </em><em>...</em><em>]</em>) – </p></li>
 <li><p><strong>gpu</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
 <li><p><strong>dtype</strong> (<a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><em>dtype</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>None</em><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><em>Type</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>_SupportsDType</em><em>[</em><a class="reference external" href="https://numpy.org/doc/stable/reference/generated/numpy.dtype.html#numpy.dtype" title="(in NumPy v1.25)"><em>dtype</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>]</em><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.11)"><em>int</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><em>SupportsIndex</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Sequence" title="(in Python v3.11)"><em>Sequence</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.SupportsIndex" title="(in Python v3.11)"><em>SupportsIndex</em></a><em>]</em><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.List" title="(in Python v3.11)"><em>List</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>] </em><em>| </em><em>_DTypeDict</em><em> | </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Tuple" title="(in Python v3.11)"><em>Tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Any" title="(in Python v3.11)"><em>Any</em></a><em>]</em>) – </p></li>
 <li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
@@ -3513,11 +3497,11 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.PartialDerivative" title="pyxu.operator.linop.diff.PartialDerivative"><span class="n">PartialDerivative</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># Shape of our image</span>
 <span class="c1"># Specify derivative order at each direction</span>
 <span class="n">df_dx</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>  <span class="c1"># Compute derivative of order 1 in first dimension</span>
@@ -3547,9 +3531,9 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\frac{\partial^</span><span class="si">{3}</span><span class="s2"> f(x,y)}{\partial x\partial y^</span><span class="si">{2}</span><span class="s2">}$"</span><span class="p">)</span>
 <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">(</span><span class="n">im</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">axs</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
 
-<span class="c1"># Test approximation error</span>
+<span class="c1"># Check approximation error</span>
 <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#abs" title="abs"><span class="nb">abs</span></a><span class="p">(</span><span class="n">out1</span> <span class="o">-</span> <span class="n">out2</span><span class="p">)</span> <span class="o">/</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#abs" title="abs"><span class="nb">abs</span></a><span class="p">(</span><span class="n">out2</span><span class="p">)),</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
+<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#abs" title="abs"><span class="nb">abs</span></a><span class="p">(</span><span class="n">out1</span> <span class="o">-</span> <span class="n">out2</span><span class="p">)),</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.colorbar.html#matplotlib.pyplot.colorbar" title="matplotlib.pyplot.colorbar"><span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span></a><span class="p">()</span>
 </pre></div>
 </div>
 <p>(<a class="reference download internal" download="" href="../../_downloads/e1a75dcc78d38d076dc2ecbd8c33f9ad/linop-11.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>)</p>
@@ -3650,11 +3634,11 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.PartialDerivative" title="pyxu.operator.linop.diff.PartialDerivative"><span class="n">PartialDerivative</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># Shape of our image</span>
 <span class="c1"># Specify derivative order at each direction</span>
 <span class="n">df_dx</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="c1"># Compute derivative of order 1 in first dimension</span>
@@ -3773,13 +3757,13 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><span class="n">Gradient</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="c1"># Define input image</span>
 <span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
 <span class="c1"># Instantiate gradient operator</span>
 <span class="n">grad</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><span class="n">Gradient</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">)</span>
@@ -3894,11 +3878,11 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Jacobian" title="pyxu.operator.Jacobian"><span class="n">Jacobian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.tile.html#numpy.tile" title="numpy.tile"><span class="n">np</span><span class="o">.</span><span class="n">tile</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.tile.html#numpy.tile" title="numpy.tile"><span class="n">np</span><span class="o">.</span><span class="n">tile</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
 <span class="n">jac</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Jacobian" title="pyxu.operator.Jacobian"><span class="n">Jacobian</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">image</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="n">n_channels</span><span class="o">=</span><span class="n">image</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
 <span class="n">out</span> <span class="o">=</span> <span class="n">jac</span><span class="o">.</span><span class="n">unravel</span><span class="p">(</span><span class="n">jac</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span>
 <span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html#matplotlib.pyplot.subplots" title="matplotlib.pyplot.subplots"><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span></a><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">15</span><span class="p">))</span>
@@ -3997,12 +3981,12 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><span class="n">Gradient</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Divergence" title="pyxu.operator.Divergence"><span class="n">Divergence</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><span class="n">Laplacian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
 <span class="n">grad</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Gradient" title="pyxu.operator.Gradient"><span class="n">Gradient</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">)</span>
 <span class="n">div</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Divergence" title="pyxu.operator.Divergence"><span class="n">Divergence</span></a><span class="p">(</span><span class="n">arg_shape</span><span class="o">=</span><span class="n">arg_shape</span><span class="p">)</span>
@@ -4071,7 +4055,7 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 { \partial x_{0}\partial x_{1} }, \, \ldots , \, \frac{ \partial^{2}\mathbf{f} }{ \partial x_{D-1}^{2} }\right).\]</div>
 </li>
 </ul>
-<p>The shape of the output <a class="reference internal" href="../abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> depends on the number of computed directions; by
+<p>The shape of the output <a class="reference internal" href="../abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a> depends on the number of computed directions; by
 default (all directions), we have <span class="math notranslate nohighlight">\(\mathbf{H} \mathbf{f} \in \mathbb{R}^{\frac{D(D-1)}{2} \times N_0 \times
 \cdots \times N_{D-1}}\)</span>.</p>
 <p>The Hessian operator’s <code class="xref py py-meth docutils literal notranslate"><span class="pre">unravel()</span></code> method allows reshaping the vectorized
@@ -4126,12 +4110,12 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Hessian" title="pyxu.operator.Hessian"><span class="n">Hessian</span></a><span class="p">,</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.PartialDerivative" title="pyxu.operator.linop.diff.PartialDerivative"><span class="n">PartialDerivative</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
 
 <span class="c1"># Instantiate Hessian operator</span>
@@ -4239,13 +4223,13 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.Laplacian" title="pyxu.operator.Laplacian"><span class="n">Laplacian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="c1"># Define input image</span>
 <span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">image</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 
 <span class="n">arg_shape</span> <span class="o">=</span> <span class="n">image</span><span class="o">.</span><span class="n">shape</span>  <span class="c1"># (1000, 1000)</span>
 <span class="c1"># Compute Laplacian</span>
@@ -4382,11 +4366,11 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.DirectionalDerivative" title="pyxu.operator.DirectionalDerivative"><span class="n">DirectionalDerivative</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">directions</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
 <span class="n">directions</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
 <span class="n">directions</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
@@ -4487,11 +4471,11 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.DirectionalGradient" title="pyxu.operator.DirectionalGradient"><span class="n">DirectionalGradient</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">directions1</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
 <span class="n">directions1</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
 <span class="n">directions1</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
@@ -4607,11 +4591,11 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.DirectionalLaplacian" title="pyxu.operator.DirectionalLaplacian"><span class="n">DirectionalLaplacian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">directions1</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
 <span class="n">directions1</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
 <span class="n">directions1</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
@@ -4725,11 +4709,11 @@ <h2><a class="toc-backref" href="#id50" role="doc-backlink">Derivatives</a><a cl
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/operator/linop.html#pyxu.operator.DirectionalHessian" title="pyxu.operator.DirectionalHessian"><span class="n">DirectionalHessian</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
 <span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mi">25</span><span class="p">)</span>
 <span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
 <span class="n">directions1</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
 <span class="n">directions1</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:</span><span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
 <span class="n">directions1</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">z</span><span class="o">.</span><span class="n">size</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
diff --git a/api/operator/map.html b/api/operator/map.html
index 6742a216..106ffe8d 100644
--- a/api/operator/map.html
+++ b/api/operator/map.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
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-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
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-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
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-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
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@@ -730,8 +719,8 @@ <h2><a class="toc-backref" href="#id1" role="doc-backlink">Element-wise Operator
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+<li><p><strong>a_max</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
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@@ -810,7 +799,7 @@ <h2><a class="toc-backref" href="#id1" role="doc-backlink">Element-wise Operator
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@@ -858,7 +847,7 @@ <h2><a class="toc-backref" href="#id1" role="doc-backlink">Element-wise Operator
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@@ -887,7 +876,7 @@ <h2><a class="toc-backref" href="#id1" role="doc-backlink">Element-wise Operator
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 <dt class="field-even">Return type<span class="colon">:</span></dt>
@@ -1155,7 +1144,7 @@ <h2><a class="toc-backref" href="#id2" role="doc-backlink">Misc</a><a class="hea
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 <dt class="field-even">Return type<span class="colon">:</span></dt>
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-<section id="pyxu-opt">
-<h1>pyxu.opt<a class="headerlink" href="#pyxu-opt" title="Link to this heading">#</a></h1>
-<nav class="contents local" id="table-of-contents">
-<p class="topic-title">Table of Contents</p>
-<ul class="simple">
-<li><p><a class="reference internal" href="#pyxu-opt-stop" id="id60">pyxu.opt.stop</a></p></li>
-<li><p><a class="reference internal" href="#pyxu-opt-solver" id="id61">pyxu.opt.solver</a></p></li>
-</ul>
-</nav>
-<section id="pyxu-opt-stop">
-<h2><a class="toc-backref" href="#id60" role="doc-backlink">pyxu.opt.stop</a><a class="headerlink" href="#pyxu-opt-stop" title="Link to this heading">#</a></h2>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.stop.MaxIter">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MaxIter</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#MaxIter"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.MaxIter" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
-<p>Stop iterative solver after a fixed number of iterations.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>If you want to add a grace period to a solver, i.e. for it to do <em>at least</em> N iterations before
-stopping based on the value of another criteria, you can AND <a class="reference internal" href="#pyxu.opt.stop.MaxIter" title="pyxu.opt.stop.MaxIter"><code class="xref py py-class docutils literal notranslate"><span class="pre">MaxIter</span></code></a>
-with the other criteria.</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="n">sc</span> <span class="o">=</span> <span class="n">MaxIter</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span> <span class="o">&amp;</span> <span class="n">AbsError</span><span class="p">(</span><span class="n">eps</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
-<span class="c1"># If N_iter &lt; 5  -&gt; never stop.</span>
-<span class="c1"># If N_iter &gt;= 5 -&gt; stop if AbsError() decides to.</span>
-</pre></div>
-</div>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>n</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>) – </p>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.opt.stop.MaxIter.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#MaxIter.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.MaxIter.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>n</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Max number of iterations allowed.</p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.stop.ManualStop">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ManualStop</span></span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#ManualStop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.ManualStop" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
-<p>Continue-forever criterion.</p>
-<p>This class is useful when calling
-<a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a>
-with mode=MANUAL/ASYNC to defer the stopping decision to an explicit call by the user, i.e.:</p>
-<ul class="simple">
-<li><p>mode=MANUAL: user must stop calling <code class="docutils literal notranslate"><span class="pre">next(solver.steps())</span></code>;</p></li>
-<li><p>mode=ASYNC: user must call <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.stop" title="pyxu.abc.solver.Solver.stop"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stop()</span></code></a>.</p></li>
-</ul>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.opt.stop.ManualStop.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#pyxu.opt.stop.ManualStop.__init__" title="Link to this definition">#</a></dt>
-<dd></dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.stop.MaxDuration">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MaxDuration</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#MaxDuration"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.MaxDuration" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
-<p>Stop iterative solver after a specified duration has elapsed.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>t</strong> (<a class="reference external" href="https://docs.python.org/3/library/datetime.html#datetime.timedelta" title="(in Python v3.11)"><em>timedelta</em></a>) – </p>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.opt.stop.MaxDuration.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#MaxDuration.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.MaxDuration.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>t</strong> (<a class="reference external" href="https://docs.python.org/3/library/datetime.html#datetime.timedelta" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">timedelta</span></code></a>) – Max runtime allowed.</p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.stop.MaxCarbon">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MaxCarbon</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">co2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#MaxCarbon"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.MaxCarbon" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
-<p>Stop iterative solver after a threshold amount of carbon dioxide (CO2) was produced by computing
-resources used to execute the optimization.</p>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>Codecarbon is not a core dependency of Pyxu and must be installed separately.</p>
-<p>On Windows and MacOS, <a class="reference external" href="https://pypi.org/project/codecarbon/">codecarbon</a> tracks power consumption of
-Intel processors using the
-<a class="reference external" href="https://www.intel.com/content/www/us/en/developer/articles/tool/power-gadget.html">Intel Power Gadget (IPG)</a>.
-IPG must be installed independently.
-(MacOS-specific: IPG must also have correct security permissions.)</p>
-</div>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>co2</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.opt.stop.MaxCarbon.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">co2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#MaxCarbon.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.MaxCarbon.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>co2</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Max allowed CO2 emissions [Kg].</p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.stop.Memorize">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Memorize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#Memorize"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.Memorize" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
-<p>Memorize a variable.
-(Special <a class="reference internal" href="abc.html#pyxu.abc.solver.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a> mostly useful for tracking objective functions in
-<a class="reference internal" href="abc.html#pyxu.abc.solver.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a>.)</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>var</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.opt.stop.Memorize.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#Memorize.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.Memorize.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>var</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variable in <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver._mstate" title="pyxu.abc.solver.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver._mstate</span></code></a> to query.
-Must be a scalar or NDArray (1D).</p>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.stop.AbsError">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">AbsError</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">eps</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'x'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">satisfy_all</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#AbsError"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.AbsError" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
-<p>Stop iterative solver after absolute norm of a variable (or function thereof) reaches threshold.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>eps</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-<li><p><strong>var</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>]</em><em>, </em><a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em><em>, </em><a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
-<li><p><strong>norm</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-<li><p><strong>satisfy_all</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.opt.stop.AbsError.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">eps</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'x'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">satisfy_all</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#AbsError.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.AbsError.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>eps</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive threshold.</p></li>
-<li><p><strong>var</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variable in <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver._mstate" title="pyxu.abc.solver.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver._mstate</span></code></a> to query.</p></li>
-<li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Callable</span></code></a>) – <p>Optional function to pre-apply to <code class="docutils literal notranslate"><span class="pre">_mstate[var]</span></code> before applying the norm.
-Defaults to the identity function. The callable should either:</p>
-<ul>
-<li><p>accept a scalar input -&gt; output a scalar, or</p></li>
-<li><p>accept an NDArray input -&gt; output an NDArray, i.e same semantics as
-<a class="reference internal" href="abc.html#pyxu.abc.operator.Map.apply" title="pyxu.abc.operator.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>.</p></li>
-</ul>
-</p></li>
-<li><p><strong>norm</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Ln norm to use &gt;= 0. (Default: L2.)</p></li>
-<li><p><strong>satisfy_all</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If True (default) and <code class="docutils literal notranslate"><span class="pre">_mstate[var]</span></code> is multi-dimensional, stop if all evaluation
-points lie below threshold.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.stop.RelError">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">RelError</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">eps</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'x'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">satisfy_all</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#RelError"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.RelError" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
-<p>Stop iterative solver after relative norm change of a variable (or function thereof) reaches
-threshold.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>eps</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-<li><p><strong>var</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>]</em><em>, </em><a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em><em>, </em><a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
-<li><p><strong>norm</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
-<li><p><strong>satisfy_all</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-<dl class="py method">
-<dt class="sig sig-object py" id="pyxu.opt.stop.RelError.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">eps</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'x'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">satisfy_all</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#RelError.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.RelError.__init__" title="Link to this definition">#</a></dt>
-<dd><dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>eps</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive threshold.</p></li>
-<li><p><strong>var</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variable in <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver._mstate" title="pyxu.abc.solver.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver._mstate</span></code></a> to query.</p></li>
-<li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Callable</span></code></a>) – <p>Optional function to pre-apply to <code class="docutils literal notranslate"><span class="pre">_mstate[var]</span></code> before applying the norm.
-Defaults to the identity function. The callable should either:</p>
-<ul>
-<li><p>accept a scalar input -&gt; output a scalar, or</p></li>
-<li><p>accept an NDArray input -&gt; output an NDArray, i.e same semantics as
-<a class="reference internal" href="abc.html#pyxu.abc.operator.Map.apply" title="pyxu.abc.operator.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>.</p></li>
-</ul>
-</p></li>
-<li><p><strong>norm</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Ln norm to use &gt;= 0. (Default: L2.)</p></li>
-<li><p><strong>satisfy_all</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>) – If True (default) and <code class="docutils literal notranslate"><span class="pre">_mstate[var]</span></code> is multi-dimensional, stop if all evaluation
-points lie below threshold.</p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-</dd></dl>
-</section>
-<section id="pyxu-opt-solver">
-<h2><a class="toc-backref" href="#id61" role="doc-backlink">pyxu.opt.solver</a><a class="headerlink" href="#pyxu-opt-solver" title="Link to this heading">#</a></h2>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pgd.PGD">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PGD</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pgd.html#PGD"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pgd.PGD" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
-<p>Proximal Gradient Descent (PGD) solver.</p>
-<p>PGD solves minimization problems of the form</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \;\mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{G}(\mathbf{x})},\]</div>
-<p>where:</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}:\mathbb{R}^N\rightarrow \mathbb{R}\)</span> is <em>convex</em> and <em>differentiable</em>, with
-<span class="math notranslate nohighlight">\(\beta\)</span>-<em>Lipschitz continuous</em> gradient, for some <span class="math notranslate nohighlight">\(\beta\in[0,+\infty[\)</span>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{G}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> is a <em>proper</em>, <em>lower
-semicontinuous</em> and <em>convex function</em> with a <em>simple proximal operator</em>.</p></li>
-</ul>
-<section id="remarks">
-<h3>Remarks<a class="headerlink" href="#remarks" title="Link to this heading">#</a></h3>
-<ul>
-<li><p>The problem is <em>feasible</em> – i.e. there exists at least one solution.</p></li>
-<li><p>The algorithm is still valid if either <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> or <span class="math notranslate nohighlight">\(\mathcal{G}\)</span> is zero.</p></li>
-<li><p>The convergence is guaranteed for step sizes <span class="math notranslate nohighlight">\(\tau\leq 1/\beta\)</span>.</p></li>
-<li><p>Various acceleration schemes are described in <a class="reference internal" href="../references.html#apgd" id="id1"><span>[APGD]</span></a>.
-PGD achieves the following (optimal) <em>convergence rate</em> with the implemented acceleration scheme
-from Chambolle &amp; Dossal:</p>
-<div class="math notranslate nohighlight">
-\[\lim\limits_{n\rightarrow \infty} n^2\left\vert \mathcal{J}(\mathbf{x}^\star)- \mathcal{J}(\mathbf{x}_n)\right\vert=0
-\qquad\&amp;\qquad
-\lim\limits_{n\rightarrow \infty} n^2\Vert \mathbf{x}_n-\mathbf{x}_{n-1}\Vert^2_\mathcal{X}=0,\]</div>
-<p>for <em>some minimiser</em> <span class="math notranslate nohighlight">\({\mathbf{x}^\star}\in\arg\min_{\mathbf{x}\in\mathbb{R}^N} \;\left\{\mathcal{J}(\mathbf{x}):=\mathcal{F}(\mathbf{x})+\mathcal{G}(\mathbf{x})\right\}\)</span>.
-In other words, both the objective functional and the PGD iterates
-<span class="math notranslate nohighlight">\(\{\mathbf{x}_n\}_{n\in\mathbb{N}}\)</span> converge at a rate <span class="math notranslate nohighlight">\(o(1/n^2)\)</span>.
-Significant practical <em>speedup</em> can be achieved for values of <span class="math notranslate nohighlight">\(d\)</span> in the range
-<span class="math notranslate nohighlight">\([50,100]\)</span> <a class="reference internal" href="../references.html#apgd" id="id2"><span>[APGD]</span></a>.</p>
-</li>
-<li><p>The relative norm change of the primal variable is used as the default stopping criterion.
-By default, the algorithm stops when the norm of the difference between two consecutive PGD
-iterates <span class="math notranslate nohighlight">\(\{\mathbf{x}_n\}_{n\in\mathbb{N}}\)</span> is smaller than 1e-4.
-Different stopping criteria can be used.</p></li>
-</ul>
-</section>
-<section id="parameters-init">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#parameters-init" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="parameters-fit">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#parameters-fit" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s).</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Gradient step size.
-Defaults to <span class="math notranslate nohighlight">\(1 / \beta\)</span> if unspecified.</p></li>
-<li><p><strong>acceleration</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">bool</span></code></a>)
-–
-If True (default), then use Chambolle &amp; Dossal acceleration scheme.</p></li>
-<li><p><strong>d</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>)
-–
-Chambolle &amp; Dossal acceleration parameter <span class="math notranslate nohighlight">\(d\)</span>.
-Should be greater than 2.
-Only meaningful if <code class="code docutils literal notranslate"><span class="pre">acceleration</span></code> is True.
-Defaults to 75 in unspecified.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.cg.CG">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">CG</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/cg.html#CG"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.cg.CG" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
-<p>Conjugate Gradient Method.</p>
-<p>The Conjugate Gradient method solves the minimization problem</p>
-<div class="math notranslate nohighlight">
-\[\min_{x\in\mathbb{R}^{N}} \frac{1}{2} \mathbf{x}^{T} \mathbf{A} \mathbf{x} - \mathbf{x}^{T} \mathbf{b},\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathbf{A}: \mathbb{R}^{N} \to \mathbb{R}^{N}\)</span> is a <em>symmetric</em> <em>positive definite</em>
-operator, and <span class="math notranslate nohighlight">\(\mathbf{b} \in \mathbb{R}^{N}\)</span>.</p>
-<p>The norm of the <a class="reference external" href="https://www.wikiwand.com/en/Conjugate_gradient_method">explicit residual</a>
-<span class="math notranslate nohighlight">\(\mathbf {r}_{k+1}:=\mathbf{b}-\mathbf{Ax}_{k+1}\)</span> is used as the default stopping criterion.
-This provides a guaranteed level of accuracy both in exact arithmetic and in the presence of
-round-off errors.
-By default, the iterations stop when the norm of the explicit residual is smaller than 1e-4.</p>
-<section id="id3">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id3" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.PosDefOp" title="pyxu.abc.operator.PosDefOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">PosDefOp</span></code></a>)
-–
-Positive-definite operator <span class="math notranslate nohighlight">\(\mathbf{A}: \mathbb{R}^{N} \to \mathbb{R}^{N}\)</span>.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id4">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id4" title="Link to this heading">#</a></h3>
-<ul>
-<li><p><strong>b</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) <span class="math notranslate nohighlight">\(\mathbf{b}\)</span> terms in the CG cost function.</p>
-<p>All problems are solved in parallel.</p>
-</li>
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, N) initial point(s).</p>
-<p>Must be broadcastable with <code class="code docutils literal notranslate"><span class="pre">b</span></code> if provided.
-Defaults to 0.</p>
-</li>
-<li><p><strong>restart_rate</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Integer</span></code></a>)
-–
-Number of iterations after which restart is applied.</p>
-<p>By default, a restart is done after ‘n’ iterations, where ‘n’ corresponds to the dimension of <span class="math notranslate nohighlight">\(\mathbf{A}\)</span>.</p>
-</li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>A</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.PosDefOp" title="pyxu.abc.operator.PosDefOp"><em>PosDefOp</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.nlcg.NLCG">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NLCG</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/nlcg.html#NLCG"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.nlcg.NLCG" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
-<p>Nonlinear Conjugate Gradient Method (NLCG).</p>
-<p>The Nonlinear Conjugate Gradient method finds a local minimum of the problem</p>
-<div class="math notranslate nohighlight">
-\[\min_{x\in\mathbb{R}^{N}} f(x),\]</div>
-<p>where <span class="math notranslate nohighlight">\(f: \mathbb{R}^{N} \to \mathbb{R}\)</span> is a <em>differentiable</em> functional.
-When <span class="math notranslate nohighlight">\(f\)</span> is quadratic, NLCG is equivalent to the Conjugate Gradient (CG) method.
-NLCG hence has similar convergence behaviour to CG if <span class="math notranslate nohighlight">\(f\)</span> is locally-quadratic.
-The converge speed may be slower however due to its line-search overhead <a class="reference internal" href="../references.html#numopt-nocwri" id="id5"><span>[NumOpt_NocWri]</span></a>.</p>
-<p>The norm of the <a class="reference external" href="https://www.wikiwand.com/en/Nonlinear_conjugate_gradient_method">gradient</a>
-<span class="math notranslate nohighlight">\(\nabla f_k = \nabla f(x_k)\)</span> is used as the default stopping criterion.
-By default, the iterations stop when the norm of the gradient is smaller than 1e-4.</p>
-<p>Multiple variants of NLCG exist.
-They differ mainly in how the weights applied to conjugate directions are updated.
-Two popular variants are implemented:</p>
-<ul>
-<li><p>The Fletcher-Reeves variant:</p>
-<div class="math notranslate nohighlight">
-\[\beta_k^\text{FR}
-=
-\frac{
-  \Vert{\nabla f_{k+1}}\Vert_{2}^{2}
-}{
-  \Vert{\nabla f_{k}}\Vert_{2}^{2}
-}.\]</div>
-</li>
-<li><p>The Polak-Ribière+ method:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\beta_k^\text{PR}
-=
-\frac{
-  \nabla f_{k+1}^T\left(\nabla f_{k+1} - \nabla f_k\right)
-}{
-  \Vert{\nabla f_{k}}\Vert_{2}^{2}
-} \\
-\beta_k^\text{PR+}
-=
-\max\left(0, \beta_k^\text{PR}\right).\end{split}\]</div>
-</li>
-</ul>
-<section id="id6">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id6" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>)
-–
-Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id7">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id7" title="Link to this heading">#</a></h3>
-<ul>
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s).</p></li>
-<li><p><strong>variant</strong> (“PR”, “FR”)
-–
-Name of the NLCG variant to use:</p>
-<ul class="simple">
-<li><p>“PR”: Polak-Ribière+ variant (default).</p></li>
-<li><p>“FR”: Fletcher-Reeves variant.</p></li>
-</ul>
-</li>
-<li><p><strong>restart_rate</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Integer</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Number of iterations after which restart is applied.</p>
-<p>By default, restart is done after <span class="math notranslate nohighlight">\(N\)</span> iterations.</p>
-</li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Optional parameters forwarded to <a class="reference internal" href="math.html#pyxu.math.linesearch.backtracking_linesearch" title="pyxu.math.linesearch.backtracking_linesearch"><code class="xref py py-func docutils literal notranslate"><span class="pre">backtracking_linesearch()</span></code></a>.</p>
-<p>If <code class="code docutils literal notranslate"><span class="pre">a0</span></code> is unspecified and <span class="math notranslate nohighlight">\(\nabla f\)</span> is <span class="math notranslate nohighlight">\(\beta\)</span>-Lipschitz continuous, then <code class="code docutils literal notranslate"><span class="pre">a0</span></code>
-is auto-chosen as <span class="math notranslate nohighlight">\(\beta^{-1}\)</span>.
-Users are expected to set <code class="code docutils literal notranslate"><span class="pre">a0</span></code> if its value cannot be auto-inferred.</p>
-<p>Other keyword parameters are passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p>
-</li>
-</ul>
-<p class="rubric">Example</p>
-<p>Consider the following quadratic optimization problem:</p>
-<p>This problem is strictly convex, hence NLCG will converge to the optimal solution:</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="kn">import</span> <span class="nn">pyxu.opt.solver</span> <span class="k">as</span> <span class="nn">pxsl</span>
-
-<span class="n">N</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span>
-<span class="n">f</span> <span class="o">=</span> <span class="n">pxo</span><span class="o">.</span><span class="n">SquaredL2Norm</span><span class="p">(</span><span class="n">N</span><span class="p">)</span><span class="o">.</span><span class="n">asloss</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="o">.</span><span class="n">argscale</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>  <span class="c1"># \norm(Ax - b)**2</span>
-
-<span class="n">nlcg</span> <span class="o">=</span> <span class="n">pxsl</span><span class="o">.</span><span class="n">NLCG</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
-<span class="n">nlcg</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">x0</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,)),</span> <span class="n">variant</span><span class="o">=</span><span class="s2">"FR"</span><span class="p">)</span>
-<span class="n">x_opt</span> <span class="o">=</span> <span class="n">nlcg</span><span class="o">.</span><span class="n">solution</span><span class="p">()</span>
-<span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">x_opt</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="n">a</span><span class="p">)</span>  <span class="c1"># True</span>
-</pre></div>
-</div>
-<p>Note however that the CG method is preferable in this context since it omits the linesearch
-overhead. The former depends on the cost of applying <span class="math notranslate nohighlight">\(A\)</span>, and may be significant.</p>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.adam.Adam">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Adam</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/adam.html#Adam"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.adam.Adam" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
-<p>Adam solver <a class="reference internal" href="../references.html#proxadam" id="id8"><span>[ProxAdam]</span></a>.</p>
-<p>Adam minimizes</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \;\mathcal{F}(\mathbf{x})},\]</div>
-<p>where:</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}:\mathbb{R}^N\rightarrow \mathbb{R}\)</span> is <em>convex</em> and <em>differentiable</em>, with
-<span class="math notranslate nohighlight">\(\beta\)</span>-<em>Lipschitz continuous</em> gradient, for some <span class="math notranslate nohighlight">\(\beta\in[0,+\infty[\)</span>.</p></li>
-</ul>
-<p>Adam is a suitable alternative to Proximal Gradient Descent (<a class="reference internal" href="#pyxu.opt.solver.pgd.PGD" title="pyxu.opt.solver.pgd.PGD"><code class="xref py py-class docutils literal notranslate"><span class="pre">PGD</span></code></a>) when:</p>
-<ul class="simple">
-<li><p>the cost function is differentiable,</p></li>
-<li><p>computing <span class="math notranslate nohighlight">\(\beta\)</span> to optimally choose the step size is infeasible,</p></li>
-<li><p>line-search methods to estimate step sizes are too expensive.</p></li>
-</ul>
-<p>Compared to PGD, Adam auto-tunes gradient updates based on stochastic estimates of <span class="math notranslate nohighlight">\(\phi_{t} =
-\mathbb{E}[\nabla\mathcal{F}]\)</span> and <span class="math notranslate nohighlight">\(\psi_{t} = \mathbb{E}[\nabla\mathcal{F}^{2}]\)</span> respectively.</p>
-<p>Adam has many named variants for particular choices of <span class="math notranslate nohighlight">\(\phi\)</span> and <span class="math notranslate nohighlight">\(\psi\)</span>:</p>
-<ul>
-<li><p>Adam:</p>
-<div class="math notranslate nohighlight">
-\[\phi_t
-=
-\frac{
-  \mathbf{m}_t
-}{
-  1-\beta_1^t
-}
-\qquad
-\psi_t
-=
-\sqrt{
-  \frac{
-    \mathbf{v}_t
-  }{
-    1-\beta_2^t
-  }
-} + \epsilon,\]</div>
-</li>
-<li><p>AMSGrad:</p>
-<div class="math notranslate nohighlight">
-\[\phi_t = \mathbf{m}_t
-\qquad
-\psi_t = \sqrt{\hat{\mathbf{v}}_t},\]</div>
-</li>
-<li><p>PAdam:</p>
-<div class="math notranslate nohighlight">
-\[\phi_t = \mathbf{m}_t
-\qquad
-\psi_t = \hat{\mathbf{v}}_t^p,\]</div>
-</li>
-</ul>
-<p>where in all cases:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\mathbf{m}_t
-=
-\beta_1\mathbf{m}_{t-1}
-+
-(1-\beta_1)\mathbf{g}_t \\
-\mathbf{v}_t
-=
-\beta_2\mathbf{v}_{t-1}
-+
-(1-\beta_2)\mathbf{g}_t^2\\
-\hat{\mathbf{v}}_t
-=
-\max(\hat{\mathbf{v}}_{t-1}, \mathbf{v}_t),\end{split}\]</div>
-<p>with <span class="math notranslate nohighlight">\(\mathbf{m}_0 = \mathbf{v}_0 = \mathbf{0}\)</span>.</p>
-<section id="id9">
-<h3>Remarks<a class="headerlink" href="#id9" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p>The convergence is guaranteed for step sizes <span class="math notranslate nohighlight">\(\alpha\leq 2/\beta\)</span>.</p></li>
-<li><p>The default stopping criterion is the relative norm change of the primal variable.
-By default, the algorithm stops when the norm of the difference between two consecutive iterates
-<span class="math notranslate nohighlight">\(\{\mathbf{x}_n\}_{n\in\mathbb{N}}\)</span> is smaller than 1e-4.
-Different stopping criteria can be used.
-It is recommended to change the stopping criterion when using the PAdam and AMSGrad variants to avoid premature
-stops.</p></li>
-</ul>
-</section>
-<section id="id10">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id10" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>)
-–
-Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id11">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id11" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s).</p></li>
-<li><p><strong>variant</strong> (“adam”, “amsgrad”, “padam”)
-–
-Name of the Adam variant to use.
-Defaults to “adam”.</p></li>
-<li><p><strong>a</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Max normalized gradient step size.
-Defaults to <span class="math notranslate nohighlight">\(1 / \beta\)</span> if unspecified.</p></li>
-<li><p><strong>b1</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>)
-–
-1st-order gradient exponential decay <span class="math notranslate nohighlight">\(\beta_{1} \in [0, 1)\)</span>.</p></li>
-<li><p><strong>b2</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>)
-–
-2nd-order gradient exponential decay <span class="math notranslate nohighlight">\(\beta_{2} \in [0, 1)\)</span>.</p></li>
-<li><p><strong>m0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, N) initial 1st-order gradient estimate corresponding to each initial point.
-Defaults to the null vector if unspecified.</p></li>
-<li><p><strong>v0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, N) initial 2nd-order gradient estimate corresponding to each initial point.
-Defaults to the null vector if unspecified.</p></li>
-<li><p><strong>p</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>)
-–
-PAdam power parameter <span class="math notranslate nohighlight">\(p \in (0, 0.5]\)</span>.
-Must be specified for PAdam, unused otherwise.</p></li>
-<li><p><strong>eps_adam</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>)
-–
-Adam noise parameter <span class="math notranslate nohighlight">\(\epsilon\)</span>.
-This term is used exclusively if <code class="code docutils literal notranslate"><span class="pre">variant="adam"</span></code>.
-Defaults to 1e-6.</p></li>
-<li><p><strong>eps_var</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>)
-–
-Avoids division by zero if estimated gradient variance is too small.
-Defaults to 1e-6.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<div class="admonition note">
-<p class="admonition-title">Note</p>
-<p>If provided, <code class="code docutils literal notranslate"><span class="pre">m0</span></code> and <code class="code docutils literal notranslate"><span class="pre">v0</span></code> must be broadcastable with <code class="code docutils literal notranslate"><span class="pre">x0</span></code>.</p>
-</div>
-<p class="rubric">Example</p>
-<p>Consider the following optimization problem:</p>
-<div class="math notranslate nohighlight">
-\[\min_{\mathbf{x}\in\mathbb{R}^N} \Vert{\mathbf{x}-\mathbf{1}}\Vert_2^2\]</div>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-
-<span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <span class="n">SquaredL2Norm</span>
-<span class="kn">from</span> <span class="nn">pyxu.opt.solver</span> <span class="kn">import</span> <span class="n">Adam</span>
-
-<span class="n">N</span> <span class="o">=</span> <span class="mi">3</span>
-<span class="n">f</span> <span class="o">=</span> <span class="n">SquaredL2Norm</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="n">N</span><span class="p">)</span><span class="o">.</span><span class="n">asloss</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-
-<span class="n">slvr</span> <span class="o">=</span> <span class="n">Adam</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
-<span class="n">slvr</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span>
-    <span class="n">x0</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,)),</span>
-    <span class="n">variant</span><span class="o">=</span><span class="s2">"padam"</span><span class="p">,</span>
-    <span class="n">p</span><span class="o">=</span><span class="mf">0.25</span><span class="p">,</span>
-<span class="p">)</span>
-<span class="n">x_opt</span> <span class="o">=</span> <span class="n">slvr</span><span class="o">.</span><span class="n">solution</span><span class="p">()</span>
-<span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">x_opt</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span>  <span class="c1"># True</span>
-</pre></div>
-</div>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.CondatVu">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">CondatVu</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">h</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pds.html#CondatVu"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pds.CondatVu" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_PrimalDualSplitting</span></code></p>
-<p>Condat-Vu (CV) primal-dual splitting algorithm.</p>
-<p>This solver is also accessible via the alias <a class="reference internal" href="#pyxu.opt.solver.pds.CV" title="pyxu.opt.solver.pds.CV"><code class="xref py py-class docutils literal notranslate"><span class="pre">CV</span></code></a>.</p>
-<p>The <em>Condat-Vu (CV)</em> primal-dual method is described in <a class="reference internal" href="../references.html#cvs" id="id12"><span>[CVS]</span></a>.
-(This particular implementation is based on the pseudo-code Algorithm 7.1 provided in <a class="reference internal" href="../references.html#funcsphere" id="id13"><span>[FuncSphere]</span></a> Chapter 7, Section1.)</p>
-<p>It can be used to solve problems of the form:</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \;\mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{G}(\mathbf{x})\;\;+\;\;\mathcal{H}(\mathcal{K} \mathbf{x})},\]</div>
-<p>where:</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}:\mathbb{R}^N\rightarrow \mathbb{R}\)</span> is <em>convex</em> and <em>differentiable</em>, with <span class="math notranslate nohighlight">\(\beta\)</span>-<em>Lipschitz continuous</em> gradient,
-for some <span class="math notranslate nohighlight">\(\beta\in[0,+\infty[\)</span>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{G}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> and <span class="math notranslate nohighlight">\(\mathcal{H}:\mathbb{R}^M\rightarrow \mathbb{R}\cup\{+\infty\}\)</span>
-are <em>proper</em>, <em>lower semicontinuous</em> and <em>convex functions</em> with <em>simple proximal operators</em>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{K}:\mathbb{R}^N\rightarrow \mathbb{R}^M\)</span> is a <em>differentiable map</em> (e.g. a <em>linear operator</em> <span class="math notranslate nohighlight">\(\mathbf{K}\)</span>), with <strong>operator norm</strong>:</p>
-<div class="math notranslate nohighlight">
-\[\Vert{\mathcal{K}}\Vert_2=\sup_{\mathbf{x}\in\mathbb{R}^N,\Vert\mathbf{x}\Vert_2=1} \Vert\mathcal{K}(\mathbf{x})\Vert_2.\]</div>
-</li>
-</ul>
-<section id="id14">
-<h3>Remarks<a class="headerlink" href="#id14" title="Link to this heading">#</a></h3>
-<ul>
-<li><p>The problem is <em>feasible</em>, i.e. there exists at least one solution.</p></li>
-<li><p>The algorithm is still valid if one or more of the terms <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>, <span class="math notranslate nohighlight">\(\mathcal{G}\)</span> or <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> is zero.</p></li>
-<li><p>The algorithm has convergence guarantees when <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> is composed with a <em>linear operator</em> <span class="math notranslate nohighlight">\(\mathbf{K}\)</span>.
-When <span class="math notranslate nohighlight">\(\mathcal{F}=0\)</span>, convergence can be proven for <em>non-linear differentiable maps</em> <span class="math notranslate nohighlight">\(\mathcal{K}\)</span> (see <a class="reference internal" href="../references.html#nlcp" id="id15"><span>[NLCP]</span></a>).
-Note that <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a> does not yet support automatic selection of hyperparameters for the case of <em>non-linear differentiable maps</em> <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
-<li><p>Assume that either of the following holds:</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\beta&gt;0\)</span> and:</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(\gamma \geq \frac{\beta}{2}\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\frac{1}{\tau}-\sigma\Vert\mathbf{K}\Vert_{2}^2\geq \gamma\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\rho \in ]0,\delta[\)</span>, where <span class="math notranslate nohighlight">\(\delta:=2-\frac{\beta}{2}\gamma^{-1}\in[1,2[\)</span> (<span class="math notranslate nohighlight">\(\delta=2\)</span> is possible when <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is <em>quadratic</em>
-and <span class="math notranslate nohighlight">\(\gamma \geq \beta\)</span>, see <a class="reference internal" href="../references.html#psa" id="id16"><span>[PSA]</span></a>).</p></li>
-</ul>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\beta=0\)</span> and:</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(\tau\sigma\Vert\mathbf{K}\Vert_{2}^2\leq 1\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\rho \in ]0,2[\)</span>.</p></li>
-</ul>
-</li>
-</ul>
-<p>Then there exists a pair <span class="math notranslate nohighlight">\((\mathbf{x}^\star,\mathbf{z}^\star)\in\mathbb{R}^N\times \mathbb{R}^M\)</span> solution s.t. the primal and dual sequences
-of  estimates <span class="math notranslate nohighlight">\((\mathbf{x}_n)_{n\in\mathbb{N}}\)</span> and <span class="math notranslate nohighlight">\((\mathbf{z}_n)_{n\in\mathbb{N}}\)</span> <em>converge</em> towards <span class="math notranslate nohighlight">\(\mathbf{x}^\star\)</span> and
-<span class="math notranslate nohighlight">\(\mathbf{z}^\star\)</span> respectively, i.e.</p>
-<div class="math notranslate nohighlight">
-\[\lim_{n\rightarrow +\infty}\Vert\mathbf{x}^\star-\mathbf{x}_n\Vert_2=0, \quad \text{and}
-\quad
-\lim_{n\rightarrow +\infty}\Vert\mathbf{z}^\star-\mathbf{z}_n\Vert_2=0.\]</div>
-</li>
-</ul>
-</section>
-<section id="id17">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id17" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.operator.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Differentiable map or linear operator <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Lipschitz constant <span class="math notranslate nohighlight">\(\beta\)</span> of <span class="math notranslate nohighlight">\(\nabla\mathcal{F}\)</span>.
-If not provided, it will be automatically estimated.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id18">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id18" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s) for the primal variable.</p></li>
-<li><p><strong>z0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, M) initial point(s) for the dual variable.
-If <code class="docutils literal notranslate"><span class="pre">None</span></code> (default), then use <code class="docutils literal notranslate"><span class="pre">K(x0)</span></code> as the initial point for the dual variable.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Primal step size.</p></li>
-<li><p><strong>sigma</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Dual step size.</p></li>
-<li><p><strong>rho</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Momentum parameter.</p></li>
-<li><p><strong>tuning_strategy</strong> (1, 2, 3)
-–
-Strategy to be employed when setting the hyperparameters (default to 1).
-See section below for more details.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<p class="rubric">Default hyperparameter values</p>
-<p>This class supports three strategies to automatically set the hyperparameters (see <a class="reference internal" href="../references.html#psa" id="id19"><span>[PSA]</span></a> for more details and numerical experiments
-comparing the performance of the three strategies):</p>
-<ul>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuning_strategy</span> <span class="pre">==</span> <span class="pre">1</span></code>: <span class="math notranslate nohighlight">\(\gamma = \beta\)</span> (safe step sizes) and <span class="math notranslate nohighlight">\(\rho=1\)</span> (no relaxation).</p>
-<p>This is the most standard way of setting the parameters in the literature.</p>
-</li>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuning_strategy</span> <span class="pre">==</span> <span class="pre">2</span></code>: <span class="math notranslate nohighlight">\(\gamma = \beta/1.9\)</span> (large step sizes) and <span class="math notranslate nohighlight">\(\rho=1\)</span> (no relaxation).</p>
-<p>This strategy favours large step sizes forbidding the use of overrelaxation.
-When <span class="math notranslate nohighlight">\(\beta=0\)</span>, coincides with the first strategy.</p>
-</li>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuning_strategy</span> <span class="pre">==</span> <span class="pre">3</span></code>: <span class="math notranslate nohighlight">\(\gamma = \beta\)</span> (safe step sizes) and <span class="math notranslate nohighlight">\(\rho=\delta - 0.1 &gt; 1\)</span> (overrelaxation).</p>
-<p>This strategy chooses smaller step sizes, but performs overrelaxation.</p>
-</li>
-</ul>
-<p>Once <span class="math notranslate nohighlight">\(\gamma\)</span> chosen, the convergence speed  of the algorithm is improved by choosing <span class="math notranslate nohighlight">\(\sigma\)</span> and <span class="math notranslate nohighlight">\(\tau\)</span> as
-large as possible and relatively well-balanced – so that both the primal and dual variables converge at the same pace.
-Whenever possible, we therefore choose perfectly balanced parameters <span class="math notranslate nohighlight">\(\sigma=\tau\)</span> saturating the convergence inequalities for a given value of <span class="math notranslate nohighlight">\(\gamma\)</span>.</p>
-<ul>
-<li><p>For <span class="math notranslate nohighlight">\(\beta&gt;0\)</span> and <span class="math notranslate nohighlight">\(\mathcal{H}\neq 0\)</span> this yields:</p>
-<div class="math notranslate nohighlight">
-\[\frac{1}{\tau}-\tau\Vert\mathbf{K}\Vert_{2}^2= \gamma \quad\Longleftrightarrow\quad -\tau^2\Vert\mathbf{K}\Vert_{2}^2-\gamma\tau+1=0,\]</div>
-<p>which admits one positive root</p>
-<div class="math notranslate nohighlight">
-\[\tau=\sigma=\frac{1}{\Vert\mathbf{K}\Vert_{2}^2}\left(-\frac{\gamma}{2}+\sqrt{\frac{\gamma^2}{4}+\Vert\mathbf{K}\Vert_{2}^2}\right).\]</div>
-</li>
-<li><p>For <span class="math notranslate nohighlight">\(\beta&gt;0\)</span> and <span class="math notranslate nohighlight">\(\mathcal{H}=0\)</span> this yields: <span class="math notranslate nohighlight">\(\tau=1/\gamma.\)</span></p></li>
-<li><p>For <span class="math notranslate nohighlight">\(\beta=0\)</span> this yields: <span class="math notranslate nohighlight">\(\tau=\sigma=\Vert\mathbf{K}\Vert_{2}^{-1}\)</span>.</p></li>
-</ul>
-<p>When <span class="math notranslate nohighlight">\(\tau\)</span> is provided (<span class="math notranslate nohighlight">\(\tau = \tau_{1}\)</span>), but not <span class="math notranslate nohighlight">\(\sigma\)</span>, the latter is chosen as:</p>
-<div class="math notranslate nohighlight">
-\[\frac{1}{\tau_{1}}-\sigma\Vert\mathbf{K}\Vert_{2}^2= \gamma \quad\Longleftrightarrow\quad \sigma=\left(\frac{1}{\tau_{1}}-\gamma\right)\frac{1}{\Vert\mathbf{K}\Vert_{2}^2}.\]</div>
-<p>When <span class="math notranslate nohighlight">\(\sigma\)</span> is provided (<span class="math notranslate nohighlight">\(\sigma = \sigma_{1}\)</span>), but not <span class="math notranslate nohighlight">\(\tau\)</span>, the latter is chosen as:</p>
-<div class="math notranslate nohighlight">
-\[\frac{1}{\tau}-\sigma_{1}\Vert\mathbf{K}\Vert_{2}^2= \gamma \quad\Longleftrightarrow\quad \tau=\frac{1}{\left(\gamma+\sigma_{1}\Vert\mathbf{K}\Vert_{2}^2\right)}.\]</div>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>When values are provided for both <span class="math notranslate nohighlight">\(\tau\)</span> and <span class="math notranslate nohighlight">\(\sigma\)</span>, it is assumed that the latter satisfy the
-convergence inequalities, but no check is explicitly performed.
-Automatic selection of hyperparameters for the case of non-linear differentiable maps <span class="math notranslate nohighlight">\(\mathcal{K}\)</span> is not supported yet.</p>
-</div>
-<p class="rubric">Example</p>
-<p>Consider the following optimisation problem:</p>
-<div class="math notranslate nohighlight">
-\[\min_{\mathbf{x}\in\mathbb{R}_+^N}\frac{1}{2}\left\|\mathbf{y}-\mathbf{G}\mathbf{x}\right\|_2^2\quad+\quad\lambda_1 \|\mathbf{D}\mathbf{x}\|_1\quad+\quad\lambda_2 \|\mathbf{x}\|_1,\]</div>
-<p>with <span class="math notranslate nohighlight">\(\mathbf{D}\in\mathbb{R}^{N\times N}\)</span> the discrete derivative operator and <span class="math notranslate nohighlight">\(\mathbf{G}\in\mathbb{R}^{L\times N}, \, \mathbf{y}\in\mathbb{R}^L, \lambda_1,\lambda_2&gt;0.\)</span>
-This problem can be solved via PDS with <span class="math notranslate nohighlight">\(\mathcal{F}(\mathbf{x})= \frac{1}{2}\left\|\mathbf{y}-\mathbf{G}\mathbf{x}\right\|_2^2\)</span>, <span class="math notranslate nohighlight">\(\mathcal{G}(\mathbf{x})=\lambda_2\|\mathbf{x}\|_1,\)</span>
-<span class="math notranslate nohighlight">\(\mathcal{H}(\mathbf{x})=\lambda \|\mathbf{x}\|_1\)</span> and <span class="math notranslate nohighlight">\(\mathbf{K}=\mathbf{D}\)</span>.</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="kn">from</span> <span class="nn">pyxu.experimental._dev</span> <span class="kn">import</span> <span class="n">DownSampling</span><span class="p">,</span> <span class="n">FirstDerivative</span>
-<span class="kn">from</span> <span class="nn">pyxu.opt.solver</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/opt.html#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><span class="n">CV</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.repeat.html#numpy.repeat" title="numpy.repeat"><span class="n">np</span><span class="o">.</span><span class="n">repeat</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.asarray.html#numpy.asarray" title="numpy.asarray"><span class="n">np</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span> <span class="mi">10</span><span class="p">)</span>
-<span class="n">N</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">size</span>
-
-<span class="n">D</span> <span class="o">=</span> <span class="n">FirstDerivative</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">N</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s2">"forward"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.operator.Map.lipschitz" title="pyxu.abc.operator.Map.lipschitz"><span class="n">D</span><span class="o">.</span><span class="n">lipschitz</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.operator.LinOp.estimate_lipschitz" title="pyxu.abc.operator.LinOp.estimate_lipschitz"><span class="n">D</span><span class="o">.</span><span class="n">estimate_lipschitz</span></a><span class="p">()</span>
-
-<span class="n">downsample</span> <span class="o">=</span> <span class="n">DownSampling</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">N</span><span class="p">,</span> <span class="n">downsampling_factor</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">downsample</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="n">loss</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.func.norm.SquaredL2Norm" title="pyxu.operator.func.norm.SquaredL2Norm"><span class="n">pxo</span><span class="o">.</span><span class="n">SquaredL2Norm</span></a><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.operator.Operator.argshift" title="pyxu.abc.operator.Operator.argshift"><span class="n">argshift</span></a><span class="p">(</span><span class="o">-</span><span class="n">y</span><span class="p">)</span>
-<span class="n">F</span> <span class="o">=</span> <span class="n">loss</span> <span class="o">*</span> <span class="n">downsample</span>
-<span class="n">F</span><span class="o">.</span><span class="n">diff_lipschitz</span> <span class="o">=</span> <span class="n">F</span><span class="o">.</span><span class="n">estimate_diff_lipschitz</span><span class="p">()</span>
-
-<a class="sphinx-codeautolink-a" href="../api/opt.html#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><span class="n">cv</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/opt.html#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><span class="n">CV</span></a><span class="p">(</span><span class="n">f</span><span class="o">=</span><span class="n">F</span><span class="p">,</span> <span class="n">g</span><span class="o">=</span><span class="mf">0.01</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.func.norm.L1Norm" title="pyxu.operator.func.norm.L1Norm"><span class="n">pxo</span><span class="o">.</span><span class="n">L1Norm</span></a><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">h</span><span class="o">=</span><span class="mf">0.1</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.func.norm.L1Norm" title="pyxu.operator.func.norm.L1Norm"><span class="n">pxo</span><span class="o">.</span><span class="n">L1Norm</span></a><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">K</span><span class="o">=</span><span class="n">D</span><span class="p">)</span>
-<span class="n">x0</span><span class="p">,</span> <span class="n">z0</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="n">N</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><span class="n">cv</span><span class="o">.</span><span class="n">fit</span></a><span class="p">(</span><span class="n">x0</span><span class="o">=</span><span class="n">x0</span><span class="p">,</span> <span class="n">z0</span><span class="o">=</span><span class="n">z0</span><span class="p">)</span>
-<span class="n">x_recons</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.solver.Solver.solution" title="pyxu.abc.solver.Solver.solution"><span class="n">cv</span><span class="o">.</span><span class="n">solution</span></a><span class="p">()[</span><span class="mi">0</span><span class="p">]</span>
-
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.stem.html#matplotlib.pyplot.stem" title="matplotlib.pyplot.stem"><span class="n">plt</span><span class="o">.</span><span class="n">stem</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">linefmt</span><span class="o">=</span><span class="s2">"C0-"</span><span class="p">,</span> <span class="n">markerfmt</span><span class="o">=</span><span class="s2">"C0o"</span><span class="p">)</span>
-<span class="n">mask_ids</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.where.html#numpy.where" title="numpy.where"><span class="n">np</span><span class="o">.</span><span class="n">where</span></a><span class="p">(</span><span class="n">downsample</span><span class="o">.</span><span class="n">downsampling_mask</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
-<span class="n">markerline</span><span class="p">,</span> <span class="n">stemlines</span><span class="p">,</span> <span class="n">baseline</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.stem.html#matplotlib.pyplot.stem" title="matplotlib.pyplot.stem"><span class="n">plt</span><span class="o">.</span><span class="n">stem</span></a><span class="p">(</span><span class="n">mask_ids</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">linefmt</span><span class="o">=</span><span class="s2">"C3-"</span><span class="p">,</span> <span class="n">markerfmt</span><span class="o">=</span><span class="s2">"C3o"</span><span class="p">)</span>
-<span class="n">markerline</span><span class="o">.</span><span class="n">set_markerfacecolor</span><span class="p">(</span><span class="s2">"none"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.stem.html#matplotlib.pyplot.stem" title="matplotlib.pyplot.stem"><span class="n">plt</span><span class="o">.</span><span class="n">stem</span></a><span class="p">(</span><span class="n">x_recons</span><span class="p">,</span> <span class="n">linefmt</span><span class="o">=</span><span class="s2">"C1--"</span><span class="p">,</span> <span class="n">markerfmt</span><span class="o">=</span><span class="s2">"C1s"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">([</span><span class="s2">"Ground truth"</span><span class="p">,</span> <span class="s2">"Observation"</span><span class="p">,</span> <span class="s2">"CV Estimate"</span><span class="p">])</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/f2dd49c204e444011bf0c8ee51349779/opt-1.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/3e00ef9813368e3b18ae614801b6914c/opt-1.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/9db61dbdbb51645a825c3d21408069d0/opt-1.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/7a45a92466c43f54218138bd4c5bfb33/opt-1.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/opt-1.png" class="plot-directive" src="../_images/opt-1.png"/>
-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.opt.solver.pds.CV" title="pyxu.opt.solver.pds.CV"><code class="xref py py-class docutils literal notranslate"><span class="pre">CV</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.ChambollePock" title="pyxu.opt.solver.pds.ChambollePock"><code class="xref py py-class docutils literal notranslate"><span class="pre">ChambollePock</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.DouglasRachford" title="pyxu.opt.solver.pds.DouglasRachford"><code class="xref py py-class docutils literal notranslate"><span class="pre">DouglasRachford</span></code></a></p>
-</div>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.CV">
-<span class="sig-name descname"><span class="pre">CV</span></span><a class="headerlink" href="#pyxu.opt.solver.pds.CV" title="Link to this definition">#</a></dt>
-<dd><p>Alias of <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>.</p>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.PD3O">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PD3O</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">h</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pds.html#PD3O"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pds.PD3O" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_PrimalDualSplitting</span></code></p>
-<p>Primal-Dual Three-Operator Splitting (PD3O) algorithm.</p>
-<p>The <em>Primal-Dual three Operator splitting (PD3O)</em> method is described in <a class="reference internal" href="../references.html#pd3o" id="id20"><span>[PD3O]</span></a>.</p>
-<p>It can be used to solve problems of the form:</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \;\Psi(\mathbf{x}):=\mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{G}(\mathbf{x})\;\;+\;\;\mathcal{H}(\mathcal{K} \mathbf{x}),}\]</div>
-<p>where:</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}:\mathbb{R}^N\rightarrow \mathbb{R}\)</span> is <em>convex</em> and <em>differentiable</em>, with <span class="math notranslate nohighlight">\(\beta\)</span>-<em>Lipschitz continuous</em> gradient,
-for some <span class="math notranslate nohighlight">\(\beta\in[0,+\infty[\)</span>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{G}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> and <span class="math notranslate nohighlight">\(\mathcal{H}:\mathbb{R}^M\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> are <em>proper</em>, <em>lower semicontinuous</em> and <em>convex functions</em> with <em>simple proximal operators</em>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{K}:\mathbb{R}^N\rightarrow \mathbb{R}^M\)</span> is a <em>differentiable map</em> (e.g. a <em>linear operator</em> <span class="math notranslate nohighlight">\(\mathbf{K}\)</span>), with <strong>operator norm</strong>:</p>
-<div class="math notranslate nohighlight">
-\[\Vert{\mathcal{K}}\Vert_2=\sup_{\mathbf{x}\in\mathbb{R}^N,\Vert\mathbf{x}\Vert_2=1} \Vert\mathcal{K}(\mathbf{x})\Vert_2.\]</div>
-</li>
-</ul>
-<section id="id21">
-<h3>Remarks<a class="headerlink" href="#id21" title="Link to this heading">#</a></h3>
-<ul>
-<li><p>The problem is <em>feasible</em> – i.e. there exists at least one solution.</p></li>
-<li><p>The algorithm is still valid if one or more of the terms <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>, <span class="math notranslate nohighlight">\(\mathcal{G}\)</span> or <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> is zero.</p></li>
-<li><p>The algorithm has convergence guarantees for the case in which <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> is composed with a <em>linear operator</em> <span class="math notranslate nohighlight">\(\mathbf{K}\)</span>.
-When <span class="math notranslate nohighlight">\(\mathcal{F}=0\)</span>, convergence can be proven for <em>non-linear differentiable maps</em> <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>. (See <a class="reference internal" href="../references.html#nlcp" id="id22"><span>[NLCP]</span></a>.)
-Note that this class does not yet support automatic selection of hyperparameters for the case of <em>non-linear differentiable maps</em> <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
-<li><p>Assume that the following holds:</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\gamma\geq\frac{\beta}{2}\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\tau \in ]0, \frac{1}{\gamma}[\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\tau\sigma\Vert\mathbf{K}\Vert_{2}^2 \leq 1\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\delta = 2-\beta\tau/2 \in [1, 2[\)</span> and <span class="math notranslate nohighlight">\(\rho \in (0, \delta]\)</span>.</p></li>
-</ul>
-<p>Then there exists a pair <span class="math notranslate nohighlight">\((\mathbf{x}^\star,\mathbf{z}^\star)\in\mathbb{R}^N\times \mathbb{R}^M\)</span> solution
-s.t. the primal and dual sequences of  estimates <span class="math notranslate nohighlight">\((\mathbf{x}_n)_{n\in\mathbb{N}}\)</span> and <span class="math notranslate nohighlight">\((\mathbf{z}_n)_{n\in\mathbb{N}}\)</span>
-<em>converge</em> towards <span class="math notranslate nohighlight">\(\mathbf{x}^\star\)</span> and <span class="math notranslate nohighlight">\(\mathbf{z}^\star\)</span> respectively (Theorem 8.2 of <a class="reference internal" href="../references.html#psa" id="id23"><span>[PSA]</span></a>), i.e.</p>
-<div class="math notranslate nohighlight">
-\[\lim_{n\rightarrow +\infty}\Vert\mathbf{x}^\star-\mathbf{x}_n\Vert_2=0, \quad \text{and} \quad  \lim_{n\rightarrow +\infty}\Vert\mathbf{z}^\star-\mathbf{z}_n\Vert_2=0.\]</div>
-<p>Futhermore, when <span class="math notranslate nohighlight">\(\rho=1\)</span>, the objective functional sequence <span class="math notranslate nohighlight">\(\left(\Psi(\mathbf{x}_n)\right)_{n\in\mathbb{N}}\)</span> can be shown to converge towards
-its minimum <span class="math notranslate nohighlight">\(\Psi^\ast\)</span> with rate <span class="math notranslate nohighlight">\(o(1/\sqrt{n})\)</span> (Theorem 1 of <a class="reference internal" href="../references.html#dpsa" id="id24"><span>[dPSA]</span></a>):</p>
-<div class="math notranslate nohighlight">
-\[\Psi(\mathbf{x}_n) - \Psi^\ast = o(1/\sqrt{n}).\]</div>
-</li>
-</ul>
-</section>
-<section id="id25">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id25" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.operator.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Differentiable map or linear operator <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Lipschitz constant <span class="math notranslate nohighlight">\(\beta\)</span> of <span class="math notranslate nohighlight">\(\nabla\mathcal{F}\)</span>.
-If not provided, it will be automatically estimated.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id26">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id26" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s) for the primal variable.</p></li>
-<li><p><strong>z0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, M) initial point(s) for the dual variable.
-If <code class="docutils literal notranslate"><span class="pre">None</span></code> (default), then use <code class="docutils literal notranslate"><span class="pre">K(x0)</span></code> as the initial point for the dual variable.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Primal step size.</p></li>
-<li><p><strong>sigma</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Dual step size.</p></li>
-<li><p><strong>rho</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Momentum parameter.</p></li>
-<li><p><strong>tuning_strategy</strong> (1, 2, 3)
-–
-Strategy to be employed when setting the hyperparameters (default to 1).
-See section below for more details.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<p class="rubric">Default hyperparameter values</p>
-<p>This class supports three strategies to automatically set the hyperparameters (see <a class="reference internal" href="../references.html#psa" id="id27"><span>[PSA]</span></a> for more details and numerical experiments
-comparing the performance of the three strategies):</p>
-<ul>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuning_strategy</span> <span class="pre">==</span> <span class="pre">1</span></code>: <span class="math notranslate nohighlight">\(\gamma = \beta\)</span> (safe step sizes) and <span class="math notranslate nohighlight">\(\rho=1\)</span> (no relaxation).</p>
-<p>This is the most standard way of setting the parameters in the literature.</p>
-</li>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuning_strategy</span> <span class="pre">==</span> <span class="pre">2</span></code>: <span class="math notranslate nohighlight">\(\gamma = \beta/1.9\)</span> (large step sizes) and <span class="math notranslate nohighlight">\(\rho=1\)</span> (no relaxation).</p>
-<p>This strategy favours large step sizes forbidding the use of overrelaxation.
-When <span class="math notranslate nohighlight">\(\beta=0\)</span>, coincides with the first strategy.</p>
-</li>
-<li><p><code class="docutils literal notranslate"><span class="pre">tuning_strategy</span> <span class="pre">==</span> <span class="pre">3</span></code>: <span class="math notranslate nohighlight">\(\gamma = \beta\)</span> (safe step sizes) and <span class="math notranslate nohighlight">\(\rho=\delta - 0.1 &gt; 1\)</span> (overrelaxation).</p>
-<p>This strategy chooses smaller step sizes, but performs overrelaxation.</p>
-</li>
-</ul>
-<p>Once <span class="math notranslate nohighlight">\(\gamma\)</span> chosen, the convergence speed  of the algorithm is improved by choosing <span class="math notranslate nohighlight">\(\sigma\)</span> and <span class="math notranslate nohighlight">\(\tau\)</span> as
-large as possible and relatively well-balanced – so that both the primal and dual variables converge at the same pace.
-Whenever possible, we therefore choose perfectly balanced parameters <span class="math notranslate nohighlight">\(\sigma=\tau\)</span> saturating the convergence inequalities for a given value of <span class="math notranslate nohighlight">\(\gamma\)</span>.</p>
-<p>In practice, the following linear programming optimization problem is solved:</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}(\tau, \, \sigma) = \operatorname{arg} \max_{(\tau^{*}, \,  \sigma^{*})} \quad &amp; \operatorname{log}(\tau^{*}) + \operatorname{log}(\sigma^{*})\\
-\text{s.t.} \quad &amp; \operatorname{log}(\tau^{*}) + \operatorname{log}(\sigma^{*}) \leq 2\operatorname{log}(\Vert\mathbf{K}\Vert_{2})\\
-&amp; \operatorname{log}(\tau^{*}) \leq -\operatorname{log}(\gamma)\\
-&amp; \operatorname{log}(\tau^{*}) = \operatorname{log}(\sigma^{*}).\end{split}\]</div>
-<p>When <span class="math notranslate nohighlight">\(\tau \leq 1/\gamma\)</span> is given (i.e., <span class="math notranslate nohighlight">\(\tau=\tau_{1}\)</span>), but not <span class="math notranslate nohighlight">\(\sigma\)</span>, the latter is chosen as:</p>
-<div class="math notranslate nohighlight">
-\[\tau_{1}\sigma\Vert\mathbf{K}\Vert_{2}^2= 1 \quad\Longleftrightarrow\quad \sigma=\frac{1}{\tau_{1}\Vert\mathbf{K}\Vert_{2}^{2}}.\]</div>
-<p>When <span class="math notranslate nohighlight">\(\sigma\)</span> is given (i.e., <span class="math notranslate nohighlight">\(\sigma=\sigma_{1}\)</span>), but not <span class="math notranslate nohighlight">\(\tau\)</span>, the latter is chosen as:</p>
-<div class="math notranslate nohighlight">
-\[\tau = \min \left\{\frac{1}{\gamma}, \frac{1}{\sigma_{1}\Vert\mathbf{K}\Vert_{2}^{2}}\right\}.\]</div>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p>When values are provided for both <span class="math notranslate nohighlight">\(\tau\)</span> and <span class="math notranslate nohighlight">\(\sigma\)</span>, it is assumed that the latter satisfy the
-convergence inequalities, but no check is explicitly performed.
-Automatic selection of hyperparameters for the case of non-linear differentiable maps <span class="math notranslate nohighlight">\(\mathcal{K}\)</span> is not supported yet.</p>
-</div>
-<p class="rubric">Example</p>
-<p>Consider the following optimisation problem:</p>
-<div class="math notranslate nohighlight">
-\[\min_{\mathbf{x}\in\mathbb{R}_+^N}\frac{1}{2}\left\|\mathbf{y}-\mathbf{G}\mathbf{x}\right\|_2^2\quad+\quad\lambda_1 \|\mathbf{D}\mathbf{x}\|_1\quad+\quad\lambda_2 \|\mathbf{x}\|_1,\]</div>
-<p>with <span class="math notranslate nohighlight">\(\mathbf{D}\in\mathbb{R}^{N\times N}\)</span> the discrete derivative operator and <span class="math notranslate nohighlight">\(\mathbf{G}\in\mathbb{R}^{L\times N}, \, \mathbf{y}\in\mathbb{R}^L, \lambda_1,\lambda_2&gt;0.\)</span>
-This problem can be solved via PD3O with <span class="math notranslate nohighlight">\(\mathcal{F}(\mathbf{x})= \frac{1}{2}\left\|\mathbf{y}-\mathbf{G}\mathbf{x}\right\|_2^2\)</span>, <span class="math notranslate nohighlight">\(\mathcal{G}(\mathbf{x})=\lambda_2\|\mathbf{x}\|_1,\)</span>
-<span class="math notranslate nohighlight">\(\mathcal{H}(\mathbf{x})=\lambda \|\mathbf{x}\|_1\)</span> and <span class="math notranslate nohighlight">\(\mathbf{K}=\mathbf{D}\)</span>.</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="kn">from</span> <span class="nn">pyxu.experimental._dev</span> <span class="kn">import</span> <span class="n">DownSampling</span><span class="p">,</span> <span class="n">FirstDerivative</span>
-<span class="kn">from</span> <span class="nn">pyxu.opt.solver</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/opt.html#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><span class="n">PD3O</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.repeat.html#numpy.repeat" title="numpy.repeat"><span class="n">np</span><span class="o">.</span><span class="n">repeat</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.asarray.html#numpy.asarray" title="numpy.asarray"><span class="n">np</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span> <span class="mi">10</span><span class="p">)</span>
-<span class="n">N</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">size</span>
-
-<span class="n">D</span> <span class="o">=</span> <span class="n">FirstDerivative</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">N</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s2">"forward"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.operator.Map.lipschitz" title="pyxu.abc.operator.Map.lipschitz"><span class="n">D</span><span class="o">.</span><span class="n">lipschitz</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.operator.LinOp.estimate_lipschitz" title="pyxu.abc.operator.LinOp.estimate_lipschitz"><span class="n">D</span><span class="o">.</span><span class="n">estimate_lipschitz</span></a><span class="p">()</span>
-
-<span class="n">downsample</span> <span class="o">=</span> <span class="n">DownSampling</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">N</span><span class="p">,</span> <span class="n">downsampling_factor</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">downsample</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-<span class="n">loss</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.func.norm.SquaredL2Norm" title="pyxu.operator.func.norm.SquaredL2Norm"><span class="n">pxo</span><span class="o">.</span><span class="n">SquaredL2Norm</span></a><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.operator.Operator.argshift" title="pyxu.abc.operator.Operator.argshift"><span class="n">argshift</span></a><span class="p">(</span><span class="o">-</span><span class="n">y</span><span class="p">)</span>
-<span class="n">F</span> <span class="o">=</span> <span class="n">loss</span> <span class="o">*</span> <span class="n">downsample</span>
-<span class="n">F</span><span class="o">.</span><span class="n">diff_lipschitz</span> <span class="o">=</span> <span class="n">F</span><span class="o">.</span><span class="n">estimate_diff_lipschitz</span><span class="p">()</span>
-
-<a class="sphinx-codeautolink-a" href="../api/opt.html#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><span class="n">pd3o</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/opt.html#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><span class="n">PD3O</span></a><span class="p">(</span><span class="n">f</span><span class="o">=</span><span class="n">F</span><span class="p">,</span> <span class="n">g</span><span class="o">=</span><span class="mf">0.01</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.func.norm.L1Norm" title="pyxu.operator.func.norm.L1Norm"><span class="n">pxo</span><span class="o">.</span><span class="n">L1Norm</span></a><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">h</span><span class="o">=</span><span class="mf">0.1</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.func.norm.L1Norm" title="pyxu.operator.func.norm.L1Norm"><span class="n">pxo</span><span class="o">.</span><span class="n">L1Norm</span></a><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">K</span><span class="o">=</span><span class="n">D</span><span class="p">)</span>
-<span class="n">x0</span><span class="p">,</span> <span class="n">z0</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="n">N</span><span class="p">))</span>
-<a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><span class="n">pd3o</span><span class="o">.</span><span class="n">fit</span></a><span class="p">(</span><span class="n">x0</span><span class="o">=</span><span class="n">x0</span><span class="p">,</span> <span class="n">z0</span><span class="o">=</span><span class="n">z0</span><span class="p">)</span>
-<span class="n">x_recons</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.solver.Solver.solution" title="pyxu.abc.solver.Solver.solution"><span class="n">pd3o</span><span class="o">.</span><span class="n">solution</span></a><span class="p">()[</span><span class="mi">0</span><span class="p">]</span>
-
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.stem.html#matplotlib.pyplot.stem" title="matplotlib.pyplot.stem"><span class="n">plt</span><span class="o">.</span><span class="n">stem</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">linefmt</span><span class="o">=</span><span class="s2">"C0-"</span><span class="p">,</span> <span class="n">markerfmt</span><span class="o">=</span><span class="s2">"C0o"</span><span class="p">)</span>
-<span class="n">mask_ids</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.where.html#numpy.where" title="numpy.where"><span class="n">np</span><span class="o">.</span><span class="n">where</span></a><span class="p">(</span><span class="n">downsample</span><span class="o">.</span><span class="n">downsampling_mask</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
-<span class="n">markerline</span><span class="p">,</span> <span class="n">stemlines</span><span class="p">,</span> <span class="n">baseline</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.stem.html#matplotlib.pyplot.stem" title="matplotlib.pyplot.stem"><span class="n">plt</span><span class="o">.</span><span class="n">stem</span></a><span class="p">(</span><span class="n">mask_ids</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">linefmt</span><span class="o">=</span><span class="s2">"C3-"</span><span class="p">,</span> <span class="n">markerfmt</span><span class="o">=</span><span class="s2">"C3o"</span><span class="p">)</span>
-<span class="n">markerline</span><span class="o">.</span><span class="n">set_markerfacecolor</span><span class="p">(</span><span class="s2">"none"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.stem.html#matplotlib.pyplot.stem" title="matplotlib.pyplot.stem"><span class="n">plt</span><span class="o">.</span><span class="n">stem</span></a><span class="p">(</span><span class="n">x_recons</span><span class="p">,</span> <span class="n">linefmt</span><span class="o">=</span><span class="s2">"C1--"</span><span class="p">,</span> <span class="n">markerfmt</span><span class="o">=</span><span class="s2">"C1s"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">([</span><span class="s2">"Ground truth"</span><span class="p">,</span> <span class="s2">"Observation"</span><span class="p">,</span> <span class="s2">"PD3O Estimate"</span><span class="p">])</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/1e56b08165a1aaab1d61109119a49a7f/opt-2.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/5f6fc21c910212a2ec51fbd06ff28311/opt-2.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/7acbb4c520fb3c12fd8bb79d870c930d/opt-2.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/e6d7379beda9ef38f71609f23015c745/opt-2.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/opt-2.png" class="plot-directive" src="../_images/opt-2.png"/>
-</figure>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.ChambollePock">
-<span class="sig-name descname"><span class="pre">ChambollePock</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">g=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">h=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">base=&lt;class</span> <span class="pre">'pyxu.opt.solver.pds.CondatVu'&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">**kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pds.html#ChambollePock"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pds.ChambollePock" title="Link to this definition">#</a></dt>
-<dd><p>Chambolle-Pock primal-dual splitting method.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.operator.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Differentiable map or linear operator <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
-<li><p><strong>base</strong> (<a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>) – Specifies the base primal-dual algorithm.
-(Default = <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>)</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</dd>
-</dl>
-<p>The <em>Chambolle-Pock (CP) primal-dual splitting</em> method can be used to solve problems of the form:</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \mathcal{G}(\mathbf{x})\;\;+\;\;\mathcal{H}(\mathbf{K} \mathbf{x}),}\]</div>
-<p>where:</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{G}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> and <span class="math notranslate nohighlight">\(\mathcal{H}:\mathbb{R}^M\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> are <em>proper</em>, <em>lower semicontinuous</em> and <em>convex functions</em> with <em>simple proximal operators</em>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{K}:\mathbb{R}^N\rightarrow \mathbb{R}^M\)</span> is a <em>differentiable map</em> (e.g. a <em>linear operator</em> <span class="math notranslate nohighlight">\(\mathbf{K}\)</span>), with <strong>operator norm</strong>:</p>
-<div class="math notranslate nohighlight">
-\[\Vert{\mathcal{K}}\Vert_2=\sup_{\mathbf{x}\in\mathbb{R}^N,\Vert\mathbf{x}\Vert_2=1} \Vert\mathcal{K}(\mathbf{x})\Vert_2.\]</div>
-</li>
-</ul>
-<section id="id28">
-<h3>Remarks<a class="headerlink" href="#id28" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p>The problem is <em>feasible</em>, i.e. there exists at least one solution.</p></li>
-<li><p>The algorithm is still valid if one of the terms <span class="math notranslate nohighlight">\(\mathcal{G}\)</span> or <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> is zero.</p></li>
-<li><p>Automatic selection of parameters is not supported for <em>non-linear differentiable maps</em> <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
-<li><p>The <em>Chambolle-Pock (CP) primal-dual splitting</em> method can be obtained by choosing <span class="math notranslate nohighlight">\(\mathcal{F}=0\)</span> in <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a> or <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>.
-Chambolle and Pock originally introduced the algorithm without relaxation (<span class="math notranslate nohighlight">\(\rho=1\)</span>) <a class="reference internal" href="../references.html#cpa" id="id29"><span>[CPA]</span></a>.
-Relaxed versions have been proposed afterwards <a class="reference internal" href="../references.html#psa" id="id30"><span>[PSA]</span></a>.
-Chambolle-Pock’s algorithm is also known as the <em>Primal-Dual Hybrid Gradient (PDHG)</em> algorithm.
-It can be seen as a preconditionned ADMM method <a class="reference internal" href="../references.html#cpa" id="id31"><span>[CPA]</span></a>.</p></li>
-</ul>
-</section>
-<section id="id32">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id32" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s) for the primal variable.</p></li>
-<li><p><strong>z0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, M) initial point(s) for the dual variable.
-If <code class="docutils literal notranslate"><span class="pre">None</span></code> (default), then use <code class="docutils literal notranslate"><span class="pre">K(x0)</span></code> as the initial point for the dual variable.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Primal step size.</p></li>
-<li><p><strong>sigma</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Dual step size.</p></li>
-<li><p><strong>rho</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Momentum parameter.</p></li>
-<li><p><strong>tuning_strategy</strong> (1, 2, 3)
-–
-Strategy to be employed when setting the hyperparameters (default to 1).
-See <code class="code docutils literal notranslate"><span class="pre">base</span></code> for more details.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.opt.solver.pds.CP" title="pyxu.opt.solver.pds.CP"><code class="xref py py-func docutils literal notranslate"><span class="pre">CP()</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.DouglasRachford" title="pyxu.opt.solver.pds.DouglasRachford"><code class="xref py py-func docutils literal notranslate"><span class="pre">DouglasRachford()</span></code></a></p>
-</div>
-</section>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.CP">
-<span class="sig-name descname"><span class="pre">CP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">g=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">h=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">base=&lt;class</span> <span class="pre">'pyxu.opt.solver.pds.CondatVu'&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">**kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pyxu.opt.solver.pds.CP" title="Link to this definition">#</a></dt>
-<dd><p>Alias of <a class="reference internal" href="#pyxu.opt.solver.pds.ChambollePock" title="pyxu.opt.solver.pds.ChambollePock"><code class="xref py py-func docutils literal notranslate"><span class="pre">ChambollePock()</span></code></a>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>base</strong> (<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><em>Type</em></a><em>[</em><em>_PrimalDualSplitting</em><em>]</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.LorisVerhoeven">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">LorisVerhoeven</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">h</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pds.html#LorisVerhoeven"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pds.LorisVerhoeven" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a></p>
-<p>Loris-Verhoeven splitting algorithm.</p>
-<p>This solver is also accessible via the alias <a class="reference internal" href="#pyxu.opt.solver.pds.LV" title="pyxu.opt.solver.pds.LV"><code class="xref py py-class docutils literal notranslate"><span class="pre">LV</span></code></a>.</p>
-<p>The <em>Loris-Verhoeven (LV) primal-dual splitting</em> can be used to solve problems of the form:</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{H}(\mathbf{K} \mathbf{x}),}\]</div>
-<p>where:</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}:\mathbb{R}^N\rightarrow \mathbb{R}\)</span> is <em>convex</em> and <em>differentiable</em>, with <span class="math notranslate nohighlight">\(\beta\)</span>-<em>Lipschitz continuous</em> gradient,
-for some <span class="math notranslate nohighlight">\(\beta\in[0,+\infty[\)</span>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{H}:\mathbb{R}^M\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> is a <em>proper</em>, <em>lower semicontinuous</em> and <em>convex function</em> with <em>simple proximal operator</em>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{K}:\mathbb{R}^N\rightarrow \mathbb{R}^M\)</span> is a <em>differentiable map</em> (e.g. a <em>linear operator</em> <span class="math notranslate nohighlight">\(\mathbf{K}\)</span>), with <strong>operator norm</strong>:</p>
-<div class="math notranslate nohighlight">
-\[\Vert{\mathcal{K}}\Vert_2=\sup_{\mathbf{x}\in\mathbb{R}^N,\Vert\mathbf{x}\Vert_2=1} \Vert\mathcal{K}(\mathbf{x})\Vert_2.\]</div>
-</li>
-</ul>
-<section id="id33">
-<h3>Remarks<a class="headerlink" href="#id33" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p>The problem is <em>feasible</em>, i.e. there exists at least one solution.</p></li>
-<li><p>The algorithm is still valid if one of the terms <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> or <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> is zero.</p></li>
-<li><p>Automatic selection of parameters is not supported for <em>non-linear differentiable maps</em> <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
-<li><p>The <em>Loris-Verhoeven (CP) primal-dual splitting</em> method can be obtained by choosing <span class="math notranslate nohighlight">\(\mathcal{G}=0\)</span> in <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>.</p></li>
-<li><p>In the specific case where <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is <em>quadratic</em>, then one can set <span class="math notranslate nohighlight">\(\rho \in ]0,\delta[\)</span> with
-<span class="math notranslate nohighlight">\(\delta=2\)</span>. (See Theorem 4.3 in <a class="reference internal" href="../references.html#psa" id="id34"><span>[PSA]</span></a>.)</p></li>
-</ul>
-</section>
-<section id="id35">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id35" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.operator.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Differentiable map or linear operator <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Lipschitz constant <span class="math notranslate nohighlight">\(\beta\)</span> of <span class="math notranslate nohighlight">\(\nabla\mathcal{F}\)</span>.
-If not provided, it will be automatically estimated.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id36">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id36" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s) for the primal variable.</p></li>
-<li><p><strong>z0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, M) initial point(s) for the dual variable.
-If <code class="docutils literal notranslate"><span class="pre">None</span></code> (default), then use <code class="docutils literal notranslate"><span class="pre">K(x0)</span></code> as the initial point for the dual variable.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Primal step size.</p></li>
-<li><p><strong>sigma</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Dual step size.</p></li>
-<li><p><strong>rho</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Momentum parameter.</p></li>
-<li><p><strong>tuning_strategy</strong> (1, 2, 3)
-–
-Strategy to be employed when setting the hyperparameters (default to 1).
-See <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a> for more details.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.DavisYin" title="pyxu.opt.solver.pds.DavisYin"><code class="xref py py-class docutils literal notranslate"><span class="pre">DavisYin</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pgd.PGD" title="pyxu.opt.solver.pgd.PGD"><code class="xref py py-class docutils literal notranslate"><span class="pre">PGD</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.ChambollePock" title="pyxu.opt.solver.pds.ChambollePock"><code class="xref py py-func docutils literal notranslate"><span class="pre">ChambollePock()</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.DouglasRachford" title="pyxu.opt.solver.pds.DouglasRachford"><code class="xref py py-func docutils literal notranslate"><span class="pre">DouglasRachford()</span></code></a></p>
-</div>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.LV">
-<span class="sig-name descname"><span class="pre">LV</span></span><a class="headerlink" href="#pyxu.opt.solver.pds.LV" title="Link to this definition">#</a></dt>
-<dd><p>Alias of <a class="reference internal" href="#pyxu.opt.solver.pds.LorisVerhoeven" title="pyxu.opt.solver.pds.LorisVerhoeven"><code class="xref py py-class docutils literal notranslate"><span class="pre">LorisVerhoeven</span></code></a>.</p>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.DavisYin">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DavisYin</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">h</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pds.html#DavisYin"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pds.DavisYin" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a></p>
-<p>Davis-Yin primal-dual splitting method.</p>
-<p>This solver is also accessible via the alias <a class="reference internal" href="#pyxu.opt.solver.pds.DY" title="pyxu.opt.solver.pds.DY"><code class="xref py py-class docutils literal notranslate"><span class="pre">DY</span></code></a>.</p>
-<p>The <em>Davis-Yin (DY) primal-dual splitting</em> method can be used to solve problems of the form:</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \;\mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{G}(\mathbf{x})\;\;+\;\;\mathcal{H}(\mathbf{x}),}\]</div>
-<p>where:</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}:\mathbb{R}^N\rightarrow \mathbb{R}\)</span> is <em>convex</em> and <em>differentiable</em>, with <span class="math notranslate nohighlight">\(\beta\)</span>-<em>Lipschitz continuous</em> gradient,
-for some <span class="math notranslate nohighlight">\(\beta\in[0,+\infty[\)</span>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{G}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> and <span class="math notranslate nohighlight">\(\mathcal{H}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> are <em>proper</em>, <em>lower semicontinuous</em> and <em>convex functions</em> with <em>simple proximal operators</em>.</p></li>
-</ul>
-<section id="id37">
-<h3>Remarks<a class="headerlink" href="#id37" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p>The problem is <em>feasible</em>, i.e. there exists at least one solution.</p></li>
-<li><p>The algorithm is still valid if one of the terms <span class="math notranslate nohighlight">\(\mathcal{G}\)</span> or <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> is zero.</p></li>
-<li><p>The <em>Davis-Yin primal-dual splitting</em> method can be obtained by choosing <span class="math notranslate nohighlight">\(\mathcal{K}=\mathbf{I}\)</span>
-(identity) and <span class="math notranslate nohighlight">\(\tau=1/\sigma\)</span> in <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>, provided a suitable change of variable <a class="reference internal" href="../references.html#psa" id="id38"><span>[PSA]</span></a>.</p></li>
-</ul>
-</section>
-<section id="id39">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id39" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>)
-–
-Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Lipschitz constant <span class="math notranslate nohighlight">\(\beta\)</span> of <span class="math notranslate nohighlight">\(\nabla\mathcal{F}\)</span>.
-If not provided, it will be automatically estimated.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id40">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id40" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s) for the primal variable.</p></li>
-<li><p><strong>z0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, N) initial point(s) for the dual variable.
-If <code class="docutils literal notranslate"><span class="pre">None</span></code> (default), then use <code class="docutils literal notranslate"><span class="pre">x0</span></code> as the initial point for the dual variable.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Primal step size.</p></li>
-<li><p><strong>sigma</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Dual step size.</p></li>
-<li><p><strong>rho</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Momentum parameter.</p></li>
-<li><p><strong>tuning_strategy</strong> (1, 2, 3)
-–
-Strategy to be employed when setting the hyperparameters (default to 1).
-See <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a> for more details.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.LorisVerhoeven" title="pyxu.opt.solver.pds.LorisVerhoeven"><code class="xref py py-class docutils literal notranslate"><span class="pre">LorisVerhoeven</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pgd.PGD" title="pyxu.opt.solver.pgd.PGD"><code class="xref py py-class docutils literal notranslate"><span class="pre">PGD</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.ChambollePock" title="pyxu.opt.solver.pds.ChambollePock"><code class="xref py py-func docutils literal notranslate"><span class="pre">ChambollePock()</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.DouglasRachford" title="pyxu.opt.solver.pds.DouglasRachford"><code class="xref py py-func docutils literal notranslate"><span class="pre">DouglasRachford()</span></code></a></p>
-</div>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.DY">
-<span class="sig-name descname"><span class="pre">DY</span></span><a class="headerlink" href="#pyxu.opt.solver.pds.DY" title="Link to this definition">#</a></dt>
-<dd><p>Alias of <a class="reference internal" href="#pyxu.opt.solver.pds.DavisYin" title="pyxu.opt.solver.pds.DavisYin"><code class="xref py py-class docutils literal notranslate"><span class="pre">DavisYin</span></code></a>.</p>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.DouglasRachford">
-<span class="sig-name descname"><span class="pre">DouglasRachford</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">g=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">h=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">base=&lt;class</span> <span class="pre">'pyxu.opt.solver.pds.CondatVu'&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">**kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pds.html#DouglasRachford"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pds.DouglasRachford" title="Link to this definition">#</a></dt>
-<dd><p>Douglas-Rachford splitting algorithm.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>base</strong> (<a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>) – Specifies the base primal-dual algorithm.
-(Default = <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>)</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</dd>
-</dl>
-<p>The <em>Douglas-Rachford (DR) primal-dual splitting</em> method can be used to solve problems of the form:</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \mathcal{G}(\mathbf{x})\;\;+\;\;\mathcal{H}(\mathbf{x}),}\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathcal{G}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> and <span class="math notranslate nohighlight">\(\mathcal{H}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> are <em>proper</em>, <em>lower semicontinuous</em> and <em>convex functions</em> with <em>simple proximal operators</em>.</p>
-<section id="id41">
-<h3>Remarks<a class="headerlink" href="#id41" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p>The problem is <em>feasible</em>, i.e. there exists at least one solution.</p></li>
-<li><p>The algorithm is still valid if one of the terms <span class="math notranslate nohighlight">\(\mathcal{G}\)</span> or <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> is zero.</p></li>
-<li><p>The <em>Douglas-Rachford (DR) primal-dual splitting</em> method can be obtained by choosing <span class="math notranslate nohighlight">\(\mathcal{F}=0\)</span>, <span class="math notranslate nohighlight">\(\mathbf{K}=\mathbf{Id}\)</span> and <span class="math notranslate nohighlight">\(\tau=1/\sigma\)</span> in <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a> or <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>.
-Douglas and Rachford originally introduced the algorithm without relaxation (<span class="math notranslate nohighlight">\(\rho=1\)</span>), but relaxed versions have been proposed afterwards <a class="reference internal" href="../references.html#psa" id="id42"><span>[PSA]</span></a>.
-When <span class="math notranslate nohighlight">\(\rho=1\)</span>, Douglas-Rachford’s algorithm is <em>functionally equivalent</em> to ADMM (up to a change of variable, see <a class="reference internal" href="../references.html#psa" id="id43"><span>[PSA]</span></a> for a derivation).</p></li>
-</ul>
-</section>
-<section id="id44">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id44" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s) for the primal variable.</p></li>
-<li><p><strong>z0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, N) initial point(s) for the dual variable.
-If <code class="docutils literal notranslate"><span class="pre">None</span></code> (default), then use <code class="docutils literal notranslate"><span class="pre">x0</span></code> as the initial point for the dual variable.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Primal step size. Defaults to 1.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.ChambollePock" title="pyxu.opt.solver.pds.ChambollePock"><code class="xref py py-func docutils literal notranslate"><span class="pre">ChambollePock()</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.ForwardBackward" title="pyxu.opt.solver.pds.ForwardBackward"><code class="xref py py-func docutils literal notranslate"><span class="pre">ForwardBackward()</span></code></a></p>
-</div>
-</section>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.DR">
-<span class="sig-name descname"><span class="pre">DR</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">g=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">h=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">base=&lt;class</span> <span class="pre">'pyxu.opt.solver.pds.CondatVu'&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">**kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pyxu.opt.solver.pds.DR" title="Link to this definition">#</a></dt>
-<dd><p>Alias of <a class="reference internal" href="#pyxu.opt.solver.pds.DouglasRachford" title="pyxu.opt.solver.pds.DouglasRachford"><code class="xref py py-func docutils literal notranslate"><span class="pre">DouglasRachford()</span></code></a>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>base</strong> (<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><em>Type</em></a><em>[</em><em>_PrimalDualSplitting</em><em>]</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.ForwardBackward">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ForwardBackward</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pds.html#ForwardBackward"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pds.ForwardBackward" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a></p>
-<p>Forward-backward splitting algorithm.</p>
-<p>This solver is also accessible via the alias <a class="reference internal" href="#pyxu.opt.solver.pds.FB" title="pyxu.opt.solver.pds.FB"><code class="xref py py-class docutils literal notranslate"><span class="pre">FB</span></code></a>.</p>
-<p>The <em>Forward-backward (FB) splitting</em> method can be used to solve problems of the form:</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \;\mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{G}(\mathbf{x}),}\]</div>
-<p>where:</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}:\mathbb{R}^N\rightarrow \mathbb{R}\)</span> is <em>convex</em> and <em>differentiable</em>, with <span class="math notranslate nohighlight">\(\beta\)</span>-<em>Lipschitz continuous</em> gradient,
-for some <span class="math notranslate nohighlight">\(\beta\in[0,+\infty[\)</span>.</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{G}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> is <em>proper</em>, <em>lower semicontinuous</em> and <em>convex function</em> with <em>simple proximal operator</em>.</p></li>
-</ul>
-<section id="id45">
-<h3>Remarks<a class="headerlink" href="#id45" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p>The problem is <em>feasible</em>, i.e. there exists at least one solution.</p></li>
-<li><p>The algorithm is still valid if one of the terms <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> or <span class="math notranslate nohighlight">\(\mathcal{G}\)</span> is zero.</p></li>
-<li><p>The <em>Forward-backward (FB) primal-dual splitting</em> method can be obtained by choosing <span class="math notranslate nohighlight">\(\mathcal{H}=0\)</span> in <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>.
-Mercier originally introduced the algorithm without relaxation (<span class="math notranslate nohighlight">\(\rho=1\)</span>) <a class="reference internal" href="../references.html#fb" id="id46"><span>[FB]</span></a>.
-Relaxed versions have been proposed afterwards <a class="reference internal" href="../references.html#psa" id="id47"><span>[PSA]</span></a>.
-The Forward-backward algorithm is also known as the <em>Proximal Gradient Descent (PGD)</em> algorithm.
-For the accelerated version of PGD, use <a class="reference internal" href="#pyxu.opt.solver.pgd.PGD" title="pyxu.opt.solver.pgd.PGD"><code class="xref py py-class docutils literal notranslate"><span class="pre">PGD</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id48">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id48" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Lipschitz constant <span class="math notranslate nohighlight">\(\beta\)</span> of <span class="math notranslate nohighlight">\(\nabla\mathcal{F}\)</span>.
-If not provided, it will be automatically estimated.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id49">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id49" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s) for the primal variable.</p></li>
-<li><p><strong>z0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, N) initial point(s) for the dual variable.
-If <code class="docutils literal notranslate"><span class="pre">None</span></code> (default), then use <code class="docutils literal notranslate"><span class="pre">x0</span></code> as the initial point for the dual variable.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Primal step size.</p></li>
-<li><p><strong>rho</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Momentum parameter.</p></li>
-<li><p><strong>tuning_strategy</strong> (1, 2, 3)
-–
-Strategy to be employed when setting the hyperparameters (default to 1).
-See <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a> for more details.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pgd.PGD" title="pyxu.opt.solver.pgd.PGD"><code class="xref py py-class docutils literal notranslate"><span class="pre">PGD</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.ChambollePock" title="pyxu.opt.solver.pds.ChambollePock"><code class="xref py py-func docutils literal notranslate"><span class="pre">ChambollePock()</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.DouglasRachford" title="pyxu.opt.solver.pds.DouglasRachford"><code class="xref py py-func docutils literal notranslate"><span class="pre">DouglasRachford()</span></code></a></p>
-</div>
-</section>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py attribute">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.FB">
-<span class="sig-name descname"><span class="pre">FB</span></span><a class="headerlink" href="#pyxu.opt.solver.pds.FB" title="Link to this definition">#</a></dt>
-<dd><p>Alias of <a class="reference internal" href="#pyxu.opt.solver.pds.ForwardBackward" title="pyxu.opt.solver.pds.ForwardBackward"><code class="xref py py-class docutils literal notranslate"><span class="pre">ForwardBackward</span></code></a>.</p>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.ProximalPoint">
-<span class="sig-name descname"><span class="pre">ProximalPoint</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">g=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">base=&lt;class</span> <span class="pre">'pyxu.opt.solver.pds.CondatVu'&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">**kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pds.html#ProximalPoint"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pds.ProximalPoint" title="Link to this definition">#</a></dt>
-<dd><p>Proximal-point method.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>base</strong> (<a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>) – Specifies the base primal-dual algorithm from which mathematical updates are inherited.
-(Default = <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>)</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</dd>
-</dl>
-<p>The <em>Proximal-point (PP)</em> method can be used to solve problems of the form:</p>
-<div class="math notranslate nohighlight">
-\[{\min_{\mathbf{x}\in\mathbb{R}^N} \;\mathcal{G}(\mathbf{x}),}\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathcal{G}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> is <em>proper</em>, <em>lower semicontinuous</em> and <em>convex function</em> with <em>simple proximal operator</em>.</p>
-<section id="id50">
-<h3>Remarks<a class="headerlink" href="#id50" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p>The problem is <em>feasible</em>, i.e. there exists at least one solution.</p></li>
-<li><p>The <em>Proximal-point</em> algorithm can be obtained by choosing <span class="math notranslate nohighlight">\(\mathcal{F}=0\)</span> and <span class="math notranslate nohighlight">\(\mathcal{H}=0\)</span> in <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a> or <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>.
-The original version of the algorithm was introduced without relaxation (<span class="math notranslate nohighlight">\(\rho=1\)</span>) <a class="reference internal" href="../references.html#pp" id="id51"><span>[PP]</span></a>.
-Relaxed versions have been proposed afterwards <a class="reference internal" href="../references.html#psa" id="id52"><span>[PSA]</span></a>.</p></li>
-</ul>
-</section>
-<section id="id53">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id53" title="Link to this heading">#</a></h3>
-<ul class="simple">
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s) for the primal variable.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Primal step size.</p></li>
-<li><p><strong>rho</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Momentum parameter.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.opt.solver.pds.PP" title="pyxu.opt.solver.pds.PP"><code class="xref py py-class docutils literal notranslate"><span class="pre">PP</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pgd.PGD" title="pyxu.opt.solver.pgd.PGD"><code class="xref py py-class docutils literal notranslate"><span class="pre">PGD</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.ChambollePock" title="pyxu.opt.solver.pds.ChambollePock"><code class="xref py py-func docutils literal notranslate"><span class="pre">ChambollePock()</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.DouglasRachford" title="pyxu.opt.solver.pds.DouglasRachford"><code class="xref py py-func docutils literal notranslate"><span class="pre">DouglasRachford()</span></code></a></p>
-</div>
-</section>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.PP">
-<span class="sig-name descname"><span class="pre">PP</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">g=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">base=&lt;class</span> <span class="pre">'pyxu.opt.solver.pds.CondatVu'&gt;</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">**kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pyxu.opt.solver.pds.PP" title="Link to this definition">#</a></dt>
-<dd><p>Alias of <a class="reference internal" href="#pyxu.opt.solver.pds.ProximalPoint" title="pyxu.opt.solver.pds.ProximalPoint"><code class="xref py py-func docutils literal notranslate"><span class="pre">ProximalPoint()</span></code></a>.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>base</strong> (<em>_PrimalDualSplitting</em><em> | </em><em>None</em>) – </p></li>
-</ul>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py class">
-<dt class="sig sig-object py" id="pyxu.opt.solver.pds.ADMM">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ADMM</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">h</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">K</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">solver</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">solver_kwargs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pds.html#ADMM"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.pds.ADMM" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">_PrimalDualSplitting</span></code></p>
-<p>Alternating Direction Method of Multipliers.</p>
-<p>The <em>Alternating Direction Method of Multipliers (ADMM)</em> can be used to solve problems of the form:</p>
-<div class="math notranslate nohighlight">
-\[\min_{\mathbf{x}\in\mathbb{R}^N} \quad \mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{H}(\mathbf{K}\mathbf{x}),\]</div>
-<p>where (see below for additional details on the assumptions):</p>
-<ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}:\mathbb{R}^N\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> is a <em>proper</em>, <em>lower semicontinuous</em> and
-<em>convex functional</em> potentially with <em>simple proximal operator</em> or <em>Lipschitz-differentiable</em>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{H}:\mathbb{R}^M\rightarrow \mathbb{R}\cup\{+\infty\}\)</span> is a <em>proper</em>, <em>lower semicontinuous</em> and
-<em>convex functional</em> with <em>simple proximal operator</em>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathbf{K}:\mathbb{R}^N\rightarrow \mathbb{R}^M\)</span> is a <em>linear operator</em> with <strong>operator norm</strong>
-<span class="math notranslate nohighlight">\(\Vert{\mathbf{K}}\Vert_2\)</span>.</p></li>
-</ul>
-<section id="id54">
-<h3>Remarks<a class="headerlink" href="#id54" title="Link to this heading">#</a></h3>
-<ul>
-<li><p>The problem is <em>feasible</em>, i.e. there exists at least one solution.</p></li>
-<li><p>The algorithm is still valid if either <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> or <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> is zero.</p></li>
-<li><p>When <span class="math notranslate nohighlight">\(\mathbf{K} = \mathbf{I}_{N}\)</span>, ADMM is equivalent to the <a class="reference internal" href="#pyxu.opt.solver.pds.DouglasRachford" title="pyxu.opt.solver.pds.DouglasRachford"><code class="xref py py-func docutils literal notranslate"><span class="pre">DouglasRachford()</span></code></a>
-method (up to a change of variable, see <a class="reference internal" href="../references.html#psa" id="id55"><span>[PSA]</span></a> for a derivation).</p></li>
-<li><p>This is an implementation of the algorithm described in Section 5.4 of <a class="reference internal" href="../references.html#psa" id="id56"><span>[PSA]</span></a>, which handles the non-smooth
-composite term <span class="math notranslate nohighlight">\(\mathcal{H}(\mathbf{K}\mathbf{x})\)</span> by means of a change of variable and an infimal
-postcomposition trick.
-The update equation of this algorithm involves the following <span class="math notranslate nohighlight">\(\mathbf{x}\)</span>-minimization step:</p>
-<div class="math notranslate nohighlight" id="equation-eq-x-minimization">
-<span class="eqno">(1)<a class="headerlink" href="#equation-eq-x-minimization" title="Link to this equation">#</a></span>\[\mathcal{V} = \operatorname*{arg\,min}_{\mathbf{x} \in \mathbb{R}^N} \quad \mathcal{F}(\mathbf{x}) + \frac1{2 \tau}
-\Vert \mathbf{K} \mathbf{x} - \mathbf{a} \Vert_2^2,\]</div>
-<p>where <span class="math notranslate nohighlight">\(\tau\)</span> is the primal step size and <span class="math notranslate nohighlight">\(\mathbf{a} \in \mathbb{R}^M\)</span> is an iteration-dependant vector.</p>
-<p>The following cases are covered in this implementation:</p>
-<ul>
-<li><p><span class="math notranslate nohighlight">\(\mathbf{K}\)</span> is <code class="docutils literal notranslate"><span class="pre">None</span></code> (i.e. the identity operator) and <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is a <a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>.
-Then, <a class="reference internal" href="#equation-eq-x-minimization">(1)</a> has a single solution provided by
-<span class="math notranslate nohighlight">\(\operatorname*{prox}_{\tau \mathcal{F}}(\mathbf{a})\)</span>.
-This yields the <em>classical ADMM algorithm</em> described in Section 5.3 of <a class="reference internal" href="../references.html#psa" id="id57"><span>[PSA]</span></a> (i.e. without the postcomposition trick).</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is a <a class="reference internal" href="abc.html#pyxu.abc.operator.QuadraticFunc" title="pyxu.abc.operator.QuadraticFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">QuadraticFunc</span></code></a>, i.e.
-<span class="math notranslate nohighlight">\(\mathcal{F}(\mathbf{x})=\frac{1}{2} \langle\mathbf{x}, \mathbf{Q}\mathbf{x}\rangle + \mathbf{c}^T\mathbf{x} + t\)</span>.
-Then the unique solution to <a class="reference internal" href="#equation-eq-x-minimization">(1)</a> is obtained by solving a linear system of the form:</p>
-<div class="math notranslate nohighlight" id="equation-eq-linear-system">
-<span class="eqno">(2)<a class="headerlink" href="#equation-eq-linear-system" title="Link to this equation">#</a></span>\[\Big( \mathbf{Q} + \frac1\tau \mathbf{K}^* \mathbf{K} \Big) \mathbf{x} =
-\frac1\tau \mathbf{K}^\ast\mathbf{a}-\mathbf{c}, \qquad \mathbf{x} \in \mathbb{R}^N.\]</div>
-<p>This linear system is solved via a sub-iterative <a class="reference internal" href="#pyxu.opt.solver.cg.CG" title="pyxu.opt.solver.cg.CG"><code class="xref py py-class docutils literal notranslate"><span class="pre">CG</span></code></a> algorithm involving the repeated
-application of <span class="math notranslate nohighlight">\(\mathbf{Q}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{K}^{*}\mathbf{K}\)</span>.
-This sub-iterative scheme may be computationally intensive if these operators do not admit fast matrix-free implementations.</p>
-</li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is a <a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>.
-Then, <a class="reference internal" href="#equation-eq-x-minimization">(1)</a> is solved via a sub-iterative <a class="reference internal" href="#pyxu.opt.solver.nlcg.NLCG" title="pyxu.opt.solver.nlcg.NLCG"><code class="xref py py-class docutils literal notranslate"><span class="pre">NLCG</span></code></a> algorithm
-involving repeated evaluation of <span class="math notranslate nohighlight">\(\nabla\mathcal{F}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{K}^{*}\mathbf{K}\)</span>.
-This sub-iterative scheme may be costly if these operators cannot be evaluated with fast algorithms.
-In this scenario, the use of multiple initial points in <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> is not supported.</p></li>
-</ul>
-<p>The user may also provide a <em>custom</em> callable solver <span class="math notranslate nohighlight">\(s: \mathbb{R}^M \times \mathbb{R} \to \mathbb{R}^N\)</span>,
-taking as input <span class="math notranslate nohighlight">\((\mathbf{a}, \tau)\)</span> and solving <a class="reference internal" href="#equation-eq-x-minimization">(1)</a>,
-i.e. <span class="math notranslate nohighlight">\(s(\mathbf{a}, \tau) \in \mathcal{V}\)</span>. (See example below.)
-If <a class="reference internal" href="#pyxu.opt.solver.pds.ADMM" title="pyxu.opt.solver.pds.ADMM"><code class="xref py py-class docutils literal notranslate"><span class="pre">ADMM</span></code></a> is initialized with such a solver, then the latter is used to solve
-<a class="reference internal" href="#equation-eq-x-minimization">(1)</a> regardless of whether one of the above-mentioned cases is met.</p>
-</li>
-<li><p>Unlike traditional implementations of ADMM, <a class="reference internal" href="#pyxu.opt.solver.pds.ADMM" title="pyxu.opt.solver.pds.ADMM"><code class="xref py py-class docutils literal notranslate"><span class="pre">ADMM</span></code></a> supports relaxation, i.e. <span class="math notranslate nohighlight">\(\rho\neq 1\)</span>.</p></li>
-</ul>
-</section>
-<section id="id58">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id58" title="Link to this heading">#</a></h3>
-<ul>
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffFunc" title="pyxu.abc.operator.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Differentiable or proximable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.LinOp" title="pyxu.abc.operator.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Linear operator <span class="math notranslate nohighlight">\(\mathbf{K}\)</span>.</p></li>
-<li><p><strong>solver</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Callable</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Custom callable to solve the <span class="math notranslate nohighlight">\(\mathbf{x}\)</span>-minimization step <a class="reference internal" href="#equation-eq-x-minimization">(1)</a>.</p>
-<p>If provided, <code class="code docutils literal notranslate"><span class="pre">solver</span></code> must have the <a class="reference external" href="https://numpy.org/neps/nep-0020-gufunc-signature-enhancement.html">NumPy signature</a>
-<code class="docutils literal notranslate"><span class="pre">(n),</span> <span class="pre">(1)</span> <span class="pre">-&gt;</span> <span class="pre">(n)</span></code>.</p>
-</li>
-<li><p><strong>solver_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Keyword parameters passed to the <code class="docutils literal notranslate"><span class="pre">__init__()</span></code> method of sub-iterative
-<a class="reference internal" href="#pyxu.opt.solver.cg.CG" title="pyxu.opt.solver.cg.CG"><code class="xref py py-class docutils literal notranslate"><span class="pre">CG</span></code></a> or <a class="reference internal" href="#pyxu.opt.solver.nlcg.NLCG" title="pyxu.opt.solver.nlcg.NLCG"><code class="xref py py-class docutils literal notranslate"><span class="pre">NLCG</span></code></a> solvers.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">solver_kwargs</span></code> is ignored if <code class="code docutils literal notranslate"><span class="pre">solver</span></code> provided.</p>
-</li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.__init__" title="pyxu.abc.solver.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.__init__()</span></code></a>.</p></li>
-</ul>
-</section>
-<section id="id59">
-<h3>Parameters (<code class="docutils literal notranslate"><span class="pre">fit()</span></code>)<a class="headerlink" href="#id59" title="Link to this heading">#</a></h3>
-<ul>
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>)
-–
-(…, N) initial point(s) for the primal variable.</p></li>
-<li><p><strong>z0</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-attr docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-(…, M) initial point(s) for the dual variable.
-If <code class="docutils literal notranslate"><span class="pre">None</span></code> (default), then use <code class="docutils literal notranslate"><span class="pre">K(x0)</span></code> as the initial point for the dual variable.</p></li>
-<li><p><strong>tau</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Primal step size.</p></li>
-<li><p><strong>rho</strong> (<a class="reference internal" href="info.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
-–
-Momentum parameter for relaxation.</p></li>
-<li><p><strong>tuning_strategy</strong> (1, 2, 3)
-–
-Strategy to be employed when setting the hyperparameters (default to 1).
-See base class for more details.</p></li>
-<li><p><strong>solver_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Keyword parameters passed to the <code class="docutils literal notranslate"><span class="pre">fit()</span></code> method of sub-iterative
-<a class="reference internal" href="#pyxu.opt.solver.cg.CG" title="pyxu.opt.solver.cg.CG"><code class="xref py py-class docutils literal notranslate"><span class="pre">CG</span></code></a> or <a class="reference internal" href="#pyxu.opt.solver.nlcg.NLCG" title="pyxu.opt.solver.nlcg.NLCG"><code class="xref py py-class docutils literal notranslate"><span class="pre">NLCG</span></code></a> solvers.</p>
-<p><code class="code docutils literal notranslate"><span class="pre">solver_kwargs</span></code> is ignored if <code class="code docutils literal notranslate"><span class="pre">solver</span></code> was provided in <code class="docutils literal notranslate"><span class="pre">__init__()</span></code>.</p>
-</li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
-–
-Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver.fit()</span></code></a>.</p></li>
-</ul>
-<div class="admonition warning">
-<p class="admonition-title">Warning</p>
-<p><code class="docutils literal notranslate"><span class="pre">tuning_strategy</span></code> docstring says to look at base class for details, but nothing mentioned there!</p>
-</div>
-<p class="rubric">Example</p>
-<p>Consider the following optimization problem:</p>
-<div class="math notranslate nohighlight">
-\[\min_{\mathbf{x}\in\mathbb{R}^N}\frac{1}{2}\left\|\mathbf{y}-\mathbf{G}\mathbf{x}\right\|_2^2\quad+\quad\lambda \|\mathbf{D}\mathbf{x}\|_1,\]</div>
-<p>with <span class="math notranslate nohighlight">\(\mathbf{D}\in\mathbb{R}^{N\times N}\)</span> the discrete second-order derivative operator,
-<span class="math notranslate nohighlight">\(\mathbf{G}\in\mathbb{R}^{M\times N}, \, \mathbf{y}\in\mathbb{R}^M, \lambda&gt;0.\)</span>
-This problem can be solved via ADMM with <span class="math notranslate nohighlight">\(\mathcal{F}(\mathbf{x})= \frac{1}{2}\left\|\mathbf{y}-\mathbf{G}\mathbf{x}\right\|_2^2\)</span>,
-<span class="math notranslate nohighlight">\(\mathcal{H}(\mathbf{x})=\lambda \|\mathbf{D}\mathbf{x}\|_1,\)</span> and <span class="math notranslate nohighlight">\(\mathbf{K}=\mathbf{D}\)</span>.
-The functional <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> being quadratic, the <span class="math notranslate nohighlight">\(\mathbf{x}\)</span>-minimization step consists in solving a linear system of
-the form <a class="reference internal" href="#equation-eq-linear-system">(2)</a>.
-Here, we demonstrate how to provide a custom solver, which consists in applying a matrix inverse, for this step.
-Otherwise, a sub-iterative <a class="reference internal" href="#pyxu.opt.solver.cg.CG" title="pyxu.opt.solver.cg.CG"><code class="xref py py-class docutils literal notranslate"><span class="pre">CG</span></code></a> algorithm would have been used automatically instead.</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <span class="nn">pyxu.abc</span> <span class="k">as</span> <span class="nn">pxa</span>
-<span class="kn">import</span> <span class="nn">pyxu.operator</span> <span class="k">as</span> <span class="nn">pxo</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/index.html#module-scipy" title="scipy"><span class="nn">scipy</span></a> <span class="k">as</span> <span class="nn">sp</span>
-<span class="kn">from</span> <span class="nn">pyxu.opt.solver</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/opt.html#pyxu.opt.solver.pds.ADMM" title="pyxu.opt.solver.pds.ADMM"><span class="n">ADMM</span></a>
-
-<span class="n">N</span> <span class="o">=</span> <span class="mi">100</span>  <span class="c1"># Dimension of the problem</span>
-
-<span class="c1"># Generate piecewise-linear ground truth</span>
-<span class="n">x_gt</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="mi">60</span><span class="p">,</span> <span class="mi">90</span><span class="p">])</span>  <span class="c1"># Knot locations</span>
-<span class="n">a_gt</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array" title="numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">])</span>  <span class="c1"># Amplitudes of the knots</span>
-<span class="n">gt</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">N</span><span class="p">)</span>  <span class="c1"># Ground-truth signal</span>
-<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#range" title="range"><span class="nb">range</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#len" title="len"><span class="nb">len</span></a><span class="p">(</span><span class="n">x_gt</span><span class="p">)):</span>
-    <span class="n">gt</span><span class="p">[</span><span class="n">x_gt</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="p">:]</span> <span class="o">+=</span> <span class="n">a_gt</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">N</span> <span class="o">-</span> <span class="n">x_gt</span><span class="p">[</span><span class="n">n</span><span class="p">])</span> <span class="o">/</span> <span class="n">N</span>
-
-<span class="c1"># Generate data (noisy samples at random locations)</span>
-<span class="n">M</span> <span class="o">=</span> <span class="mi">20</span>  <span class="c1"># Number of data points</span>
-<span class="n">rng</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/random/generator.html#numpy.random.default_rng" title="numpy.random.default_rng"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span></a><span class="p">(</span><span class="n">seed</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
-<span class="n">x_samp</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">N</span> <span class="o">//</span> <span class="n">M</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="n">M</span><span class="p">)</span> <span class="o">+</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">step</span><span class="o">=</span><span class="n">N</span> <span class="o">//</span> <span class="n">M</span><span class="p">)</span>  <span class="c1"># sampling locations</span>
-<span class="n">sigma</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="mf">1e-2</span>  <span class="c1"># noise variance</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">gt</span><span class="p">[</span><span class="n">x_samp</span><span class="p">]</span> <span class="o">+</span> <span class="n">sigma</span> <span class="o">*</span> <span class="n">rng</span><span class="o">.</span><span class="n">standard_normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">M</span><span class="p">)</span>  <span class="c1"># noisy data points</span>
-
-<span class="c1"># Data-fidelity term</span>
-<a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.lil_matrix.html#scipy.sparse.lil_matrix" title="scipy.sparse._lil.lil_matrix"><span class="n">subsamp_mat</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.lil_matrix.html#scipy.sparse.lil_matrix" title="scipy.sparse._lil.lil_matrix"><span class="n">sp</span><span class="o">.</span><span class="n">sparse</span><span class="o">.</span><span class="n">lil_matrix</span></a><span class="p">((</span><span class="n">M</span><span class="p">,</span> <span class="n">N</span><span class="p">))</span>
-<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#range" title="range"><span class="nb">range</span></a><span class="p">(</span><span class="n">M</span><span class="p">):</span>
-    <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.lil_matrix.html#scipy.sparse.lil_matrix" title="scipy.sparse._lil.lil_matrix"><span class="n">subsamp_mat</span></a><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">x_samp</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">G</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.operator.LinOp.from_array" title="pyxu.abc.operator.LinOp.from_array"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span><span class="o">.</span><span class="n">from_array</span></a><span class="p">(</span><span class="n">subsamp_mat</span><span class="o">.</span><span class="n">tocsr</span><span class="p">())</span>
-<span class="n">F</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.func.norm.SquaredL2Norm" title="pyxu.operator.func.norm.SquaredL2Norm"><span class="n">pxo</span><span class="o">.</span><span class="n">SquaredL2Norm</span></a><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="n">y</span><span class="o">.</span><span class="n">size</span><span class="p">)</span><span class="o">.</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.operator.Operator.argshift" title="pyxu.abc.operator.Operator.argshift"><span class="n">argshift</span></a><span class="p">(</span><span class="o">-</span><span class="n">y</span><span class="p">)</span> <span class="o">*</span> <span class="n">G</span>
-<span class="n">F</span><span class="o">.</span><span class="n">diff_lipschitz</span> <span class="o">=</span> <span class="n">F</span><span class="o">.</span><span class="n">estimate_diff_lipschitz</span><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="s2">"svd"</span><span class="p">)</span>
-
-<span class="c1"># Regularization term (promotes sparse second derivatives)</span>
-<span class="n">deriv_mat</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.diags.html#scipy.sparse.diags" title="scipy.sparse.diags"><span class="n">sp</span><span class="o">.</span><span class="n">sparse</span><span class="o">.</span><span class="n">diags</span></a><span class="p">(</span><span class="n">diagonals</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">offsets</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">N</span> <span class="o">-</span> <span class="mi">2</span><span class="p">,</span> <span class="n">N</span><span class="p">))</span>
-<span class="n">D</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.operator.LinOp.from_array" title="pyxu.abc.operator.LinOp.from_array"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span><span class="o">.</span><span class="n">from_array</span></a><span class="p">(</span><span class="n">deriv_mat</span><span class="p">)</span>
-<span class="n">_lambda</span> <span class="o">=</span> <span class="mf">1e-1</span>  <span class="c1"># regularization parameter</span>
-<span class="n">H</span> <span class="o">=</span> <span class="n">_lambda</span> <span class="o">*</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.func.norm.L1Norm" title="pyxu.operator.func.norm.L1Norm"><span class="n">pxo</span><span class="o">.</span><span class="n">L1Norm</span></a><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="n">D</span><span class="o">.</span><span class="n">codim</span><span class="p">)</span>
-
-<span class="c1"># Solver for ADMM</span>
-<span class="n">tau</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">_lambda</span>  <span class="c1"># internal ADMM parameter</span>
-<span class="c1"># Inverse operator to solve the linear system</span>
-<span class="n">A_inv</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.inv.html#scipy.linalg.inv" title="scipy.linalg.inv"><span class="n">sp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span></a><span class="p">(</span><span class="n">G</span><span class="o">.</span><span class="n">gram</span><span class="p">()</span><span class="o">.</span><span class="n">asarray</span><span class="p">()</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">tau</span><span class="p">)</span> <span class="o">*</span> <span class="n">D</span><span class="o">.</span><span class="n">gram</span><span class="p">()</span><span class="o">.</span><span class="n">asarray</span><span class="p">())</span>
-
-<span class="k">def</span> <span class="nf">solver_ADMM</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">tau</span><span class="p">):</span>
-    <span class="n">b</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">tau</span><span class="p">)</span> <span class="o">*</span> <span class="n">D</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="o">+</span> <span class="n">G</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">A_inv</span> <span class="o">@</span> <span class="n">b</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
-
-
-<span class="c1"># Solve optimization problem</span>
-<a class="sphinx-codeautolink-a" href="../api/opt.html#pyxu.opt.solver.pds.ADMM" title="pyxu.opt.solver.pds.ADMM"><span class="n">admm</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/opt.html#pyxu.opt.solver.pds.ADMM" title="pyxu.opt.solver.pds.ADMM"><span class="n">ADMM</span></a><span class="p">(</span><span class="n">f</span><span class="o">=</span><span class="n">F</span><span class="p">,</span> <span class="n">h</span><span class="o">=</span><span class="n">H</span><span class="p">,</span> <span class="n">K</span><span class="o">=</span><span class="n">D</span><span class="p">,</span> <span class="n">solver</span><span class="o">=</span><span class="n">solver_ADMM</span><span class="p">,</span><span class="n">show_progress</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>  <span class="c1"># with solver</span>
-<a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.solver.Solver.fit" title="pyxu.abc.solver.Solver.fit"><span class="n">admm</span><span class="o">.</span><span class="n">fit</span></a><span class="p">(</span><span class="n">x0</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.zeros.html#numpy.zeros" title="numpy.zeros"><span class="n">np</span><span class="o">.</span><span class="n">zeros</span></a><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">tau</span><span class="o">=</span><span class="n">tau</span><span class="p">)</span>
-<span class="n">x_opt</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.solver.Solver.solution" title="pyxu.abc.solver.Solver.solution"><span class="n">admm</span><span class="o">.</span><span class="n">solution</span></a><span class="p">()</span>  <span class="c1"># reconstructed signal</span>
-
-<span class="c1"># Plots</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">gt</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Ground truth"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">x_samp</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s2">"kx"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Noisy data points"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.arange.html#numpy.arange" title="numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">N</span><span class="p">),</span> <span class="n">x_opt</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Reconstructed signal"</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html#matplotlib.pyplot.legend" title="matplotlib.pyplot.legend"><span class="n">plt</span><span class="o">.</span><span class="n">legend</span></a><span class="p">()</span>
-</pre></div>
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-<p>(<a class="reference download internal" download="" href="../_downloads/4769d18f8e2c0bf193e34be59a343ebb/opt-3.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/e92a40fb9538516e44ee3d2080a0bba4/opt-3.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/aef880f23607764f0dad2e327f5d24fd/opt-3.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/2b553e753c10e27428470a2afb36677c/opt-3.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
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-</figure>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.opt.solver.pds.CondatVu" title="pyxu.opt.solver.pds.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.PD3O" title="pyxu.opt.solver.pds.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pgd.PGD" title="pyxu.opt.solver.pgd.PGD"><code class="xref py py-class docutils literal notranslate"><span class="pre">PGD</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.ChambollePock" title="pyxu.opt.solver.pds.ChambollePock"><code class="xref py py-func docutils literal notranslate"><span class="pre">ChambollePock()</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.pds.DouglasRachford" title="pyxu.opt.solver.pds.DouglasRachford"><code class="xref py py-func docutils literal notranslate"><span class="pre">DouglasRachford()</span></code></a></p>
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-<dl class="field-list simple">
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-<dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.Func" title="pyxu.abc.operator.Func"><em>Func</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.operator.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>solver</strong> (<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.11)"><em>float</em></a><em>]</em><em>, </em><a class="reference internal" href="info.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
-<li><p><strong>solver_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><em>dict</em></a><em> | </em><em>None</em>) – </p></li>
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-<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.stop.RelError.__init__"><code class="docutils literal notranslate"><span class="pre">RelError.__init__()</span></code></a></li>
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-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pgd.PGD"><code class="docutils literal notranslate"><span class="pre">PGD</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.cg.CG"><code class="docutils literal notranslate"><span class="pre">CG</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.nlcg.NLCG"><code class="docutils literal notranslate"><span class="pre">NLCG</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.adam.Adam"><code class="docutils literal notranslate"><span class="pre">Adam</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.CondatVu"><code class="docutils literal notranslate"><span class="pre">CondatVu</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.CV"><code class="docutils literal notranslate"><span class="pre">CV</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.PD3O"><code class="docutils literal notranslate"><span class="pre">PD3O</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.ChambollePock"><code class="docutils literal notranslate"><span class="pre">ChambollePock()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.CP"><code class="docutils literal notranslate"><span class="pre">CP()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.LorisVerhoeven"><code class="docutils literal notranslate"><span class="pre">LorisVerhoeven</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.LV"><code class="docutils literal notranslate"><span class="pre">LV</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.DavisYin"><code class="docutils literal notranslate"><span class="pre">DavisYin</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.DY"><code class="docutils literal notranslate"><span class="pre">DY</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.DouglasRachford"><code class="docutils literal notranslate"><span class="pre">DouglasRachford()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.DR"><code class="docutils literal notranslate"><span class="pre">DR()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.ForwardBackward"><code class="docutils literal notranslate"><span class="pre">ForwardBackward</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.FB"><code class="docutils literal notranslate"><span class="pre">FB</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.ProximalPoint"><code class="docutils literal notranslate"><span class="pre">ProximalPoint()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.PP"><code class="docutils literal notranslate"><span class="pre">PP()</span></code></a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.opt.solver.pds.ADMM"><code class="docutils literal notranslate"><span class="pre">ADMM</span></code></a></li>
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diff --git a/api/opt.solver.html b/api/opt.solver.html
index ccff7d79..cac93364 100644
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 <li class="toctree-l1"><a class="reference internal" href="math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="util/array_module.html">pyxu.util.array_module</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../references.html"><strong>References</strong></a></li>
 </ul>
@@ -292,7 +281,7 @@ <h1>pyxu.opt.solver<a class="headerlink" href="#pyxu-opt-solver" title="Link to
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.solver.PGD">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PGD</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/pgd.html#PGD"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.PGD" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
 <p>Proximal Gradient Descent (PGD) solver.</p>
 <p>PGD solves minimization problems of the form</p>
 <div class="math notranslate nohighlight">
@@ -330,15 +319,15 @@ <h2>Remarks<a class="headerlink" href="#remarks" title="Link to this heading">#<
 <section id="parameters-init">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#parameters-init" title="Link to this heading">#</a></h2>
 <ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="parameters-fit">
@@ -359,14 +348,14 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 is True.  Defaults to 75 in unspecified.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 </section>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -374,7 +363,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.solver.CG">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">CG</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/cg.html#CG"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.CG" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
 <p>Conjugate Gradient Method.</p>
 <p>The Conjugate Gradient method solves the minimization problem</p>
 <div class="math notranslate nohighlight">
@@ -388,12 +377,12 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <section id="id3">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id3" title="Link to this heading">#</a></h2>
 <ul class="simple">
-<li><p><strong>A</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.PosDefOp" title="pyxu.abc.PosDefOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">PosDefOp</span></code></a>)
+<li><p><strong>A</strong> (<a class="reference internal" href="abc.html#pyxu.abc.PosDefOp" title="pyxu.abc.PosDefOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">PosDefOp</span></code></a>)
 –
 Positive-definite operator <span class="math notranslate nohighlight">\(\mathbf{A}: \mathbb{R}^{N} \to \mathbb{R}^{N}\)</span>.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="id4">
@@ -416,19 +405,19 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 </li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 </section>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>A</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.PosDefOp" title="pyxu.abc.operator.PosDefOp"><em>PosDefOp</em></a>) – </p>
+<dd class="field-odd"><p><strong>A</strong> (<a class="reference internal" href="abc.html#pyxu.abc.PosDefOp" title="pyxu.abc.operator.PosDefOp"><em>PosDefOp</em></a>) – </p>
 </dd>
 </dl>
 </dd></dl>
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.solver.NLCG">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NLCG</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/nlcg.html#NLCG"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.NLCG" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
 <p>Nonlinear Conjugate Gradient Method (NLCG).</p>
 <p>The Nonlinear Conjugate Gradient method finds a local minimum of the problem</p>
 <div class="math notranslate nohighlight">
@@ -470,12 +459,12 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <section id="id6">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id6" title="Link to this heading">#</a></h2>
 <ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>)
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>)
 –
 Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="id7">
@@ -502,7 +491,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 Optional parameters forwarded to <a class="reference internal" href="math.html#pyxu.math.backtracking_linesearch" title="pyxu.math.backtracking_linesearch"><code class="xref py py-func docutils literal notranslate"><span class="pre">backtracking_linesearch()</span></code></a>.</p>
 <p>If <code class="code docutils literal notranslate"><span class="pre">a0</span></code> is unspecified and <span class="math notranslate nohighlight">\(\nabla f\)</span> is <span class="math notranslate nohighlight">\(\beta\)</span>-Lipschitz continuous, then <code class="code docutils literal notranslate"><span class="pre">a0</span></code> is auto-chosen as
 <span class="math notranslate nohighlight">\(\beta^{-1}\)</span>.  Users are expected to set <code class="code docutils literal notranslate"><span class="pre">a0</span></code> if its value cannot be auto-inferred.</p>
-<p>Other keyword parameters are passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p>
+<p>Other keyword parameters are passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p>
 </li>
 </ul>
 <p class="rubric">Example</p>
@@ -527,14 +516,14 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 </section>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p>
+<dd class="field-odd"><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p>
 </dd>
 </dl>
 </dd></dl>
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.solver.Adam">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Adam</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/solver/adam.html#Adam"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.solver.Adam" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.solver.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a></p>
 <p>Adam solver <a class="reference internal" href="../references.html#proxadam" id="id8"><span>[ProxAdam]</span></a>.</p>
 <p>Adam minimizes</p>
 <div class="math notranslate nohighlight">
@@ -616,12 +605,12 @@ <h2>Remarks<a class="headerlink" href="#id9" title="Link to this heading">#</a><
 <section id="id10">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id10" title="Link to this heading">#</a></h2>
 <ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>)
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>)
 –
 Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="id11">
@@ -661,7 +650,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 Avoids division by zero if estimated gradient variance is too small.  Defaults to 1e-6.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <div class="admonition note">
 <p class="admonition-title">Note</p>
@@ -692,7 +681,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 </section>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p>
+<dd class="field-odd"><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a>) – </p>
 </dd>
 </dl>
 </dd></dl>
@@ -761,16 +750,16 @@ <h2>Remarks<a class="headerlink" href="#id14" title="Link to this heading">#</a>
 <section id="id17">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id17" title="Link to this heading">#</a></h2>
 <ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Differentiable map or linear operator <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
 <li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
@@ -779,7 +768,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__i
 If not provided, it will be automatically estimated.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="id18">
@@ -807,7 +796,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 See section below for more details.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <p class="rubric">Default hyperparameter values</p>
 <p>This class supports three strategies to automatically set the hyperparameters (see <a class="reference internal" href="../references.html#psa" id="id19"><span>[PSA]</span></a> for more details and
@@ -906,11 +895,11 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>beta</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -976,16 +965,16 @@ <h2>Remarks<a class="headerlink" href="#id21" title="Link to this heading">#</a>
 <section id="id25">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id25" title="Link to this heading">#</a></h2>
 <ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Differentiable map or linear operator <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
 <li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
@@ -994,7 +983,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__i
 If not provided, it will be automatically estimated.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="id26">
@@ -1022,7 +1011,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 See section below for more details.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <p class="rubric">Default hyperparameter values</p>
 <p>This class supports three strategies to automatically set the hyperparameters (see <a class="reference internal" href="../references.html#psa" id="id27"><span>[PSA]</span></a> for more details and
@@ -1113,11 +1102,11 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>beta</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -1129,12 +1118,12 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Differentiable map or linear operator <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Differentiable map or linear operator <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
 <li><p><strong>base</strong> (<a class="reference internal" href="#pyxu.opt.solver.CondatVu" title="pyxu.opt.solver.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.PD3O" title="pyxu.opt.solver.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>) – Specifies the base primal-dual algorithm.
 (Default = <a class="reference internal" href="#pyxu.opt.solver.CondatVu" title="pyxu.opt.solver.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>)</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </dd>
 </dl>
@@ -1190,7 +1179,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 See <code class="code docutils literal notranslate"><span class="pre">base</span></code> for more details.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
@@ -1205,9 +1194,9 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
 <li><p><strong>base</strong> (<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><em>Type</em></a><em>[</em><em>_PrimalDualSplitting</em><em>]</em>) – </p></li>
 </ul>
 </dd>
@@ -1249,13 +1238,13 @@ <h2>Remarks<a class="headerlink" href="#id33" title="Link to this heading">#</a>
 <section id="id35">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id35" title="Link to this heading">#</a></h2>
 <ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.DiffMap"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffMap</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Differentiable map or linear operator <span class="math notranslate nohighlight">\(\mathcal{K}\)</span>.</p></li>
 <li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
@@ -1264,7 +1253,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__i
 If not provided, it will be automatically estimated.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="id36">
@@ -1292,7 +1281,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 See <a class="reference internal" href="#pyxu.opt.solver.PD3O" title="pyxu.opt.solver.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a> for more details.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
@@ -1302,10 +1291,10 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>beta</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -1344,13 +1333,13 @@ <h2>Remarks<a class="headerlink" href="#id37" title="Link to this heading">#</a>
 <section id="id39">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id39" title="Link to this heading">#</a></h2>
 <ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>)
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>)
 –
 Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
 <li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
@@ -1359,7 +1348,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__i
 If not provided, it will be automatically estimated.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="id40">
@@ -1387,7 +1376,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 See <a class="reference internal" href="#pyxu.opt.solver.PD3O" title="pyxu.opt.solver.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a> for more details.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
@@ -1397,10 +1386,10 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>beta</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -1417,11 +1406,11 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
 <li><p><strong>base</strong> (<a class="reference internal" href="#pyxu.opt.solver.CondatVu" title="pyxu.opt.solver.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.PD3O" title="pyxu.opt.solver.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>) – Specifies the base primal-dual algorithm.
 (Default = <a class="reference internal" href="#pyxu.opt.solver.CondatVu" title="pyxu.opt.solver.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>)</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </dd>
 </dl>
@@ -1459,7 +1448,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 Primal step size. Defaults to 1.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
@@ -1474,8 +1463,8 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
 <li><p><strong>base</strong> (<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Type" title="(in Python v3.11)"><em>Type</em></a><em>[</em><em>_PrimalDualSplitting</em><em>]</em>) – </p></li>
 </ul>
 </dd>
@@ -1512,10 +1501,10 @@ <h2>Remarks<a class="headerlink" href="#id45" title="Link to this heading">#</a>
 <section id="id48">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id48" title="Link to this heading">#</a></h2>
 <ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Differentiable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
 <li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-attr docutils literal notranslate"><span class="pre">Real</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
@@ -1524,7 +1513,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__i
 If not provided, it will be automatically estimated.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="id49">
@@ -1549,7 +1538,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 See <a class="reference internal" href="#pyxu.opt.solver.CondatVu" title="pyxu.opt.solver.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a> for more details.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
@@ -1559,9 +1548,9 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>beta</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><em>DiffFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>beta</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em> | </em><em>None</em>) – </p></li>
 </ul>
 </dd>
 </dl>
@@ -1578,10 +1567,10 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>) – Proximable function <span class="math notranslate nohighlight">\(\mathcal{G}\)</span>.</p></li>
 <li><p><strong>base</strong> (<a class="reference internal" href="#pyxu.opt.solver.CondatVu" title="pyxu.opt.solver.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>, <a class="reference internal" href="#pyxu.opt.solver.PD3O" title="pyxu.opt.solver.PD3O"><code class="xref py py-class docutils literal notranslate"><span class="pre">PD3O</span></code></a>) – Specifies the base primal-dual algorithm from which mathematical updates are inherited.
 (Default = <a class="reference internal" href="#pyxu.opt.solver.CondatVu" title="pyxu.opt.solver.CondatVu"><code class="xref py py-class docutils literal notranslate"><span class="pre">CondatVu</span></code></a>)</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </dd>
 </dl>
@@ -1613,7 +1602,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 Momentum parameter.</p></li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
@@ -1628,7 +1617,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>g</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>g</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
 <li><p><strong>base</strong> (<em>_PrimalDualSplitting</em><em> | </em><em>None</em>) – </p></li>
 </ul>
 </dd>
@@ -1670,10 +1659,10 @@ <h2>Remarks<a class="headerlink" href="#id54" title="Link to this heading">#</a>
 <p>The following cases are covered in this implementation:</p>
 <ul>
 <li><p><span class="math notranslate nohighlight">\(\mathbf{K}\)</span> is <code class="docutils literal notranslate"><span class="pre">None</span></code> (i.e. the identity operator) and <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is a
-<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>.  Then, <a class="reference internal" href="#equation-eq-x-minimization">(1)</a> has a single solution provided by
+<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>.  Then, <a class="reference internal" href="#equation-eq-x-minimization">(1)</a> has a single solution provided by
 <span class="math notranslate nohighlight">\(\operatorname*{prox}_{\tau \mathcal{F}}(\mathbf{a})\)</span>.  This yields the <em>classical ADMM algorithm</em>
 described in Section 5.3 of <a class="reference internal" href="../references.html#psa" id="id57"><span>[PSA]</span></a> (i.e. without the postcomposition trick).</p></li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is a <a class="reference internal" href="abc/operator.html#pyxu.abc.QuadraticFunc" title="pyxu.abc.QuadraticFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">QuadraticFunc</span></code></a>, i.e.  <span class="math notranslate nohighlight">\(\mathcal{F}(\mathbf{x})=\frac{1}{2}
+<li><p><span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is a <a class="reference internal" href="abc.html#pyxu.abc.QuadraticFunc" title="pyxu.abc.QuadraticFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">QuadraticFunc</span></code></a>, i.e.  <span class="math notranslate nohighlight">\(\mathcal{F}(\mathbf{x})=\frac{1}{2}
 \langle\mathbf{x}, \mathbf{Q}\mathbf{x}\rangle + \mathbf{c}^T\mathbf{x} + t\)</span>.  Then the unique solution to
 <a class="reference internal" href="#equation-eq-x-minimization">(1)</a> is obtained by solving a linear system of the form:</p>
 <div class="math notranslate nohighlight" id="equation-eq-linear-system">
@@ -1683,11 +1672,11 @@ <h2>Remarks<a class="headerlink" href="#id54" title="Link to this heading">#</a>
 repeated application of <span class="math notranslate nohighlight">\(\mathbf{Q}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{K}^{*}\mathbf{K}\)</span>.  This sub-iterative scheme may
 be computationally intensive if these operators do not admit fast matrix-free implementations.</p>
 </li>
-<li><p><span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is a <a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>.  Then, <a class="reference internal" href="#equation-eq-x-minimization">(1)</a> is solved via a
+<li><p><span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is a <a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>.  Then, <a class="reference internal" href="#equation-eq-x-minimization">(1)</a> is solved via a
 sub-iterative <a class="reference internal" href="#pyxu.opt.solver.NLCG" title="pyxu.opt.solver.NLCG"><code class="xref py py-class docutils literal notranslate"><span class="pre">NLCG</span></code></a> algorithm involving repeated evaluation of
 <span class="math notranslate nohighlight">\(\nabla\mathcal{F}\)</span> and <span class="math notranslate nohighlight">\(\mathbf{K}^{*}\mathbf{K}\)</span>.  This sub-iterative scheme may be costly if
 these operators cannot be evaluated with fast algorithms.  In this scenario, the use of multiple initial points
-in <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> is not supported.</p></li>
+in <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> is not supported.</p></li>
 </ul>
 <p>The user may also provide a <em>custom</em> callable solver <span class="math notranslate nohighlight">\(s: \mathbb{R}^M \times \mathbb{R} \to \mathbb{R}^N\)</span>,
 taking as input <span class="math notranslate nohighlight">\((\mathbf{a}, \tau)\)</span> and solving <a class="reference internal" href="#equation-eq-x-minimization">(1)</a>, i.e. <span class="math notranslate nohighlight">\(s(\mathbf{a},
@@ -1702,13 +1691,13 @@ <h2>Remarks<a class="headerlink" href="#id54" title="Link to this heading">#</a>
 <section id="id58">
 <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__init__()</span></code>)<a class="headerlink" href="#id58" title="Link to this heading">#</a></h2>
 <ul>
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.DiffFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">DiffFunc</span></code></a>, <a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Differentiable or proximable function <span class="math notranslate nohighlight">\(\mathcal{F}\)</span>.</p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.ProxFunc"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProxFunc</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Proximable function <span class="math notranslate nohighlight">\(\mathcal{H}\)</span>.</p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.LinOp" title="pyxu.abc.LinOp"><code class="xref py py-class docutils literal notranslate"><span class="pre">LinOp</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
 –
 Linear operator <span class="math notranslate nohighlight">\(\mathbf{K}\)</span>.</p></li>
 <li><p><strong>solver</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Callable</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.11)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">None</span></code></a>)
@@ -1724,7 +1713,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">__i
 </li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.__init__" title="pyxu.abc.Solver.__init__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.__init__()</span></code></a>.</p></li>
 </ul>
 </section>
 <section id="id59">
@@ -1755,7 +1744,7 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 </li>
 <li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>)
 –
-Other keyword parameters passed on to <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
+Other keyword parameters passed on to <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pyxu.abc.Solver.fit()</span></code></a>.</p></li>
 </ul>
 <div class="admonition warning">
 <p class="admonition-title">Warning</p>
@@ -1845,9 +1834,9 @@ <h2>Parameters (<code class="docutils literal notranslate"><span class="pre">fit
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>f</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.Func" title="pyxu.abc.operator.Func"><em>Func</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>h</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
-<li><p><strong>K</strong> (<a class="reference internal" href="abc/operator.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference internal" href="abc.html#pyxu.abc.Func" title="pyxu.abc.operator.Func"><em>Func</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>h</strong> (<a class="reference internal" href="abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><em>ProxFunc</em></a><em> | </em><em>None</em>) – </p></li>
+<li><p><strong>K</strong> (<a class="reference internal" href="abc.html#pyxu.abc.DiffMap" title="pyxu.abc.operator.DiffMap"><em>DiffMap</em></a><em> | </em><em>None</em>) – </p></li>
 <li><p><strong>solver</strong> (<a class="reference external" href="https://docs.python.org/3/library/typing.html#typing.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.11)"><em>float</em></a><em>]</em><em>, </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
 <li><p><strong>solver_kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><em>dict</em></a><em> | </em><em>None</em>) – </p></li>
 </ul>
diff --git a/api/opt.stop.html b/api/opt.stop.html
index 87280592..a535ac8b 100644
--- a/api/opt.stop.html
+++ b/api/opt.stop.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -406,16 +406,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="operator/blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
@@ -427,13 +422,7 @@
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">pyxu.opt.stop</a></li>
 <li class="toctree-l1"><a class="reference internal" href="runtime.html">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="util/array_module.html">pyxu.util.array_module</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../references.html"><strong>References</strong></a></li>
 </ul>
@@ -498,7 +487,7 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.stop.MaxIter">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MaxIter</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#MaxIter"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.MaxIter" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
 <p>Stop iterative solver after a fixed number of iterations.</p>
 <div class="admonition note">
 <p class="admonition-title">Note</p>
@@ -530,13 +519,13 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.stop.ManualStop">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ManualStop</span></span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#ManualStop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.ManualStop" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
 <p>Continue-forever criterion.</p>
-<p>This class is useful when calling <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> with mode=MANUAL/ASYNC to defer the stopping
+<p>This class is useful when calling <a class="reference internal" href="abc.html#pyxu.abc.Solver.fit" title="pyxu.abc.Solver.fit"><code class="xref py py-meth docutils literal notranslate"><span class="pre">fit()</span></code></a> with mode=MANUAL/ASYNC to defer the stopping
 decision to an explicit call by the user, i.e.:</p>
 <ul class="simple">
 <li><p>mode=MANUAL: user must stop calling <code class="docutils literal notranslate"><span class="pre">next(solver.steps())</span></code>;</p></li>
-<li><p>mode=ASYNC: user must call <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver.stop" title="pyxu.abc.Solver.stop"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stop()</span></code></a>.</p></li>
+<li><p>mode=ASYNC: user must call <a class="reference internal" href="abc.html#pyxu.abc.Solver.stop" title="pyxu.abc.Solver.stop"><code class="xref py py-meth docutils literal notranslate"><span class="pre">stop()</span></code></a>.</p></li>
 </ul>
 <dl class="py method">
 <dt class="sig sig-object py" id="pyxu.opt.stop.ManualStop.__init__">
@@ -548,7 +537,7 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.stop.MaxDuration">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MaxDuration</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#MaxDuration"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.MaxDuration" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
 <p>Stop iterative solver after a specified duration has elapsed.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -570,7 +559,7 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.stop.MaxCarbon">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">MaxCarbon</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">co2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#MaxCarbon"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.MaxCarbon" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
 <p>Stop iterative solver after a threshold amount of carbon dioxide (CO2) was produced by computing resources used to
 execute the optimization.</p>
 <div class="admonition note">
@@ -582,7 +571,7 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 </div>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>co2</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p>
+<dd class="field-odd"><p><strong>co2</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p>
 </dd>
 </dl>
 <dl class="py method">
@@ -600,9 +589,9 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.stop.Memorize">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Memorize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#Memorize"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.Memorize" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
-<p>Memorize a variable.  (Special <a class="reference internal" href="abc/solver.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a> mostly useful for tracking objective
-functions in <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a>.)</p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
+<p>Memorize a variable.  (Special <a class="reference internal" href="abc.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a> mostly useful for tracking objective
+functions in <a class="reference internal" href="abc.html#pyxu.abc.Solver" title="pyxu.abc.Solver"><code class="xref py py-class docutils literal notranslate"><span class="pre">Solver</span></code></a>.)</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><p><strong>var</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p>
@@ -613,7 +602,7 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#Memorize.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.Memorize.__init__" title="Link to this definition">#</a></dt>
 <dd><dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>var</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variable in <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">pyxu.abc.Solver._mstate</span></code></a> to query.  Must be a scalar or NDArray (1D).</p>
+<dd class="field-odd"><p><strong>var</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variable in <a class="reference internal" href="abc.html#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">pyxu.abc.Solver._mstate</span></code></a> to query.  Must be a scalar or NDArray (1D).</p>
 </dd>
 </dl>
 </dd></dl>
@@ -623,15 +612,15 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.stop.AbsError">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">AbsError</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">eps</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'x'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">satisfy_all</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#AbsError"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.AbsError" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
 <p>Stop iterative solver after absolute norm of a variable (or function thereof) reaches threshold.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>eps</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
+<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 <li><p><strong>var</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>]</em><em>, </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em><em>, </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
-<li><p><strong>norm</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em>]</em><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em><em>, </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
+<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 <li><p><strong>satisfy_all</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
 </ul>
 </dd>
@@ -643,12 +632,12 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>eps</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive threshold.</p></li>
-<li><p><strong>var</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variable in <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">pyxu.abc.Solver._mstate</span></code></a> to query.</p></li>
+<li><p><strong>var</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variable in <a class="reference internal" href="abc.html#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">pyxu.abc.Solver._mstate</span></code></a> to query.</p></li>
 <li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Callable</span></code></a>) – <p>Optional function to pre-apply to <code class="docutils literal notranslate"><span class="pre">_mstate[var]</span></code> before applying the norm.  Defaults to the identity
 function. The callable should either:</p>
 <ul>
 <li><p>accept a scalar input -&gt; output a scalar, or</p></li>
-<li><p>accept an NDArray input -&gt; output an NDArray, i.e same semantics as <a class="reference internal" href="abc/operator.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>.</p></li>
+<li><p>accept an NDArray input -&gt; output an NDArray, i.e same semantics as <a class="reference internal" href="abc.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>.</p></li>
 </ul>
 </p></li>
 <li><p><strong>norm</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Ln norm to use &gt;= 0. (Default: L2.)</p></li>
@@ -664,15 +653,15 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <dl class="py class">
 <dt class="sig sig-object py" id="pyxu.opt.stop.RelError">
 <em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">RelError</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">eps</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'x'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">satisfy_all</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/opt/stop.html#RelError"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.opt.stop.RelError" title="Link to this definition">#</a></dt>
-<dd><p>Bases: <a class="reference internal" href="abc/solver.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
+<dd><p>Bases: <a class="reference internal" href="abc.html#pyxu.abc.StoppingCriterion" title="pyxu.abc.solver.StoppingCriterion"><code class="xref py py-class docutils literal notranslate"><span class="pre">StoppingCriterion</span></code></a></p>
 <p>Stop iterative solver after relative norm change of a variable (or function thereof) reaches threshold.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>eps</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
+<li><p><strong>eps</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 <li><p><strong>var</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection" title="(in Python v3.11)"><em>Collection</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><em>str</em></a><em>]</em>) – </p></li>
-<li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>]</em><em>, </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em><em>, </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
-<li><p><strong>norm</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a>) – </p></li>
+<li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em>]</em><em>, </em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a><em>] </em><em>| </em><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a><em>[</em><em>[</em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em><em>, </em><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><em>NDArray</em></a><em>]</em>) – </p></li>
+<li><p><strong>norm</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a>) – </p></li>
 <li><p><strong>satisfy_all</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
 </ul>
 </dd>
@@ -684,12 +673,12 @@ <h1>pyxu.opt.stop<a class="headerlink" href="#pyxu-opt-stop" title="Link to this
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>eps</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Positive threshold.</p></li>
-<li><p><strong>var</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variable in <a class="reference internal" href="abc/solver.html#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">pyxu.abc.Solver._mstate</span></code></a> to query.</p></li>
+<li><p><strong>var</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – Variable in <a class="reference internal" href="abc.html#pyxu.abc.Solver._mstate" title="pyxu.abc.Solver._mstate"><code class="xref py py-attr docutils literal notranslate"><span class="pre">pyxu.abc.Solver._mstate</span></code></a> to query.</p></li>
 <li><p><strong>f</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Callable</span></code></a>) – <p>Optional function to pre-apply to <code class="docutils literal notranslate"><span class="pre">_mstate[var]</span></code> before applying the norm.  Defaults to the identity
 function. The callable should either:</p>
 <ul>
 <li><p>accept a scalar input -&gt; output a scalar, or</p></li>
-<li><p>accept an NDArray input -&gt; output an NDArray, i.e same semantics as <a class="reference internal" href="abc/operator.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>.</p></li>
+<li><p>accept an NDArray input -&gt; output an NDArray, i.e same semantics as <a class="reference internal" href="abc.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>.</p></li>
 </ul>
 </p></li>
 <li><p><strong>norm</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>, <a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Ln norm to use &gt;= 0. (Default: L2.)</p></li>
diff --git a/api/runtime.html b/api/runtime.html
index 293b606e..6e6f72fb 100644
--- a/api/runtime.html
+++ b/api/runtime.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -406,16 +406,11 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1 has-children"><a class="reference internal" href="abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/operator.html">pyxu.abc.operator</a></li>
-<li class="toctree-l2"><a class="reference internal" href="abc/solver.html">pyxu.abc.solver</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="abc.html">pyxu.abc</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.deps.html">pyxu.info.deps</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.ptype.html">pyxu.info.ptype</a></li>
 <li class="toctree-l1"><a class="reference internal" href="info.warning.html">pyxu.info.warning</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l1 has-children"><a class="reference internal" href="operator/index.html">pyxu.operator</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="operator/blocks.html">pyxu.operator.blocks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/func.html">pyxu.operator.func</a></li>
 <li class="toctree-l2"><a class="reference internal" href="operator/linop.html">pyxu.operator.linop</a></li>
@@ -427,13 +422,7 @@
 <li class="toctree-l1"><a class="reference internal" href="opt.stop.html">pyxu.opt.stop</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">pyxu.runtime</a></li>
 <li class="toctree-l1"><a class="reference internal" href="math.html">pyxu.math</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="util/index.html">pyxu.util</a><input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-3"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="util/array_module.html">pyxu.util.array_module</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/complex.html">pyxu.util.complex</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/misc.html">pyxu.util.misc</a></li>
-<li class="toctree-l2"><a class="reference internal" href="util/operator.html">pyxu.util.operator</a></li>
-</ul>
-</li>
+<li class="toctree-l1"><a class="reference internal" href="util.html">pyxu.util</a></li>
 <li class="toctree-l1"><a class="reference internal" href="experimental.sampler.html">pyxu.experimental.sampler</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../references.html"><strong>References</strong></a></li>
 </ul>
@@ -584,7 +573,7 @@
 <p>Returns the difference between 1 and the next smallest representable float larger than 1.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="numbers.Real"><em>Real</em></a></p>
+<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Real" title="(in Python v3.11)"><em>Real</em></a></p>
 </dd>
 </dl>
 </dd></dl>
diff --git a/api/util.html b/api/util.html
index 14d06bd3..bb9af955 100644
--- a/api/util.html
+++ b/api/util.html
@@ -18,7 +18,7 @@
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" rel="preload" type="font/woff2"/>
-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
 <link href="../_static/sphinx-codeautolink.css?v=125d5c1c" rel="stylesheet" type="text/css"/>
 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -28,11 +28,11 @@
 <link href="../_static/sg_gallery-dataframe.css?v=2082cf3c" rel="stylesheet" type="text/css"/>
 <link href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" rel="stylesheet" type="text/css"/>
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-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
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@@ -139,7 +139,7 @@
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-<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="mailto: matthieu.simeoni@gmail.com" rel="noopener" target="_blank" title="Contact"><span><i class="fa-brands fa-telegram"></i></span>
+<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="mailto: contact@pyxu.org" rel="noopener" target="_blank" title="Contact"><span><i class="fa-brands fa-telegram"></i></span>
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@@ -212,7 +212,7 @@
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@@ -270,263 +276,345 @@
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 <article class="bd-article" role="main">
-<section id="module-pyxu.util">
-<span id="pyxu-util"></span><h1>pyxu.util<a class="headerlink" href="#module-pyxu.util" title="Link to this heading">#</a></h1>
+<section id="pyxu-util">
+<h1>pyxu.util<a class="headerlink" href="#pyxu-util" title="Link to this heading">#</a></h1>
+<nav class="contents local" id="table-of-contents">
+<p class="topic-title">Table of Contents</p>
+<ul class="simple">
+<li><p><a class="reference internal" href="#pyxu-util-array-module" id="id1">pyxu.util.array_module</a></p></li>
+<li><p><a class="reference internal" href="#pyxu-util-complex" id="id2">pyxu.util.complex</a></p></li>
+<li><p><a class="reference internal" href="#pyxu-util-misc" id="id3">pyxu.util.misc</a></p></li>
+<li><p><a class="reference internal" href="#pyxu-util-operator" id="id4">pyxu.util.operator</a></p></li>
+</ul>
+</nav>
+<section id="pyxu-util-array-module">
+<h2><a class="toc-backref" href="#id1" role="doc-backlink">pyxu.util.array_module</a><a class="headerlink" href="#pyxu-util-array-module" title="Link to this heading">#</a></h2>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.misc.peaks">
-<span class="sig-name descname"><span class="pre">peaks</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#peaks"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.misc.peaks" title="Link to this definition">#</a></dt>
-<dd><p>Matlab 2D peaks function.</p>
-<p>Peaks is a function of two variables, obtained by translating and scaling Gaussian distributions.  (See <a class="reference external" href="https://www.mathworks.com/help/matlab/ref/peaks.html">Matlab’s
-peaks function</a>.)</p>
-<p>This function is useful for testing purposes.</p>
+<dt class="sig sig-object py" id="pyxu.util.get_array_module">
+<span class="sig-name descname"><span class="pre">get_array_module</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fallback</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#get_array_module"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.get_array_module" title="Link to this definition">#</a></dt>
+<dd><p>Get the array namespace corresponding to a given object.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – X coordinates.</p></li>
-<li><p><strong>y</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – Y coordinates.</p></li>
+<li><p><strong>x</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>) – Any object compatible with the interface of NumPy arrays.</p></li>
+<li><p><strong>fallback</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArrayModule</span></code></a>) – Fallback module if <code class="code docutils literal notranslate"><span class="pre">x</span></code> is not a NumPy-like array.  Default behaviour: raise error if fallback used.</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>z</strong> – Values of the 2D function <code class="docutils literal notranslate"><span class="pre">peaks</span></code> at the points specified by the entries of <code class="code docutils literal notranslate"><span class="pre">x</span></code> and <code class="code docutils literal notranslate"><span class="pre">y</span></code>.</p>
+<dd class="field-even"><p><strong>namespace</strong> – The namespace to use to manipulate <code class="code docutils literal notranslate"><span class="pre">x</span></code>, or <code class="code docutils literal notranslate"><span class="pre">fallback</span></code> if provided.</p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArrayModule</span></code></a></p>
 </dd>
 </dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">z</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/7a96e89967447e1042b7a00e8e9f004a/util-1.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/6c763f0d1d1bca3dea56eef770528674/util-1.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/09a11b0e08c73736be787c749bfba607/util-1.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/5be70851f96b004b61b84e14faba6d02/util-1.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/util-1.png" class="plot-directive" src="../_images/util-1.png"/>
-</figure>
 </dd></dl>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.misc.star_like_sample">
-<span class="sig-name descname"><span class="pre">star_like_sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">N</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">w</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">po</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">NDArrayInfo.NUMPY</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#star_like_sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.misc.star_like_sample" title="Link to this definition">#</a></dt>
-<dd><p>Star-like test image.</p>
-<p>Generates a (N, N) square image of a star-like object normalized between 0 and 1.  Based on <a class="reference external" href="https://github.com/Biomedical-Imaging-Group/GlobalBioIm/blob/master/Util/StarLikeSample.m">GlobalBioIm’s
-StarLikeSample function</a>.  This function is
-useful for testing purposes as it contains high-frequency information.</p>
+<dt class="sig sig-object py" id="pyxu.util.redirect">
+<span class="sig-name descname"><span class="pre">redirect</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">i</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#redirect"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.redirect" title="Link to this definition">#</a></dt>
+<dd><p>Change codepath for supplied array backends.</p>
+<p>Some functions/methods cannot be written in module-agnostic fashion. The action of this decorator is summarized
+below:</p>
+<ul class="simple">
+<li><p>Analyze an array-valued parameter (<code class="code docutils literal notranslate"><span class="pre">x</span></code>) of the wrapped function/method (<code class="code docutils literal notranslate"><span class="pre">f</span></code>).</p></li>
+<li><p>If <code class="code docutils literal notranslate"><span class="pre">x</span></code> lies in one of the supplied array namespaces: re-route execution to the specified function.</p></li>
+<li><p>If <code class="code docutils literal notranslate"><span class="pre">x</span></code> lies in none of the supplied array namespaces: execute <code class="code docutils literal notranslate"><span class="pre">f</span></code>.</p></li>
+</ul>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>N</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Size of the image (must be an even number).</p></li>
-<li><p><strong>w</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – The number of branches of the sample will be 4*w.</p></li>
-<li><p><strong>s</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Slope of the sigmoid function <span class="math notranslate nohighlight">\(\frac1{1+\exp[s (x-x_{0})]}\)</span> attenuating the boundaries.</p></li>
-<li><p><strong>po</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Power-raising factor for the final image (to have smoother edges).</p></li>
-<li><p><strong>x0</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Radial shift of the sigmoid function <span class="math notranslate nohighlight">\(\frac1{1+\exp[s (x-x_{0})]}\)</span>.</p></li>
-<li><p><strong>ndi</strong> (<a class="reference internal" href="info.deps.html#pyxu.info.deps.NDArrayInfo" title="pyxu.info.deps.NDArrayInfo"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayInfo</span></code></a>) – Desired array module for the output.</p></li>
+<li><p><strong>i</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – name of the array-like variable in <code class="code docutils literal notranslate"><span class="pre">f</span></code> to base dispatch on.</p></li>
+<li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – <ul>
+<li><p>key[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>]: array backend short-name as defined in <a class="reference internal" href="info.deps.html#pyxu.info.deps.NDArrayInfo" title="pyxu.info.deps.NDArrayInfo"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayInfo</span></code></a>.</p></li>
+<li><p>value[<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">collections.abc.Callable</span></code></a>]: function/method to dispatch to.</p></li>
+</ul>
+</p></li>
 </ul>
 </dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>image</strong> – (N, N) image of star-like sample.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a></p>
 </dd>
 </dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.star_like_sample" title="pyxu.util.misc.star_like_sample"><span class="n">star_like_sample</span></a>
-
-<span class="n">star</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.star_like_sample" title="pyxu.util.misc.star_like_sample"><span class="n">star_like_sample</span></a><span class="p">(</span><span class="n">N</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mi">8</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">po</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">star</span><span class="p">)</span>
-</pre></div>
-</div>
-<p>(<a class="reference download internal" download="" href="../_downloads/0fc82206eb78ed17440026ce6f7cb455/util-2.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/92b871487a1a9b8139c3540b67b17b89/util-2.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/97ed94caa646cf7937bbaa1dba9f3fc9/util-2.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/5420c90dcdf9b097dbed8ebf47bc7a03/util-2.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
-<figure class="align-default">
-<img alt="../_images/util-2.png" class="plot-directive" src="../_images/util-2.png"/>
-</figure>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.operator._dask_zip">
-<span class="sig-name descname"><span class="pre">_dask_zip</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">func</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out_dtype</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/operator.html#_dask_zip"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.operator._dask_zip" title="Link to this definition">#</a></dt>
-<dd><p>Map functions in parallel via Dask.</p>
-<p>Computes the equivalent of <code class="docutils literal notranslate"><span class="pre">out</span> <span class="pre">=</span> <span class="pre">[f(x)</span> <span class="pre">for</span> <span class="pre">(f,</span> <span class="pre">x)</span> <span class="pre">in</span> <span class="pre">zip(func,</span> <span class="pre">data)]</span></code>, with the following semantics:</p>
+<p class="rubric">Notes</p>
+<p>Auto-dispatch via <a class="reference internal" href="#pyxu.util.redirect" title="pyxu.util.redirect"><code class="xref py py-func docutils literal notranslate"><span class="pre">redirect()</span></code></a> assumes the dispatcher/dispatchee have the same parameterization, i.e.:</p>
 <ul class="simple">
-<li><p>If <code class="code docutils literal notranslate"><span class="pre">data</span></code> contains only NUMPY/CUPY arrays, then <code class="docutils literal notranslate"><span class="pre">out</span></code> is computed as above.</p></li>
-<li><p>If <code class="code docutils literal notranslate"><span class="pre">data</span></code> contains only DASK arrays, then entries of <code class="docutils literal notranslate"><span class="pre">out</span></code> are computed:</p>
-<ul>
-<li><p>if <code class="code docutils literal notranslate"><span class="pre">parallel</span></code> enabled  -&gt; dask-delay each <code class="code docutils literal notranslate"><span class="pre">func</span></code>, then evaluate in parallel.</p></li>
-<li><p>if <code class="code docutils literal notranslate"><span class="pre">parallel</span></code> disabled -&gt; dask-delay each <code class="code docutils literal notranslate"><span class="pre">func</span></code>, then evaluate in sequence.
-(This is useful if <code class="code docutils literal notranslate"><span class="pre">func</span></code> s share a common resource, thus not thread-safe.)</p></li>
-</ul>
-</li>
+<li><p>if <code class="code docutils literal notranslate"><span class="pre">f</span></code> is a function -&gt; dispatch possible to another callable with identical signature (i.e., function or
+staticmethod)</p></li>
+<li><p>if <code class="code docutils literal notranslate"><span class="pre">f</span></code> is a staticmethod -&gt; dispatch possible to another callable with identical signature (i.e., function or
+staticmethod)</p></li>
+<li><p>if <code class="code docutils literal notranslate"><span class="pre">f</span></code> is an instance-method -&gt; dispatch to another instance-method of the class with identical signature.</p></li>
 </ul>
-<p>For Dask-array inputs, this amounts to creating a task graph with virtual dependencies between successive <code class="code docutils literal notranslate"><span class="pre">func</span></code>
-calls. In other words, the task graph looks like:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">_dask_zip</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">parallel</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">out</span>
+<p class="rubric">Example</p>
+<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span> <span class="k">return</span> <span class="s2">"f"</span>
 
-              <span class="o">+----+</span>              <span class="o">+----+</span>
-    <span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">--&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">blk</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-+--&gt;|</span><span class="nb">list</span><span class="o">|--&gt;</span><span class="n">out</span>
-        <span class="o">.</span>     <span class="o">+----+</span>          <span class="o">|</span>   <span class="o">+----+</span>
-        <span class="o">.</span>                     <span class="o">|</span>
-        <span class="o">.</span>     <span class="o">+----+</span>          <span class="o">|</span>
-    <span class="n">data</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="o">--&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">blk</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="o">-+</span>
-              <span class="o">+----+</span>
+<span class="nd">@redirect</span><span class="p">(</span><span class="s1">'x'</span><span class="p">,</span> <span class="n">NUMPY</span><span class="o">=</span><span class="n">f</span><span class="p">)</span>    <span class="c1"># if 'x' is of type NDArrayInfo.NUMPY, i.e. has</span>
+<span class="k">def</span> <span class="nf">g</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span> <span class="k">return</span> <span class="s2">"g"</span>    <span class="c1"># short-name 'NUMPY' -&gt; reroute execution to `f`</span>
 
-<span class="o">==========================================================================================================</span>
-<span class="n">_dask_zip</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">parallel</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">out</span>
-                                                                                       <span class="o">+----+</span>
-                        <span class="o">+-------------------+----------------+--------------------+----+</span><span class="nb">list</span><span class="o">|--&gt;</span><span class="n">out</span>
-                        <span class="o">|</span>                   <span class="o">|</span>                <span class="o">|</span>                    <span class="o">|</span>    <span class="o">+----+</span>
-                        <span class="o">|</span>                   <span class="o">|</span>                <span class="o">|</span>                    <span class="o">|</span>
-              <span class="o">+----+</span>    <span class="o">|</span>        <span class="o">+----+</span>     <span class="o">|</span>      <span class="o">+---+</span>     <span class="o">|</span>         <span class="o">+----+</span>     <span class="o">|</span>
-    <span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">--&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">out</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-+-&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">out</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">--&gt;|...|--&gt;</span><span class="n">out</span><span class="p">[</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-+-&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">out</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
-              <span class="o">+----+</span>          <span class="o">|</span>  <span class="o">+----+</span>            <span class="o">+---+</span>            <span class="o">|</span>  <span class="o">+----+</span>
-                              <span class="o">|</span>                                     <span class="o">|</span>
-    <span class="n">data</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-------------------+</span>                                     <span class="o">|</span>
-        <span class="o">.</span>                                                           <span class="o">|</span>
-        <span class="o">.</span>                                                           <span class="o">|</span>
-        <span class="o">.</span>                                                           <span class="o">|</span>
-    <span class="n">data</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="o">---------------------------------------------------------+</span>
+<span class="n">x1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<span class="n">x2</span> <span class="o">=</span> <span class="n">da</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">1</span>
+<span class="n">g</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">y</span><span class="p">),</span> <span class="n">g</span><span class="p">(</span><span class="n">x2</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>  <span class="c1"># 'f', 'g'</span>
 </pre></div>
 </div>
+</dd></dl>
+<dl class="py function">
+<dt class="sig sig-object py" id="pyxu.util.compute">
+<span class="sig-name descname"><span class="pre">compute</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'compute'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#compute"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.compute" title="Link to this definition">#</a></dt>
+<dd><p>Force computation of Dask collections.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>func</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – <p>Functions to apply to each element of <code class="code docutils literal notranslate"><span class="pre">data</span></code>.</p>
-<p>Function signatures are <code class="docutils literal notranslate"><span class="pre">Callable[[NDArray],</span> <span class="pre">NDArray]</span></code>.</p>
-</p></li>
-<li><p><strong>data</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – (N_data,) arrays to act on.</p></li>
-<li><p><strong>out_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – <p>Shapes of <code class="docutils literal notranslate"><span class="pre">func[i](data[i])</span></code>.</p>
-<p>This parameter is only used if inputs are DASK arrays.  Its goal is to transform
-<a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> objects back to array form.</p>
-</p></li>
-<li><p><strong>out_dtype</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – <p>Dtypes of <code class="docutils literal notranslate"><span class="pre">func[i](data[i])</span></code>.</p>
-<p>This parameter is only used if inputs are DASK arrays.  Its goal is to transform
-<a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> objects back to array form.</p>
-</p></li>
-<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
+<li><p><strong>*args</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – Any number of objects.  If it is a dask object, it is evaluated and the result is returned.  Non-dask arguments
+are passed through unchanged.  Python collections are traversed to find/evaluate dask objects within.  (Use
+<code class="code docutils literal notranslate"><span class="pre">traverse</span></code> =False to disable this behavior.)</p></li>
+<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>) – Dask evaluation strategy: compute or persist.</p></li>
+<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Extra keyword parameters forwarded to <a class="reference external" href="https://docs.dask.org/en/stable/api.html#dask.compute" title="(in Dask)"><code class="xref py py-func docutils literal notranslate"><span class="pre">dask.compute()</span></code></a> or <a class="reference external" href="https://docs.dask.org/en/stable/api.html#dask.persist" title="(in Dask)"><code class="xref py py-func docutils literal notranslate"><span class="pre">dask.persist()</span></code></a>.</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><p><strong>out</strong> – (N_data,) objects acted upon.</p>
-<p>Outputs have the same backend/dtype as inputs, or as specified by <code class="code docutils literal notranslate"><span class="pre">out_[shape,dtype]</span></code>.</p>
-</p>
+<dd class="field-even"><p><strong>*cargs</strong> – Evaluated objects. Non-dask arguments are passed through unchanged.</p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a></p>
+<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a></p>
 </dd>
 </dl>
 </dd></dl>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.operator._array_ize">
-<span class="sig-name descname"><span class="pre">_array_ize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/operator.html#_array_ize"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.operator._array_ize" title="Link to this definition">#</a></dt>
-<dd><p>Transform a Dask-delayed object into its Dask-array counterpart.</p>
-<p>This function is a no-op if <code class="code docutils literal notranslate"><span class="pre">data</span></code> is not a <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> object.</p>
+<dt class="sig sig-object py" id="pyxu.util.to_NUMPY">
+<span class="sig-name descname"><span class="pre">to_NUMPY</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#to_NUMPY"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.to_NUMPY" title="Link to this definition">#</a></dt>
+<dd><p>Convert an array from a specific backend to NUMPY.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – Array to be converted.</p>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>y</strong> – Array with NumPy backend.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+</dd>
+</dl>
+<p class="rubric">Notes</p>
+<p>This function is a no-op if the array is already a NumPy array.</p>
+</dd></dl>
+</section>
+<section id="pyxu-util-complex">
+<h2><a class="toc-backref" href="#id2" role="doc-backlink">pyxu.util.complex</a><a class="headerlink" href="#pyxu-util-complex" title="Link to this heading">#</a></h2>
+<dl class="py function">
+<dt class="sig sig-object py" id="pyxu.util.view_as_complex_mat">
+<span class="sig-name descname"><span class="pre">view_as_complex_mat</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rmat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real_input</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real_output</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/complex.html#view_as_complex_mat"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.view_as_complex_mat" title="Link to this definition">#</a></dt>
+<dd><p>View real-valued matrix as its complex-valued equivalent.  (Inverse of <a class="reference internal" href="#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a>.)</p>
+<p>Useful to transform real-valued matrix/vector products to their complex-valued counterparts.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>data</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a>) – Object to act upon.</p></li>
-<li><p><strong>shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – <p>Shape of <code class="code docutils literal notranslate"><span class="pre">data</span></code>.</p>
-<p>This parameter is only used if <code class="code docutils literal notranslate"><span class="pre">data</span></code> is a <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> object.  Its goal is to transform
-the former back to array form.</p>
-</p></li>
-<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – <p>Dtype of <code class="code docutils literal notranslate"><span class="pre">data</span></code>.</p>
-<p>This parameter is only used if <code class="code docutils literal notranslate"><span class="pre">data</span></code> is a <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> object.  Its goal is to transform
-the former back to array form.</p>
+<li><p><strong>rmat</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – <p>Real-valued matrix.  Accepted dimensions depend on the values of <code class="code docutils literal notranslate"><span class="pre">real_input</span></code> and <code class="code docutils literal notranslate"><span class="pre">real_output</span></code>:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">|</span> <span class="n">real_input</span> <span class="o">|</span> <span class="n">real_output</span> <span class="o">|</span> <span class="n">rmat</span><span class="o">.</span><span class="n">shape</span> <span class="o">|</span>
+<span class="o">|------------|-------------|------------|</span>
+<span class="o">|</span> <span class="kc">False</span>      <span class="o">|</span> <span class="kc">False</span>       <span class="o">|</span> <span class="p">(</span><span class="mi">2</span><span class="n">M</span><span class="p">,</span> <span class="mi">2</span><span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
+<span class="o">|</span> <span class="kc">False</span>      <span class="o">|</span> <span class="kc">True</span>        <span class="o">|</span> <span class="p">(</span> <span class="n">M</span><span class="p">,</span> <span class="mi">2</span><span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
+<span class="o">|</span> <span class="kc">True</span>       <span class="o">|</span> <span class="kc">False</span>       <span class="o">|</span> <span class="p">(</span><span class="mi">2</span><span class="n">M</span><span class="p">,</span>  <span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
+<span class="o">|</span> <span class="kc">True</span>       <span class="o">|</span> <span class="kc">True</span>        <span class="o">|</span> <span class="p">(</span> <span class="n">M</span><span class="p">,</span>  <span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
+</pre></div>
+</div>
 </p></li>
+<li><p><strong>real_input</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
+<li><p><strong>real_output</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>arr</strong> – Dask-backed NDArray if <code class="code docutils literal notranslate"><span class="pre">data</span></code> was a <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> object; no-op otherwise.</p>
+<dd class="field-even"><p><strong>cmat</strong> – (M, N) complex-valued matrix.</p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
 <dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
 </dd>
 </dl>
+<p class="rubric">Examples</p>
+<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <span class="n">view_as_real_mat</span><span class="p">,</span> <span class="n">view_as_complex_mat</span>
+
+<span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span> <span class="mf">0.</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="p">,</span>  <span class="mf">1.</span><span class="p">,</span> <span class="o">-</span><span class="mf">3.</span><span class="p">,</span>  <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">4.</span><span class="p">],</span>
+              <span class="p">[</span> <span class="mf">2.</span><span class="p">,</span>  <span class="mf">0.</span><span class="p">,</span>  <span class="mf">3.</span><span class="p">,</span>  <span class="mf">1.</span><span class="p">,</span>  <span class="mf">4.</span><span class="p">,</span>  <span class="mf">2.</span><span class="p">],</span>
+              <span class="p">[</span> <span class="mf">3.</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.</span><span class="p">,</span>  <span class="mf">4.</span><span class="p">,</span> <span class="o">-</span><span class="mf">6.</span><span class="p">,</span>  <span class="mf">5.</span><span class="p">,</span> <span class="o">-</span><span class="mf">7.</span><span class="p">],</span>
+              <span class="p">[</span> <span class="mf">5.</span><span class="p">,</span>  <span class="mf">3.</span><span class="p">,</span>  <span class="mf">6.</span><span class="p">,</span>  <span class="mf">4.</span><span class="p">,</span>  <span class="mf">7.</span><span class="p">,</span>  <span class="mf">5.</span><span class="p">]])</span>
+
+<span class="n">B</span> <span class="o">=</span> <span class="n">view_as_complex</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>  <span class="c1"># array([[0.+2.j, 1.+3.j, 2.+4.j],</span>
+                        <span class="c1">#        [3.+5.j, 4.+6.j, 5.+7.j]])</span>
+</pre></div>
+</div>
+<p class="rubric">Notes</p>
+<ul>
+<li><p>Complex-valued matrices are returned unchanged.</p></li>
+<li><p>Real-valued matrices are mapped into a complex-valued matrix <span class="math notranslate nohighlight">\({A}\in\mathbb{C}^{M\times N}\)</span> as follows:</p>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{2M\times 2N}\)</span>:  <span class="math notranslate nohighlight">\(A_{m,n} = \hat{A}_{2m-1,2n-1} + j \hat{A}_{2m,2n-1}\)</span>,</p></li>
+<li><p><span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{M\times 2N}\)</span>:  <span class="math notranslate nohighlight">\(A_{m,n} = \hat{A}_{m,2n-1} - j \hat{A}_{m,2n}\)</span>,</p></li>
+<li><p><span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{2M\times N}\)</span>:  <span class="math notranslate nohighlight">\(A_{m,n} = \hat{A}_{2m-1,n} + j \hat{A}_{2m,n}\)</span>,</p></li>
+<li><p><span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{M\times N}\)</span>:  <span class="math notranslate nohighlight">\(A_{m,n} = \hat{A}_{m,n} + 0j\)</span>,</p></li>
+</ul>
+<p>for <span class="math notranslate nohighlight">\(1\leq n \leq N\)</span>, <span class="math notranslate nohighlight">\(1\leq m\leq M\)</span>.</p>
+</li>
+</ul>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a></p>
+</div>
 </dd></dl>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.as_canonical_shape">
-<span class="sig-name descname"><span class="pre">as_canonical_shape</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#as_canonical_shape"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.as_canonical_shape" title="Link to this definition">#</a></dt>
-<dd><p>Transform a lone integer into a valid tuple-based shape specifier.</p>
+<dt class="sig sig-object py" id="pyxu.util.view_as_complex">
+<span class="sig-name descname"><span class="pre">view_as_complex</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/complex.html#view_as_complex"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.view_as_complex" title="Link to this definition">#</a></dt>
+<dd><p>View real-valued array as its complex-valued bijection.  (Inverse of <a class="reference internal" href="#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>x</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p>
+<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, 2N) real-valued array.</p>
 </dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a> | <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)">tuple</a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>, …]</p>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>y</strong> – (…, N) complex-valued array.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
 </dd>
 </dl>
+<p class="rubric">Examples</p>
+<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <span class="n">view_as_real</span><span class="p">,</span> <span class="n">view_as_complex</span>
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">6.0</span><span class="p">)</span>      <span class="c1"># array([0., 1., 2., 3., 4., 5.])</span>
+<span class="n">y</span> <span class="o">=</span> <span class="n">view_as_complex</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># array([0.+1.j, 2.+3.j, 4.+5.j])</span>
+<span class="n">view_as_real</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">==</span> <span class="n">x</span>    <span class="c1"># True</span>
+</pre></div>
+</div>
+<p class="rubric">Notes</p>
+<p>Complex-valued inputs are returned unchanged.  For real-valued inputs, this function acts on the last axis as:</p>
+<div class="math notranslate nohighlight">
+\[y_n = x_{2n-1}+j \, x_{2n}, \qquad 1\leq n\leq N.\]</div>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a></p>
+</div>
 </dd></dl>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.compute">
-<span class="sig-name descname"><span class="pre">compute</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'compute'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#compute"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.compute" title="Link to this definition">#</a></dt>
-<dd><p>Force computation of Dask collections.</p>
+<dt class="sig sig-object py" id="pyxu.util.view_as_real_mat">
+<span class="sig-name descname"><span class="pre">view_as_real_mat</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cmat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real_input</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real_output</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/complex.html#view_as_real_mat"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.view_as_real_mat" title="Link to this definition">#</a></dt>
+<dd><p>View complex-valued matrix as its real-valued equivalent.  (Inverse of <a class="reference internal" href="#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a>.)</p>
+<p>Useful to transform complex-valued matrix/vector products to their real-valued counterparts.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>*args</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – Any number of objects.  If it is a dask object, it is evaluated and the result is returned.  Non-dask arguments
-are passed through unchanged.  Python collections are traversed to find/evaluate dask objects within.  (Use
-<code class="code docutils literal notranslate"><span class="pre">traverse</span></code> =False to disable this behavior.)</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>) – Dask evaluation strategy: compute or persist.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Extra keyword parameters forwarded to <a class="reference external" href="https://docs.dask.org/en/stable/api.html#dask.compute" title="(in Dask)"><code class="xref py py-func docutils literal notranslate"><span class="pre">dask.compute()</span></code></a> or <a class="reference external" href="https://docs.dask.org/en/stable/api.html#dask.persist" title="(in Dask)"><code class="xref py py-func docutils literal notranslate"><span class="pre">dask.persist()</span></code></a>.</p></li>
+<li><p><strong>cmat</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (M, N) complex-valued matrix.</p></li>
+<li><p><strong>real_input</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
+<li><p><strong>real_output</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>*cargs</strong> – Evaluated objects. Non-dask arguments are passed through unchanged.</p>
+<dd class="field-even"><p><p><strong>rmat</strong> –</p>
+<p>The output shape depends on the values of <code class="code docutils literal notranslate"><span class="pre">real_input</span></code> and <code class="code docutils literal notranslate"><span class="pre">real_output</span></code>:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">|</span> <span class="n">real_input</span> <span class="o">|</span> <span class="n">real_output</span> <span class="o">|</span> <span class="n">rmat</span><span class="o">.</span><span class="n">shape</span> <span class="o">|</span>
+<span class="o">|------------|-------------|------------|</span>
+<span class="o">|</span> <span class="kc">False</span>      <span class="o">|</span> <span class="kc">False</span>       <span class="o">|</span> <span class="p">(</span><span class="mi">2</span><span class="n">M</span><span class="p">,</span> <span class="mi">2</span><span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
+<span class="o">|</span> <span class="kc">False</span>      <span class="o">|</span> <span class="kc">True</span>        <span class="o">|</span> <span class="p">(</span> <span class="n">M</span><span class="p">,</span> <span class="mi">2</span><span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
+<span class="o">|</span> <span class="kc">True</span>       <span class="o">|</span> <span class="kc">False</span>       <span class="o">|</span> <span class="p">(</span><span class="mi">2</span><span class="n">M</span><span class="p">,</span>  <span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
+<span class="o">|</span> <span class="kc">True</span>       <span class="o">|</span> <span class="kc">True</span>        <span class="o">|</span> <span class="p">(</span> <span class="n">M</span><span class="p">,</span>  <span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
+</pre></div>
+</div>
+</p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a></p>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
 </dd>
 </dl>
+<p class="rubric">Examples</p>
+<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <span class="n">view_as_real_mat</span><span class="p">,</span> <span class="n">view_as_complex_mat</span>
+
+<span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span>
+    <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[:</span><span class="mi">6</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">8</span><span class="p">],</span> <span class="c1"># array([[0.+2.j, 1.+3.j, 2.+4.j],</span>
+    <span class="n">newshape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span>             <span class="c1">#        [3.+5.j, 4.+6.j, 5.+7.j]])</span>
+<span class="p">)</span>
+<span class="n">B</span> <span class="o">=</span> <span class="n">view_as_real_mat</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>          <span class="c1"># array([[ 0., -2.,  1., -3.,  2., -4.],</span>
+                                 <span class="c1">#        [ 2.,  0.,  3.,  1.,  4.,  2.],</span>
+                                 <span class="c1">#        [ 3., -5.,  4., -6.,  5., -7.],</span>
+                                 <span class="c1">#        [ 5.,  3.,  6.,  4.,  7.,  5.]])</span>
+</pre></div>
+</div>
+<p class="rubric">Notes</p>
+<ul>
+<li><p>Real-valued matrices are returned unchanged.</p></li>
+<li><p>Complex-valued matrices <span class="math notranslate nohighlight">\(A\in\mathbb{C}^{M\times N}\)</span> are mapped into a real-valued matrix
+<span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{2M\times 2N}\)</span> defined, for <span class="math notranslate nohighlight">\(1\leq n \leq N\)</span>, <span class="math notranslate nohighlight">\(1\leq m\leq M\)</span> as</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\hat{A}_{2m-1,2n-1} = \mathcal{R}(A_{m,n}),
+&amp; \quad
+\hat{A}_{2m-1,2n} = -\mathcal{I}(A_{m,n}),\\
+\hat{A}_{2m,2n-1} = \mathcal{I}(A_{m,n}),
+&amp; \quad
+\hat{A}_{2m,2n}=\mathcal{R}(A_{m,n}).\end{split}\]</div>
+<p>If <code class="docutils literal notranslate"><span class="pre">real_[in|out]put=True</span></code>, then even columns/rows (or both) are furthermore dropped.  We have <code class="docutils literal notranslate"><span class="pre">view_as_real(A</span>
+<span class="pre">@</span> <span class="pre">x)</span> <span class="pre">=</span> <span class="pre">view_as_real_mat(A)</span> <span class="pre">@</span> <span class="pre">view_as_real(x)</span></code>.</p>
+</li>
+</ul>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a></p>
+</div>
 </dd></dl>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.copy_if_unsafe">
-<span class="sig-name descname"><span class="pre">copy_if_unsafe</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#copy_if_unsafe"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.copy_if_unsafe" title="Link to this definition">#</a></dt>
-<dd><p>Copy array if it is unsafe to do in-place updates on it.</p>
-<p>In-place updates are unsafe if:</p>
-<ul class="simple">
-<li><p>the array is read-only, OR</p></li>
-<li><p>the array is a view onto another array.</p></li>
-</ul>
+<dt class="sig sig-object py" id="pyxu.util.view_as_real">
+<span class="sig-name descname"><span class="pre">view_as_real</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/complex.html#view_as_real"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.view_as_real" title="Link to this definition">#</a></dt>
+<dd><p>View complex-valued array as its real-valued bijection.  (Inverse of <a class="reference internal" href="#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a>.)</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – </p>
+<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, N) complex-valued array.</p>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>y</strong></p>
+<dd class="field-even"><p><strong>y</strong> – (…, 2N) real-valued array.</p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
 <dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
 </dd>
 </dl>
+<p class="rubric">Examples</p>
+<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <span class="n">view_as_real</span><span class="p">,</span> <span class="n">view_as_complex</span>
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[:</span><span class="mi">3</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">5</span><span class="p">]</span>   <span class="c1"># array([0.+2.j, 1.+3.j, 2.+4.j])</span>
+<span class="n">y</span> <span class="o">=</span> <span class="n">view_as_real</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>               <span class="c1"># array([0., 2., 1., 3., 2., 4.])</span>
+<span class="n">view_as_complex</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">==</span> <span class="n">x</span>           <span class="c1"># True</span>
+</pre></div>
+</div>
+<p class="rubric">Notes</p>
+<p>Real-valued inputs are returned unchanged.  For complex-valued inputs, this function acts on the last axis as:</p>
+<div class="math notranslate nohighlight">
+\[y_{2n-1} = \mathcal{R}(x_n),
+\quad
+y_{2n} = \mathcal{I}(x_n),
+\quad 1\leq n\leq N,\]</div>
+<p>where <span class="math notranslate nohighlight">\(\mathcal{R}, \mathcal{I}\)</span> denote the real/imaginary parts respectively.</p>
+<div class="admonition seealso">
+<p class="admonition-title">See also</p>
+<p><a class="reference internal" href="#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a></p>
+</div>
 </dd></dl>
+</section>
+<section id="pyxu-util-misc">
+<h2><a class="toc-backref" href="#id3" role="doc-backlink">pyxu.util.misc</a><a class="headerlink" href="#pyxu-util-misc" title="Link to this heading">#</a></h2>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.get_array_module">
-<span class="sig-name descname"><span class="pre">get_array_module</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fallback</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#get_array_module"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.get_array_module" title="Link to this definition">#</a></dt>
-<dd><p>Get the array namespace corresponding to a given object.</p>
+<dt class="sig sig-object py" id="pyxu.util.copy_if_unsafe">
+<span class="sig-name descname"><span class="pre">copy_if_unsafe</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#copy_if_unsafe"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.copy_if_unsafe" title="Link to this definition">#</a></dt>
+<dd><p>Copy array if it is unsafe to do in-place updates on it.</p>
+<p>In-place updates are unsafe if:</p>
+<ul class="simple">
+<li><p>the array is read-only, OR</p></li>
+<li><p>the array is a view onto another array.</p></li>
+</ul>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>x</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>) – Any object compatible with the interface of NumPy arrays.</p></li>
-<li><p><strong>fallback</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArrayModule</span></code></a>) – Fallback module if <code class="code docutils literal notranslate"><span class="pre">x</span></code> is not a NumPy-like array.  Default behaviour: raise error if fallback used.</p></li>
-</ul>
+<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – </p>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>namespace</strong> – The namespace to use to manipulate <code class="code docutils literal notranslate"><span class="pre">x</span></code>, or <code class="code docutils literal notranslate"><span class="pre">fallback</span></code> if provided.</p>
+<dd class="field-even"><p><strong>y</strong></p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.ArrayModule" title="pyxu.info.ptype.ArrayModule"><code class="xref py py-class docutils literal notranslate"><span class="pre">ArrayModule</span></code></a></p>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
 </dd>
 </dl>
 </dd></dl>
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.import_module">
-<span class="sig-name descname"><span class="pre">import_module</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fail_on_error</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/inspect.html#import_module"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.import_module" title="Link to this definition">#</a></dt>
+<span class="sig-name descname"><span class="pre">import_module</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fail_on_error</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#import_module"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.import_module" title="Link to this definition">#</a></dt>
 <dd><p>Load a Python module dynamically.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -542,7 +630,7 @@
 </dd></dl>
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.infer_composition_shape">
-<span class="sig-name descname"><span class="pre">infer_composition_shape</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sh1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sh2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/operator.html#infer_composition_shape"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.infer_composition_shape" title="Link to this definition">#</a></dt>
+<span class="sig-name descname"><span class="pre">infer_composition_shape</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sh1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sh2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#infer_composition_shape"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.infer_composition_shape" title="Link to this definition">#</a></dt>
 <dd><p>Infer shape of arithmetic operation <span class="math notranslate nohighlight">\(A \circ B\)</span>.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -558,7 +646,7 @@
 </dd></dl>
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.infer_sum_shape">
-<span class="sig-name descname"><span class="pre">infer_sum_shape</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sh1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sh2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/operator.html#infer_sum_shape"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.infer_sum_shape" title="Link to this definition">#</a></dt>
+<span class="sig-name descname"><span class="pre">infer_sum_shape</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sh1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sh2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#infer_sum_shape"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.infer_sum_shape" title="Link to this definition">#</a></dt>
 <dd><p>Infer shape of arithmetic operation <span class="math notranslate nohighlight">\(A + B\)</span>.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -591,7 +679,7 @@
 </dd></dl>
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.parse_params">
-<span class="sig-name descname"><span class="pre">parse_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">func</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/inspect.html#parse_params"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.parse_params" title="Link to this definition">#</a></dt>
+<span class="sig-name descname"><span class="pre">parse_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">func</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#parse_params"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.parse_params" title="Link to this definition">#</a></dt>
 <dd><p>Get function parameterization.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Returns<span class="colon">:</span></dt>
@@ -604,7 +692,7 @@
 </dd></dl>
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.read_only">
-<span class="sig-name descname"><span class="pre">read_only</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#read_only"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.read_only" title="Link to this definition">#</a></dt>
+<span class="sig-name descname"><span class="pre">read_only</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#read_only"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.read_only" title="Link to this definition">#</a></dt>
 <dd><p>Make an array read-only.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
@@ -619,70 +707,98 @@
 </dl>
 </dd></dl>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.redirect">
-<span class="sig-name descname"><span class="pre">redirect</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">i</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#redirect"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.redirect" title="Link to this definition">#</a></dt>
-<dd><p>Change codepath for supplied array backends.</p>
-<p>Some functions/methods cannot be written in module-agnostic fashion. The action of this decorator is summarized
-below:</p>
-<ul class="simple">
-<li><p>Analyze an array-valued parameter (<code class="code docutils literal notranslate"><span class="pre">x</span></code>) of the wrapped function/method (<code class="code docutils literal notranslate"><span class="pre">f</span></code>).</p></li>
-<li><p>If <code class="code docutils literal notranslate"><span class="pre">x</span></code> lies in one of the supplied array namespaces: re-route execution to the specified function.</p></li>
-<li><p>If <code class="code docutils literal notranslate"><span class="pre">x</span></code> lies in none of the supplied array namespaces: execute <code class="code docutils literal notranslate"><span class="pre">f</span></code>.</p></li>
-</ul>
+<dt class="sig sig-object py" id="pyxu.util.misc.peaks">
+<span class="sig-name descname"><span class="pre">peaks</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#peaks"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.misc.peaks" title="Link to this definition">#</a></dt>
+<dd><p>Matlab 2D peaks function.</p>
+<p>Peaks is a function of two variables, obtained by translating and scaling Gaussian distributions.  (See <a class="reference external" href="https://www.mathworks.com/help/matlab/ref/peaks.html">Matlab’s
+peaks function</a>.)</p>
+<p>This function is useful for testing purposes.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>i</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.VarName" title="pyxu.info.ptype.VarName"><code class="xref py py-class docutils literal notranslate"><span class="pre">VarName</span></code></a>) – name of the array-like variable in <code class="code docutils literal notranslate"><span class="pre">f</span></code> to base dispatch on.</p></li>
-<li><p><strong>kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Mapping" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Mapping</span></code></a>) – <ul>
-<li><p>key[<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>]: array backend short-name as defined in <a class="reference internal" href="info.deps.html#pyxu.info.deps.NDArrayInfo" title="pyxu.info.deps.NDArrayInfo"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayInfo</span></code></a>.</p></li>
-<li><p>value[<a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">collections.abc.Callable</span></code></a>]: function/method to dispatch to.</p></li>
-</ul>
-</p></li>
+<li><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – X coordinates.</p></li>
+<li><p><strong>y</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – Y coordinates.</p></li>
 </ul>
 </dd>
-<dt class="field-even">Return type<span class="colon">:</span></dt>
-<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable" title="(in Python v3.11)"><em>Callable</em></a></p>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>z</strong> – Values of the 2D function <code class="docutils literal notranslate"><span class="pre">peaks</span></code> at the points specified by the entries of <code class="code docutils literal notranslate"><span class="pre">x</span></code> and <code class="code docutils literal notranslate"><span class="pre">y</span></code>.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
 </dd>
 </dl>
-<p class="rubric">Notes</p>
-<p>Auto-dispatch via <a class="reference internal" href="#pyxu.util.redirect" title="pyxu.util.redirect"><code class="xref py py-func docutils literal notranslate"><span class="pre">redirect()</span></code></a> assumes the dispatcher/dispatchee have the same parameterization, i.e.:</p>
-<ul class="simple">
-<li><p>if <code class="code docutils literal notranslate"><span class="pre">f</span></code> is a function -&gt; dispatch possible to another callable with identical signature (i.e., function or
-staticmethod)</p></li>
-<li><p>if <code class="code docutils literal notranslate"><span class="pre">f</span></code> is a staticmethod -&gt; dispatch possible to another callable with identical signature (i.e., function or
-staticmethod)</p></li>
-<li><p>if <code class="code docutils literal notranslate"><span class="pre">f</span></code> is an instance-method -&gt; dispatch to another instance-method of the class with identical signature.</p></li>
-</ul>
-<p class="rubric">Example</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span> <span class="k">return</span> <span class="s2">"f"</span>
+<p class="rubric">Examples</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
 
-<span class="nd">@redirect</span><span class="p">(</span><span class="s1">'x'</span><span class="p">,</span> <span class="n">NUMPY</span><span class="o">=</span><span class="n">f</span><span class="p">)</span>    <span class="c1"># if 'x' is of type NDArrayInfo.NUMPY, i.e. has</span>
-<span class="k">def</span> <span class="nf">g</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span> <span class="k">return</span> <span class="s2">"g"</span>    <span class="c1"># short-name 'NUMPY' -&gt; reroute execution to `f`</span>
+<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
+<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
+<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
+<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">z</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>(<a class="reference download internal" download="" href="../_downloads/7a96e89967447e1042b7a00e8e9f004a/util-1.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/6c763f0d1d1bca3dea56eef770528674/util-1.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/09a11b0e08c73736be787c749bfba607/util-1.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/5be70851f96b004b61b84e14faba6d02/util-1.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
+<figure class="align-default">
+<img alt="../_images/util-1.png" class="plot-directive" src="../_images/util-1.png"/>
+</figure>
+</dd></dl>
+<dl class="py function">
+<dt class="sig sig-object py" id="pyxu.util.misc.star_like_sample">
+<span class="sig-name descname"><span class="pre">star_like_sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">N</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">w</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">po</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">NDArrayInfo.NUMPY</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/misc.html#star_like_sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.misc.star_like_sample" title="Link to this definition">#</a></dt>
+<dd><p>Star-like test image.</p>
+<p>Generates a (N, N) square image of a star-like object normalized between 0 and 1.  Based on <a class="reference external" href="https://github.com/Biomedical-Imaging-Group/GlobalBioIm/blob/master/Util/StarLikeSample.m">GlobalBioIm’s
+StarLikeSample function</a>.  This function is
+useful for testing purposes as it contains high-frequency information.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>N</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Size of the image (must be an even number).</p></li>
+<li><p><strong>w</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – The number of branches of the sample will be 4*w.</p></li>
+<li><p><strong>s</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Slope of the sigmoid function <span class="math notranslate nohighlight">\(\frac1{1+\exp[s (x-x_{0})]}\)</span> attenuating the boundaries.</p></li>
+<li><p><strong>po</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Integer" title="pyxu.info.ptype.Integer"><code class="xref py py-class docutils literal notranslate"><span class="pre">Integer</span></code></a>) – Power-raising factor for the final image (to have smoother edges).</p></li>
+<li><p><strong>x0</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.Real" title="pyxu.info.ptype.Real"><code class="xref py py-class docutils literal notranslate"><span class="pre">Real</span></code></a>) – Radial shift of the sigmoid function <span class="math notranslate nohighlight">\(\frac1{1+\exp[s (x-x_{0})]}\)</span>.</p></li>
+<li><p><strong>ndi</strong> (<a class="reference internal" href="info.deps.html#pyxu.info.deps.NDArrayInfo" title="pyxu.info.deps.NDArrayInfo"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayInfo</span></code></a>) – Desired array module for the output.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>image</strong> – (N, N) image of star-like sample.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+</dd>
+</dl>
+<p class="rubric">Examples</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.star_like_sample" title="pyxu.util.misc.star_like_sample"><span class="n">star_like_sample</span></a>
 
-<span class="n">x1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
-<span class="n">x2</span> <span class="o">=</span> <span class="n">da</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x1</span><span class="p">)</span>
-<span class="n">y</span> <span class="o">=</span> <span class="mi">1</span>
-<span class="n">g</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">y</span><span class="p">),</span> <span class="n">g</span><span class="p">(</span><span class="n">x2</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>  <span class="c1"># 'f', 'g'</span>
+<span class="n">star</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.misc.star_like_sample" title="pyxu.util.misc.star_like_sample"><span class="n">star_like_sample</span></a><span class="p">(</span><span class="n">N</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mi">8</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">po</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
+<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
+<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">star</span><span class="p">)</span>
 </pre></div>
 </div>
+<p>(<a class="reference download internal" download="" href="../_downloads/0fc82206eb78ed17440026ce6f7cb455/util-2.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../_downloads/92b871487a1a9b8139c3540b67b17b89/util-2.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/97ed94caa646cf7937bbaa1dba9f3fc9/util-2.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../_downloads/5420c90dcdf9b097dbed8ebf47bc7a03/util-2.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
+<figure class="align-default">
+<img alt="../_images/util-2.png" class="plot-directive" src="../_images/util-2.png"/>
+</figure>
 </dd></dl>
+</section>
+<section id="pyxu-util-operator">
+<h2><a class="toc-backref" href="#id4" role="doc-backlink">pyxu.util.operator</a><a class="headerlink" href="#pyxu-util-operator" title="Link to this heading">#</a></h2>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.to_NUMPY">
-<span class="sig-name descname"><span class="pre">to_NUMPY</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/array_module.html#to_NUMPY"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.to_NUMPY" title="Link to this definition">#</a></dt>
-<dd><p>Convert an array from a specific backend to NUMPY.</p>
+<dt class="sig sig-object py" id="pyxu.util.as_canonical_shape">
+<span class="sig-name descname"><span class="pre">as_canonical_shape</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/operator.html#as_canonical_shape"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.as_canonical_shape" title="Link to this definition">#</a></dt>
+<dd><p>Transform a lone integer into a valid tuple-based shape specifier.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – Array to be converted.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>y</strong> – Array with NumPy backend.</p>
+<dd class="field-odd"><p><strong>x</strong> (<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em> | </em><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)"><em>tuple</em></a><em>[</em><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a><em>, </em><em>...</em><em>]</em>) – </p>
 </dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+<dt class="field-even">Return type<span class="colon">:</span></dt>
+<dd class="field-even"><p><a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a> | <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#tuple" title="(in Python v3.11)">tuple</a>[<a class="reference external" href="https://docs.python.org/3/library/numbers.html#numbers.Integral" title="(in Python v3.11)"><em>Integral</em></a>, …]</p>
 </dd>
 </dl>
-<p class="rubric">Notes</p>
-<p>This function is a no-op if the array is already a NumPy array.</p>
 </dd></dl>
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.vectorize">
@@ -724,195 +840,106 @@
 </div>
 </dd></dl>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.view_as_complex">
-<span class="sig-name descname"><span class="pre">view_as_complex</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/complex.html#view_as_complex"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.view_as_complex" title="Link to this definition">#</a></dt>
-<dd><p>View real-valued array as its complex-valued bijection.  (Inverse of <a class="reference internal" href="#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>.)</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, 2N) real-valued array.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>y</strong> – (…, N) complex-valued array.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <span class="n">view_as_real</span><span class="p">,</span> <span class="n">view_as_complex</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">6.0</span><span class="p">)</span>      <span class="c1"># array([0., 1., 2., 3., 4., 5.])</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">view_as_complex</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>  <span class="c1"># array([0.+1.j, 2.+3.j, 4.+5.j])</span>
-<span class="n">view_as_real</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">==</span> <span class="n">x</span>    <span class="c1"># True</span>
-</pre></div>
-</div>
-<p class="rubric">Notes</p>
-<p>Complex-valued inputs are returned unchanged.  For real-valued inputs, this function acts on the last axis as:</p>
-<div class="math notranslate nohighlight">
-\[y_n = x_{2n-1}+j \, x_{2n}, \qquad 1\leq n\leq N.\]</div>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.view_as_complex_mat">
-<span class="sig-name descname"><span class="pre">view_as_complex_mat</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rmat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real_input</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real_output</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/complex.html#view_as_complex_mat"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.view_as_complex_mat" title="Link to this definition">#</a></dt>
-<dd><p>View real-valued matrix as its complex-valued equivalent.  (Inverse of <a class="reference internal" href="#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a>.)</p>
-<p>Useful to transform real-valued matrix/vector products to their complex-valued counterparts.</p>
+<dt class="sig sig-object py" id="pyxu.util.operator._array_ize">
+<span class="sig-name descname"><span class="pre">_array_ize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dtype</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/operator.html#_array_ize"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.operator._array_ize" title="Link to this definition">#</a></dt>
+<dd><p>Transform a Dask-delayed object into its Dask-array counterpart.</p>
+<p>This function is a no-op if <code class="code docutils literal notranslate"><span class="pre">data</span></code> is not a <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> object.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>rmat</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – <p>Real-valued matrix.  Accepted dimensions depend on the values of <code class="code docutils literal notranslate"><span class="pre">real_input</span></code> and <code class="code docutils literal notranslate"><span class="pre">real_output</span></code>:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">|</span> <span class="n">real_input</span> <span class="o">|</span> <span class="n">real_output</span> <span class="o">|</span> <span class="n">rmat</span><span class="o">.</span><span class="n">shape</span> <span class="o">|</span>
-<span class="o">|------------|-------------|------------|</span>
-<span class="o">|</span> <span class="kc">False</span>      <span class="o">|</span> <span class="kc">False</span>       <span class="o">|</span> <span class="p">(</span><span class="mi">2</span><span class="n">M</span><span class="p">,</span> <span class="mi">2</span><span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
-<span class="o">|</span> <span class="kc">False</span>      <span class="o">|</span> <span class="kc">True</span>        <span class="o">|</span> <span class="p">(</span> <span class="n">M</span><span class="p">,</span> <span class="mi">2</span><span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
-<span class="o">|</span> <span class="kc">True</span>       <span class="o">|</span> <span class="kc">False</span>       <span class="o">|</span> <span class="p">(</span><span class="mi">2</span><span class="n">M</span><span class="p">,</span>  <span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
-<span class="o">|</span> <span class="kc">True</span>       <span class="o">|</span> <span class="kc">True</span>        <span class="o">|</span> <span class="p">(</span> <span class="n">M</span><span class="p">,</span>  <span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
-</pre></div>
-</div>
+<li><p><strong>data</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>, <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a>) – Object to act upon.</p></li>
+<li><p><strong>shape</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArrayShape" title="pyxu.info.ptype.NDArrayShape"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArrayShape</span></code></a>) – <p>Shape of <code class="code docutils literal notranslate"><span class="pre">data</span></code>.</p>
+<p>This parameter is only used if <code class="code docutils literal notranslate"><span class="pre">data</span></code> is a <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> object.  Its goal is to transform
+the former back to array form.</p>
+</p></li>
+<li><p><strong>dtype</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.DType" title="pyxu.info.ptype.DType"><code class="xref py py-class docutils literal notranslate"><span class="pre">DType</span></code></a>) – <p>Dtype of <code class="code docutils literal notranslate"><span class="pre">data</span></code>.</p>
+<p>This parameter is only used if <code class="code docutils literal notranslate"><span class="pre">data</span></code> is a <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> object.  Its goal is to transform
+the former back to array form.</p>
 </p></li>
-<li><p><strong>real_input</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-<li><p><strong>real_output</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>cmat</strong> – (M, N) complex-valued matrix.</p>
+<dd class="field-even"><p><strong>arr</strong> – Dask-backed NDArray if <code class="code docutils literal notranslate"><span class="pre">data</span></code> was a <a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> object; no-op otherwise.</p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
 <dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
 </dd>
 </dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <span class="n">view_as_real_mat</span><span class="p">,</span> <span class="n">view_as_complex_mat</span>
-
-<span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span> <span class="mf">0.</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.</span><span class="p">,</span>  <span class="mf">1.</span><span class="p">,</span> <span class="o">-</span><span class="mf">3.</span><span class="p">,</span>  <span class="mf">2.</span><span class="p">,</span> <span class="o">-</span><span class="mf">4.</span><span class="p">],</span>
-              <span class="p">[</span> <span class="mf">2.</span><span class="p">,</span>  <span class="mf">0.</span><span class="p">,</span>  <span class="mf">3.</span><span class="p">,</span>  <span class="mf">1.</span><span class="p">,</span>  <span class="mf">4.</span><span class="p">,</span>  <span class="mf">2.</span><span class="p">],</span>
-              <span class="p">[</span> <span class="mf">3.</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.</span><span class="p">,</span>  <span class="mf">4.</span><span class="p">,</span> <span class="o">-</span><span class="mf">6.</span><span class="p">,</span>  <span class="mf">5.</span><span class="p">,</span> <span class="o">-</span><span class="mf">7.</span><span class="p">],</span>
-              <span class="p">[</span> <span class="mf">5.</span><span class="p">,</span>  <span class="mf">3.</span><span class="p">,</span>  <span class="mf">6.</span><span class="p">,</span>  <span class="mf">4.</span><span class="p">,</span>  <span class="mf">7.</span><span class="p">,</span>  <span class="mf">5.</span><span class="p">]])</span>
-
-<span class="n">B</span> <span class="o">=</span> <span class="n">view_as_complex</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>  <span class="c1"># array([[0.+2.j, 1.+3.j, 2.+4.j],</span>
-                        <span class="c1">#        [3.+5.j, 4.+6.j, 5.+7.j]])</span>
-</pre></div>
-</div>
-<p class="rubric">Notes</p>
-<ul>
-<li><p>Complex-valued matrices are returned unchanged.</p></li>
-<li><p>Real-valued matrices are mapped into a complex-valued matrix <span class="math notranslate nohighlight">\({A}\in\mathbb{C}^{M\times N}\)</span> as follows:</p>
+</dd></dl>
+<dl class="py function">
+<dt class="sig sig-object py" id="pyxu.util.operator._dask_zip">
+<span class="sig-name descname"><span class="pre">_dask_zip</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">func</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">data</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out_shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out_dtype</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">parallel</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/operator.html#_dask_zip"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.operator._dask_zip" title="Link to this definition">#</a></dt>
+<dd><p>Map functions in parallel via Dask.</p>
+<p>Computes the equivalent of <code class="docutils literal notranslate"><span class="pre">out</span> <span class="pre">=</span> <span class="pre">[f(x)</span> <span class="pre">for</span> <span class="pre">(f,</span> <span class="pre">x)</span> <span class="pre">in</span> <span class="pre">zip(func,</span> <span class="pre">data)]</span></code>, with the following semantics:</p>
 <ul class="simple">
-<li><p><span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{2M\times 2N}\)</span>:  <span class="math notranslate nohighlight">\(A_{m,n} = \hat{A}_{2m-1,2n-1} + j \hat{A}_{2m,2n-1}\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{M\times 2N}\)</span>:  <span class="math notranslate nohighlight">\(A_{m,n} = \hat{A}_{m,2n-1} - j \hat{A}_{m,2n}\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{2M\times N}\)</span>:  <span class="math notranslate nohighlight">\(A_{m,n} = \hat{A}_{2m-1,n} + j \hat{A}_{2m,n}\)</span>,</p></li>
-<li><p><span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{M\times N}\)</span>:  <span class="math notranslate nohighlight">\(A_{m,n} = \hat{A}_{m,n} + 0j\)</span>,</p></li>
+<li><p>If <code class="code docutils literal notranslate"><span class="pre">data</span></code> contains only NUMPY/CUPY arrays, then <code class="docutils literal notranslate"><span class="pre">out</span></code> is computed as above.</p></li>
+<li><p>If <code class="code docutils literal notranslate"><span class="pre">data</span></code> contains only DASK arrays, then entries of <code class="docutils literal notranslate"><span class="pre">out</span></code> are computed:</p>
+<ul>
+<li><p>if <code class="code docutils literal notranslate"><span class="pre">parallel</span></code> enabled  -&gt; dask-delay each <code class="code docutils literal notranslate"><span class="pre">func</span></code>, then evaluate in parallel.</p></li>
+<li><p>if <code class="code docutils literal notranslate"><span class="pre">parallel</span></code> disabled -&gt; dask-delay each <code class="code docutils literal notranslate"><span class="pre">func</span></code>, then evaluate in sequence.
+(This is useful if <code class="code docutils literal notranslate"><span class="pre">func</span></code> s share a common resource, thus not thread-safe.)</p></li>
 </ul>
-<p>for <span class="math notranslate nohighlight">\(1\leq n \leq N\)</span>, <span class="math notranslate nohighlight">\(1\leq m\leq M\)</span>.</p>
 </li>
 </ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.view_as_real">
-<span class="sig-name descname"><span class="pre">view_as_real</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/complex.html#view_as_real"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.view_as_real" title="Link to this definition">#</a></dt>
-<dd><p>View complex-valued array as its real-valued bijection.  (Inverse of <a class="reference internal" href="#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a>.)</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (…, N) complex-valued array.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>y</strong> – (…, 2N) real-valued array.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <span class="n">view_as_real</span><span class="p">,</span> <span class="n">view_as_complex</span>
-<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[:</span><span class="mi">3</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">5</span><span class="p">]</span>   <span class="c1"># array([0.+2.j, 1.+3.j, 2.+4.j])</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">view_as_real</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>               <span class="c1"># array([0., 2., 1., 3., 2., 4.])</span>
-<span class="n">view_as_complex</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">==</span> <span class="n">x</span>           <span class="c1"># True</span>
+<p>For Dask-array inputs, this amounts to creating a task graph with virtual dependencies between successive <code class="code docutils literal notranslate"><span class="pre">func</span></code>
+calls. In other words, the task graph looks like:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">_dask_zip</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">parallel</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">out</span>
+
+              <span class="o">+----+</span>              <span class="o">+----+</span>
+    <span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">--&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">blk</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-+--&gt;|</span><span class="nb">list</span><span class="o">|--&gt;</span><span class="n">out</span>
+        <span class="o">.</span>     <span class="o">+----+</span>          <span class="o">|</span>   <span class="o">+----+</span>
+        <span class="o">.</span>                     <span class="o">|</span>
+        <span class="o">.</span>     <span class="o">+----+</span>          <span class="o">|</span>
+    <span class="n">data</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="o">--&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">blk</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="o">-+</span>
+              <span class="o">+----+</span>
+
+<span class="o">==========================================================================================================</span>
+<span class="n">_dask_zip</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">parallel</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">out</span>
+                                                                                       <span class="o">+----+</span>
+                        <span class="o">+-------------------+----------------+--------------------+----+</span><span class="nb">list</span><span class="o">|--&gt;</span><span class="n">out</span>
+                        <span class="o">|</span>                   <span class="o">|</span>                <span class="o">|</span>                    <span class="o">|</span>    <span class="o">+----+</span>
+                        <span class="o">|</span>                   <span class="o">|</span>                <span class="o">|</span>                    <span class="o">|</span>
+              <span class="o">+----+</span>    <span class="o">|</span>        <span class="o">+----+</span>     <span class="o">|</span>      <span class="o">+---+</span>     <span class="o">|</span>         <span class="o">+----+</span>     <span class="o">|</span>
+    <span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">--&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">out</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-+-&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">out</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">--&gt;|...|--&gt;</span><span class="n">out</span><span class="p">[</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">-+-&gt;|</span><span class="n">func</span><span class="o">|--&gt;</span><span class="n">out</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+              <span class="o">+----+</span>          <span class="o">|</span>  <span class="o">+----+</span>            <span class="o">+---+</span>            <span class="o">|</span>  <span class="o">+----+</span>
+                              <span class="o">|</span>                                     <span class="o">|</span>
+    <span class="n">data</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-------------------+</span>                                     <span class="o">|</span>
+        <span class="o">.</span>                                                           <span class="o">|</span>
+        <span class="o">.</span>                                                           <span class="o">|</span>
+        <span class="o">.</span>                                                           <span class="o">|</span>
+    <span class="n">data</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="o">---------------------------------------------------------+</span>
 </pre></div>
 </div>
-<p class="rubric">Notes</p>
-<p>Real-valued inputs are returned unchanged.  For complex-valued inputs, this function acts on the last axis as:</p>
-<div class="math notranslate nohighlight">
-\[y_{2n-1} = \mathcal{R}(x_n),
-\quad
-y_{2n} = \mathcal{I}(x_n),
-\quad 1\leq n\leq N,\]</div>
-<p>where <span class="math notranslate nohighlight">\(\mathcal{R}, \mathcal{I}\)</span> denote the real/imaginary parts respectively.</p>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_real_mat" title="pyxu.util.view_as_real_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a></p>
-</div>
-</dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.view_as_real_mat">
-<span class="sig-name descname"><span class="pre">view_as_real_mat</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cmat</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real_input</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real_output</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../_modules/pyxu/util/complex.html#view_as_real_mat"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.view_as_real_mat" title="Link to this definition">#</a></dt>
-<dd><p>View complex-valued matrix as its real-valued equivalent.  (Inverse of <a class="reference internal" href="#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a>.)</p>
-<p>Useful to transform complex-valued matrix/vector products to their real-valued counterparts.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>cmat</strong> (<a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – (M, N) complex-valued matrix.</p></li>
-<li><p><strong>real_input</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
-<li><p><strong>real_output</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
+<li><p><strong>func</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – <p>Functions to apply to each element of <code class="code docutils literal notranslate"><span class="pre">data</span></code>.</p>
+<p>Function signatures are <code class="docutils literal notranslate"><span class="pre">Callable[[NDArray],</span> <span class="pre">NDArray]</span></code>.</p>
+</p></li>
+<li><p><strong>data</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – (N_data,) arrays to act on.</p></li>
+<li><p><strong>out_shape</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – <p>Shapes of <code class="docutils literal notranslate"><span class="pre">func[i](data[i])</span></code>.</p>
+<p>This parameter is only used if inputs are DASK arrays.  Its goal is to transform
+<a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> objects back to array form.</p>
+</p></li>
+<li><p><strong>out_dtype</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – <p>Dtypes of <code class="docutils literal notranslate"><span class="pre">func[i](data[i])</span></code>.</p>
+<p>This parameter is only used if inputs are DASK arrays.  Its goal is to transform
+<a class="reference external" href="https://docs.dask.org/en/stable/delayed-api.html#dask.delayed.Delayed" title="(in Dask)"><code class="xref py py-class docutils literal notranslate"><span class="pre">Delayed</span></code></a> objects back to array form.</p>
+</p></li>
+<li><p><strong>parallel</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.11)"><em>bool</em></a>) – </p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><p><strong>rmat</strong> –</p>
-<p>The output shape depends on the values of <code class="code docutils literal notranslate"><span class="pre">real_input</span></code> and <code class="code docutils literal notranslate"><span class="pre">real_output</span></code>:</p>
-<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">|</span> <span class="n">real_input</span> <span class="o">|</span> <span class="n">real_output</span> <span class="o">|</span> <span class="n">rmat</span><span class="o">.</span><span class="n">shape</span> <span class="o">|</span>
-<span class="o">|------------|-------------|------------|</span>
-<span class="o">|</span> <span class="kc">False</span>      <span class="o">|</span> <span class="kc">False</span>       <span class="o">|</span> <span class="p">(</span><span class="mi">2</span><span class="n">M</span><span class="p">,</span> <span class="mi">2</span><span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
-<span class="o">|</span> <span class="kc">False</span>      <span class="o">|</span> <span class="kc">True</span>        <span class="o">|</span> <span class="p">(</span> <span class="n">M</span><span class="p">,</span> <span class="mi">2</span><span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
-<span class="o">|</span> <span class="kc">True</span>       <span class="o">|</span> <span class="kc">False</span>       <span class="o">|</span> <span class="p">(</span><span class="mi">2</span><span class="n">M</span><span class="p">,</span>  <span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
-<span class="o">|</span> <span class="kc">True</span>       <span class="o">|</span> <span class="kc">True</span>        <span class="o">|</span> <span class="p">(</span> <span class="n">M</span><span class="p">,</span>  <span class="n">N</span><span class="p">)</span>   <span class="o">|</span>
-</pre></div>
-</div>
+<dd class="field-even"><p><p><strong>out</strong> – (N_data,) objects acted upon.</p>
+<p>Outputs have the same backend/dtype as inputs, or as specified by <code class="code docutils literal notranslate"><span class="pre">out_[shape,dtype]</span></code>.</p>
 </p>
 </dd>
 <dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a></p>
 </dd>
 </dl>
-<p class="rubric">Examples</p>
-<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <span class="n">view_as_real_mat</span><span class="p">,</span> <span class="n">view_as_complex_mat</span>
-
-<span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span>
-    <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[:</span><span class="mi">6</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">8</span><span class="p">],</span> <span class="c1"># array([[0.+2.j, 1.+3.j, 2.+4.j],</span>
-    <span class="n">newshape</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span>             <span class="c1">#        [3.+5.j, 4.+6.j, 5.+7.j]])</span>
-<span class="p">)</span>
-<span class="n">B</span> <span class="o">=</span> <span class="n">view_as_real_mat</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>          <span class="c1"># array([[ 0., -2.,  1., -3.,  2., -4.],</span>
-                                 <span class="c1">#        [ 2.,  0.,  3.,  1.,  4.,  2.],</span>
-                                 <span class="c1">#        [ 3., -5.,  4., -6.,  5., -7.],</span>
-                                 <span class="c1">#        [ 5.,  3.,  6.,  4.,  7.,  5.]])</span>
-</pre></div>
-</div>
-<p class="rubric">Notes</p>
-<ul>
-<li><p>Real-valued matrices are returned unchanged.</p></li>
-<li><p>Complex-valued matrices <span class="math notranslate nohighlight">\(A\in\mathbb{C}^{M\times N}\)</span> are mapped into a real-valued matrix
-<span class="math notranslate nohighlight">\(\hat{A}\in\mathbb{R}^{2M\times 2N}\)</span> defined, for <span class="math notranslate nohighlight">\(1\leq n \leq N\)</span>, <span class="math notranslate nohighlight">\(1\leq m\leq M\)</span> as</p>
-<div class="math notranslate nohighlight">
-\[\begin{split}\hat{A}_{2m-1,2n-1} = \mathcal{R}(A_{m,n}),
-&amp; \quad
-\hat{A}_{2m-1,2n} = -\mathcal{I}(A_{m,n}),\\
-\hat{A}_{2m,2n-1} = \mathcal{I}(A_{m,n}),
-&amp; \quad
-\hat{A}_{2m,2n}=\mathcal{R}(A_{m,n}).\end{split}\]</div>
-<p>If <code class="docutils literal notranslate"><span class="pre">real_[in|out]put=True</span></code>, then even columns/rows (or both) are furthermore dropped.  We have <code class="docutils literal notranslate"><span class="pre">view_as_real(A</span>
-<span class="pre">@</span> <span class="pre">x)</span> <span class="pre">=</span> <span class="pre">view_as_real_mat(A)</span> <span class="pre">@</span> <span class="pre">view_as_real(x)</span></code>.</p>
-</li>
-</ul>
-<div class="admonition seealso">
-<p class="admonition-title">See also</p>
-<p><a class="reference internal" href="#pyxu.util.view_as_real" title="pyxu.util.view_as_real"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_real()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex" title="pyxu.util.view_as_complex"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a>, <a class="reference internal" href="#pyxu.util.view_as_complex_mat" title="pyxu.util.view_as_complex_mat"><code class="xref py py-func docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a></p>
-</div>
 </dd></dl>
 </section>
+</section>
 </article>
 <footer class="bd-footer-article">
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@@ -943,27 +970,39 @@
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 <nav class="bd-toc-nav page-toc">
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-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.misc.peaks"><code class="docutils literal notranslate"><span class="pre">peaks()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.misc.star_like_sample"><code class="docutils literal notranslate"><span class="pre">star_like_sample()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.operator._dask_zip"><code class="docutils literal notranslate"><span class="pre">_dask_zip()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.operator._array_ize"><code class="docutils literal notranslate"><span class="pre">_array_ize()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.as_canonical_shape"><code class="docutils literal notranslate"><span class="pre">as_canonical_shape()</span></code></a></li>
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-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.infer_sum_shape"><code class="docutils literal notranslate"><span class="pre">infer_sum_shape()</span></code></a></li>
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-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.vectorize"><code class="docutils literal notranslate"><span class="pre">vectorize()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.view_as_complex"><code class="docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.view_as_complex_mat"><code class="docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.view_as_real"><code class="docutils literal notranslate"><span class="pre">view_as_real()</span></code></a></li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.view_as_real_mat"><code class="docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu-util-array-module">pyxu.util.array_module</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.get_array_module"><code class="docutils literal notranslate"><span class="pre">get_array_module()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.redirect"><code class="docutils literal notranslate"><span class="pre">redirect()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.compute"><code class="docutils literal notranslate"><span class="pre">compute()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.to_NUMPY"><code class="docutils literal notranslate"><span class="pre">to_NUMPY()</span></code></a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu-util-complex">pyxu.util.complex</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.view_as_complex_mat"><code class="docutils literal notranslate"><span class="pre">view_as_complex_mat()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.view_as_complex"><code class="docutils literal notranslate"><span class="pre">view_as_complex()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.view_as_real_mat"><code class="docutils literal notranslate"><span class="pre">view_as_real_mat()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.view_as_real"><code class="docutils literal notranslate"><span class="pre">view_as_real()</span></code></a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu-util-misc">pyxu.util.misc</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.copy_if_unsafe"><code class="docutils literal notranslate"><span class="pre">copy_if_unsafe()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.import_module"><code class="docutils literal notranslate"><span class="pre">import_module()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.infer_composition_shape"><code class="docutils literal notranslate"><span class="pre">infer_composition_shape()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.infer_sum_shape"><code class="docutils literal notranslate"><span class="pre">infer_sum_shape()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.next_fast_len"><code class="docutils literal notranslate"><span class="pre">next_fast_len()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.parse_params"><code class="docutils literal notranslate"><span class="pre">parse_params()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.read_only"><code class="docutils literal notranslate"><span class="pre">read_only()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.misc.peaks"><code class="docutils literal notranslate"><span class="pre">peaks()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.misc.star_like_sample"><code class="docutils literal notranslate"><span class="pre">star_like_sample()</span></code></a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu-util-operator">pyxu.util.operator</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.as_canonical_shape"><code class="docutils literal notranslate"><span class="pre">as_canonical_shape()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.vectorize"><code class="docutils literal notranslate"><span class="pre">vectorize()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.operator._array_ize"><code class="docutils literal notranslate"><span class="pre">_array_ize()</span></code></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.operator._dask_zip"><code class="docutils literal notranslate"><span class="pre">_dask_zip()</span></code></a></li>
+</ul>
+</li>
 </ul>
 </nav></div>
 <div class="sidebar-secondary-item">
diff --git a/api/util/array_module.html b/api/util/array_module.html
index 201a5d2d..978e80f2 100644
--- a/api/util/array_module.html
+++ b/api/util/array_module.html
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-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
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@@ -38,13 +38,13 @@
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-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -567,6 +567,48 @@ <h1>pyxu.util.array_module<a class="headerlink" href="#pyxu-util-array-module" t
 </div>
 </dd></dl>
 
+<dl class="py function">
+<dt class="sig sig-object py" id="pyxu.util.compute">
+<span class="sig-name descname"><span class="pre">compute</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'compute'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/array_module.html#compute"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.compute" title="Link to this definition">#</a></dt>
+<dd><p>Force computation of Dask collections.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>*args</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – Any number of objects.  If it is a dask object, it is evaluated and the result is returned.  Non-dask arguments
+are passed through unchanged.  Python collections are traversed to find/evaluate dask objects within.  (Use
+<code class="code docutils literal notranslate"><span class="pre">traverse</span></code> =False to disable this behavior.)</p></li>
+<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>) – Dask evaluation strategy: compute or persist.</p></li>
+<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Extra keyword parameters forwarded to <a class="reference external" href="https://docs.dask.org/en/stable/api.html#dask.compute" title="(in Dask)"><code class="xref py py-func docutils literal notranslate"><span class="pre">dask.compute()</span></code></a> or <a class="reference external" href="https://docs.dask.org/en/stable/api.html#dask.persist" title="(in Dask)"><code class="xref py py-func docutils literal notranslate"><span class="pre">dask.persist()</span></code></a>.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>*cargs</strong> – Evaluated objects. Non-dask arguments are passed through unchanged.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a></p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="pyxu.util.to_NUMPY">
+<span class="sig-name descname"><span class="pre">to_NUMPY</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/array_module.html#to_NUMPY"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.to_NUMPY" title="Link to this definition">#</a></dt>
+<dd><p>Convert an array from a specific backend to NUMPY.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
+<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – Array to be converted.</p>
+</dd>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p><strong>y</strong> – Array with NumPy backend.</p>
+</dd>
+<dt class="field-odd">Return type<span class="colon">:</span></dt>
+<dd class="field-odd"><p><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
+</dd>
+</dl>
+<p class="rubric">Notes</p>
+<p>This function is a no-op if the array is already a NumPy array.</p>
+</dd></dl>
+
 </section>
 
 
@@ -618,6 +660,8 @@ <h1>pyxu.util.array_module<a class="headerlink" href="#pyxu-util-array-module" t
     <ul class="visible nav section-nav flex-column">
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.get_array_module"><code class="docutils literal notranslate"><span class="pre">get_array_module()</span></code></a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.redirect"><code class="docutils literal notranslate"><span class="pre">redirect()</span></code></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.compute"><code class="docutils literal notranslate"><span class="pre">compute()</span></code></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pyxu.util.to_NUMPY"><code class="docutils literal notranslate"><span class="pre">to_NUMPY()</span></code></a></li>
 </ul>
   </nav></div>
 
diff --git a/api/util/complex.html b/api/util/complex.html
index 34dfa94a..3937ffa4 100644
--- a/api/util/complex.html
+++ b/api/util/complex.html
@@ -28,7 +28,7 @@
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-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
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-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
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     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
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diff --git a/api/util/index.html b/api/util/index.html
index 43a20d4a..1fa8bf6c 100644
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+++ b/api/util/index.html
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-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
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@@ -38,13 +38,13 @@
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-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
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-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
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diff --git a/api/util/misc.html b/api/util/misc.html
index d9bc1317..a9c40205 100644
--- a/api/util/misc.html
+++ b/api/util/misc.html
@@ -1,125 +1,199 @@
 
 <!DOCTYPE html>
 
-<html data-theme="light" lang="en">
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-<meta charset="utf-8"/>
-<meta content="width=device-width, initial-scale=1.0" name="viewport"/><meta content="width=device-width, initial-scale=1" name="viewport"/>
-<title>pyxu.util.misc — Pyxu Documentation</title>
-<script data-cfasync="false">
+
+<html lang="en" data-theme="light">
+
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
+
+    <title>pyxu.util.misc &#8212; Pyxu Documentation</title>
+  
+  
+  
+  <script data-cfasync="false">
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+    
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+    <div class="me-auto navbar-header-items__center">
+      
+        <div class="navbar-item"><nav class="navbar-nav">
+  <p class="sidebar-header-items__title"
+     role="heading"
+     aria-level="1"
+     aria-label="Site Navigation">
     Site Navigation
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-<ul class="bd-navbar-elements navbar-nav">
-<li class="nav-item">
-<a class="nav-link nav-internal" href="../../intro/index.html">
+  <ul class="bd-navbar-elements navbar-nav">
+    
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../intro/index.html">
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-<li class="nav-item">
-<a class="nav-link nav-internal" href="../../guide/index.html">
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../guide/index.html">
                         User Guide
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-<a class="nav-link nav-internal" href="../../examples/index.html">
+                    </li>
+                
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+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../examples/index.html">
                         Example Gallery
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-</li>
-<li class="nav-item current active">
-<a class="nav-link nav-internal" href="../index.html">
+                    </li>
+                
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+                    <li class="nav-item current active">
+                      <a class="nav-link nav-internal" href="../index.html">
                         API Reference
                       </a>
-</li>
-<li class="nav-item">
-<a class="nav-link nav-internal" href="../../fair/index.html">
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../fair/index.html">
                         Extending Pyxu
                       </a>
-</li>
-</ul>
+                    </li>
+                
+  </ul>
 </nav></div>
-</div>
-<div class="navbar-header-items__end">
-<div class="navbar-item navbar-persistent--container">
+      
+    </div>
+    
+    
+    <div class="navbar-header-items__end">
+      
+        <div class="navbar-item navbar-persistent--container">
+          
 <script>
 document.write(`
   <button class="btn btn-sm navbar-btn search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
@@ -127,28 +201,68 @@
   </button>
 `);
 </script>
-</div>
-<div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
-<div class="navbar-item"><ul aria-label="Icon Links" class="navbar-icon-links navbar-nav">
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-<li class="nav-item">
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-<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="https://imaging.epfl.ch/" rel="noopener" target="_blank" title="EPFL Center for Imaging"><img alt="EPFL Center for Imaging" class="icon-link-image" src="../../_static/imaging.png"/></a>
-</li>
+        </div>
+      
+      
+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
+      
+        <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
+    aria-label="Icon Links">
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://github.com/matthieumeo/pyxu" title="GitHub" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-github"></i></span>
+            <label class="sr-only">GitHub</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://pypi.org/project/pyxu/" title="PyPI" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-python"></i></span>
+            <label class="sr-only">PyPI</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+            <label class="sr-only">Contact</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://imaging.epfl.ch/" title="EPFL Center for Imaging" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><img src="../../_static/imaging.png" class="icon-link-image" alt="EPFL Center for Imaging"/></a>
+        </li>
 </ul></div>
-</div>
-</div>
-<div class="navbar-persistent--mobile">
+      
+    </div>
+    
+  </div>
+  
+  
+    <div class="navbar-persistent--mobile">
 <script>
 document.write(`
   <button class="btn btn-sm navbar-btn search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
@@ -156,75 +270,144 @@
   </button>
 `);
 </script>
+    </div>
+  
+
+  
+    <label class="sidebar-toggle secondary-toggle" for="__secondary">
+      <span class="fa-solid fa-outdent"></span>
+    </label>
+  
 </div>
-<label class="sidebar-toggle secondary-toggle" for="__secondary">
-<span class="fa-solid fa-outdent"></span>
-</label>
-</div>
-</nav>
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-<div class="navbar-item"><nav class="navbar-nav">
-<p aria-label="Site Navigation" aria-level="1" class="sidebar-header-items__title" role="heading">
+
+    </nav>
+  
+  <div class="bd-container">
+    <div class="bd-container__inner bd-page-width">
+      
+      <div class="bd-sidebar-primary bd-sidebar">
+        
+
+  
+  <div class="sidebar-header-items sidebar-primary__section">
+    
+    
+      <div class="sidebar-header-items__center">
+        
+          <div class="navbar-item"><nav class="navbar-nav">
+  <p class="sidebar-header-items__title"
+     role="heading"
+     aria-level="1"
+     aria-label="Site Navigation">
     Site Navigation
   </p>
-<ul class="bd-navbar-elements navbar-nav">
-<li class="nav-item">
-<a class="nav-link nav-internal" href="../../intro/index.html">
+  <ul class="bd-navbar-elements navbar-nav">
+    
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../intro/index.html">
                         Getting Started
                       </a>
-</li>
-<li class="nav-item">
-<a class="nav-link nav-internal" href="../../guide/index.html">
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../guide/index.html">
                         User Guide
                       </a>
-</li>
-<li class="nav-item">
-<a class="nav-link nav-internal" href="../../examples/index.html">
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../examples/index.html">
                         Example Gallery
                       </a>
-</li>
-<li class="nav-item current active">
-<a class="nav-link nav-internal" href="../index.html">
+                    </li>
+                
+
+                    <li class="nav-item current active">
+                      <a class="nav-link nav-internal" href="../index.html">
                         API Reference
                       </a>
-</li>
-<li class="nav-item">
-<a class="nav-link nav-internal" href="../../fair/index.html">
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../fair/index.html">
                         Extending Pyxu
                       </a>
-</li>
-</ul>
+                    </li>
+                
+  </ul>
 </nav></div>
-</div>
-<div class="sidebar-header-items__end">
-<div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
-<div class="navbar-item"><ul aria-label="Icon Links" class="navbar-icon-links navbar-nav">
-<li class="nav-item">
-<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="https://github.com/matthieumeo/pyxu" rel="noopener" target="_blank" title="GitHub"><span><i class="fa-brands fa-github"></i></span>
-<label class="sr-only">GitHub</label></a>
-</li>
-<li class="nav-item">
-<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="https://pypi.org/project/pyxu/" rel="noopener" target="_blank" title="PyPI"><span><i class="fa-brands fa-python"></i></span>
-<label class="sr-only">PyPI</label></a>
-</li>
-<li class="nav-item">
-<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="mailto: contact@pyxu.org" rel="noopener" target="_blank" title="Contact"><span><i class="fa-brands fa-telegram"></i></span>
-<label class="sr-only">Contact</label></a>
-</li>
-<li class="nav-item">
-<a class="nav-link" data-bs-placement="bottom" data-bs-toggle="tooltip" href="https://imaging.epfl.ch/" rel="noopener" target="_blank" title="EPFL Center for Imaging"><img alt="EPFL Center for Imaging" class="icon-link-image" src="../../_static/imaging.png"/></a>
-</li>
+        
+      </div>
+    
+    
+    
+      <div class="sidebar-header-items__end">
+        
+          <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
+        
+          <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
+    aria-label="Icon Links">
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://github.com/matthieumeo/pyxu" title="GitHub" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-github"></i></span>
+            <label class="sr-only">GitHub</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://pypi.org/project/pyxu/" title="PyPI" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-python"></i></span>
+            <label class="sr-only">PyPI</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+            <label class="sr-only">Contact</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://imaging.epfl.ch/" title="EPFL Center for Imaging" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><img src="../../_static/imaging.png" class="icon-link-image" alt="EPFL Center for Imaging"/></a>
+        </li>
 </ul></div>
-</div>
-</div>
-<div class="sidebar-primary-items__start sidebar-primary__section">
-<div class="sidebar-primary-item"><nav aria-label="Section Navigation" class="bd-docs-nav bd-links">
-<p aria-level="1" class="bd-links__title" role="heading">Section Navigation</p>
-<div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
+        
+      </div>
+    
+  </div>
+  
+    <div class="sidebar-primary-items__start sidebar-primary__section">
+        <div class="sidebar-primary-item"><nav class="bd-docs-nav bd-links"
+     aria-label="Section Navigation">
+  <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
+  <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
 <li class="toctree-l1 has-children"><a class="reference internal" href="../abc/index.html">pyxu.abc</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="../abc/arithmetic.html">pyxu.abc.arithmetic</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../abc/operator.html">pyxu.abc.operator</a></li>
@@ -258,61 +441,66 @@
 </ul>
 </div>
 </nav></div>
-</div>
-<div class="sidebar-primary-items__end sidebar-primary__section">
-</div>
-<div id="rtd-footer-container"></div>
-</div>
-<main class="bd-main" id="main-content">
-<div class="bd-content">
-<div class="bd-article-container">
-<div class="bd-header-article">
+    </div>
+  
+  
+  <div class="sidebar-primary-items__end sidebar-primary__section">
+  </div>
+  
+  <div id="rtd-footer-container"></div>
+
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+      </div>
+      
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+        
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+          <div class="bd-content">
+            <div class="bd-article-container">
+              
+              <div class="bd-header-article">
 <div class="header-article-items header-article__inner">
-<div class="header-article-items__start">
-<div class="header-article-item">
+  
+    <div class="header-article-items__start">
+      
+        <div class="header-article-item">
+
+
+
 <nav aria-label="Breadcrumbs">
-<ul aria-label="Breadcrumb" class="bd-breadcrumbs" role="navigation">
-<li class="breadcrumb-item breadcrumb-home">
-<a aria-label="Home" class="nav-link" href="../../index.html">
-<i class="fa-solid fa-home"></i>
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-</li>
-<li class="breadcrumb-item"><a class="nav-link" href="../index.html">API Reference</a></li>
-<li class="breadcrumb-item"><a class="nav-link" href="index.html">pyxu.util</a></li>
-<li aria-current="page" class="breadcrumb-item active">pyxu.util.misc</li>
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+  <ul class="bd-breadcrumbs" role="navigation" aria-label="Breadcrumb">
+    
+    <li class="breadcrumb-item breadcrumb-home">
+      <a href="../../index.html" class="nav-link" aria-label="Home">
+        <i class="fa-solid fa-home"></i>
+      </a>
+    </li>
+    
+    <li class="breadcrumb-item"><a href="../index.html" class="nav-link">API Reference</a></li>
+    
+    
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">pyxu.util</a></li>
+    
+    <li class="breadcrumb-item active" aria-current="page">pyxu.util.misc</li>
+  </ul>
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+      
+    </div>
+  
+  
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-</div>
+              
+              
+              
+                
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-<article class="bd-article" role="main">
-<section id="pyxu-util-misc">
+                <article class="bd-article" role="main">
+                  
+  <section id="pyxu-util-misc">
 <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to this heading">#</a></h1>
 <dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.compute">
-<span class="sig-name descname"><span class="pre">compute</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'compute'</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#compute"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.compute" title="Link to this definition">#</a></dt>
-<dd><p>Force computation of Dask collections.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><ul class="simple">
-<li><p><strong>*args</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>) – Any number of objects.  If it is a dask object, it is evaluated and the result is returned.  Non-dask arguments
-are passed through unchanged.  Python collections are traversed to find/evaluate dask objects within.  (Use
-<code class="code docutils literal notranslate"><span class="pre">traverse</span></code> =False to disable this behavior.)</p></li>
-<li><p><strong>mode</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#str" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>) – Dask evaluation strategy: compute or persist.</p></li>
-<li><p><strong>**kwargs</strong> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#dict" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">dict</span></code></a>) – Extra keyword parameters forwarded to <a class="reference external" href="https://docs.dask.org/en/stable/api.html#dask.compute" title="(in Dask)"><code class="xref py py-func docutils literal notranslate"><span class="pre">dask.compute()</span></code></a> or <a class="reference external" href="https://docs.dask.org/en/stable/api.html#dask.persist" title="(in Dask)"><code class="xref py py-func docutils literal notranslate"><span class="pre">dask.persist()</span></code></a>.</p></li>
-</ul>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>*cargs</strong> – Evaluated objects. Non-dask arguments are passed through unchanged.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a>, <a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.11)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a></p>
-</dd>
-</dl>
-</dd></dl>
-<dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.copy_if_unsafe">
 <span class="sig-name descname"><span class="pre">copy_if_unsafe</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#copy_if_unsafe"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.copy_if_unsafe" title="Link to this definition">#</a></dt>
 <dd><p>Copy array if it is unsafe to do in-place updates on it.</p>
@@ -333,6 +521,7 @@ <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to th
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.import_module">
 <span class="sig-name descname"><span class="pre">import_module</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fail_on_error</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#import_module"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.import_module" title="Link to this definition">#</a></dt>
@@ -349,6 +538,7 @@ <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to th
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.infer_composition_shape">
 <span class="sig-name descname"><span class="pre">infer_composition_shape</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sh1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sh2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#infer_composition_shape"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.infer_composition_shape" title="Link to this definition">#</a></dt>
@@ -365,6 +555,7 @@ <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to th
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.infer_sum_shape">
 <span class="sig-name descname"><span class="pre">infer_sum_shape</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sh1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sh2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#infer_sum_shape"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.infer_sum_shape" title="Link to this definition">#</a></dt>
@@ -381,6 +572,7 @@ <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to th
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.next_fast_len">
 <span class="sig-name descname"><span class="pre">next_fast_len</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">N</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">even</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#next_fast_len"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.next_fast_len" title="Link to this definition">#</a></dt>
@@ -398,6 +590,7 @@ <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to th
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.parse_params">
 <span class="sig-name descname"><span class="pre">parse_params</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">func</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#parse_params"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.parse_params" title="Link to this definition">#</a></dt>
@@ -411,6 +604,7 @@ <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to th
 </dd>
 </dl>
 </dd></dl>
+
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.read_only">
 <span class="sig-name descname"><span class="pre">read_only</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#read_only"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.read_only" title="Link to this definition">#</a></dt>
@@ -427,24 +621,7 @@ <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to th
 </dd>
 </dl>
 </dd></dl>
-<dl class="py function">
-<dt class="sig sig-object py" id="pyxu.util.to_NUMPY">
-<span class="sig-name descname"><span class="pre">to_NUMPY</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#to_NUMPY"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.to_NUMPY" title="Link to this definition">#</a></dt>
-<dd><p>Convert an array from a specific backend to NUMPY.</p>
-<dl class="field-list simple">
-<dt class="field-odd">Parameters<span class="colon">:</span></dt>
-<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a>) – Array to be converted.</p>
-</dd>
-<dt class="field-even">Returns<span class="colon">:</span></dt>
-<dd class="field-even"><p><strong>y</strong> – Array with NumPy backend.</p>
-</dd>
-<dt class="field-odd">Return type<span class="colon">:</span></dt>
-<dd class="field-odd"><p><a class="reference internal" href="../info.ptype.html#pyxu.info.ptype.NDArray" title="pyxu.info.ptype.NDArray"><code class="xref py py-class docutils literal notranslate"><span class="pre">NDArray</span></code></a></p>
-</dd>
-</dl>
-<p class="rubric">Notes</p>
-<p>This function is a no-op if the array is already a NumPy array.</p>
-</dd></dl>
+
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.misc.peaks">
 <span class="sig-name descname"><span class="pre">peaks</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#peaks"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.misc.peaks" title="Link to this definition">#</a></dt>
@@ -467,22 +644,23 @@ <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to th
 </dd>
 </dl>
 <p class="rubric">Examples</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a>
-
-<span class="n">x</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linspace.html#numpy.linspace" title="numpy.linspace"><span class="n">np</span><span class="o">.</span><span class="n">linspace</span></a><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
-<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="n">z</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.peaks" title="pyxu.util.misc.peaks"><span class="n">peaks</span></a><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">z</span><span class="p">)</span>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <span class="n">peaks</span>
+
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
+<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
+<span class="n">z</span> <span class="o">=</span> <span class="n">peaks</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>(<a class="reference download internal" download="" href="../../_downloads/739ba029231bd1dda67ee36c2098ce61/misc-1.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/a8f55c09b56e805c33f3734d2271c8c8/misc-1.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/2314282464680aff6f1f1e0daaf707e5/misc-1.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/e86ae7ff57577dab32fe27b228573552/misc-1.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
 <figure class="align-default">
-<img alt="../../_images/misc-1.png" class="plot-directive" src="../../_images/misc-1.png"/>
+<img alt="../../_images/misc-1.png" class="plot-directive" src="../../_images/misc-1.png" />
 </figure>
 </dd></dl>
+
 <dl class="py function">
 <dt class="sig sig-object py" id="pyxu.util.misc.star_like_sample">
 <span class="sig-name descname"><span class="pre">star_like_sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">N</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">w</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">po</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">NDArrayInfo.NUMPY</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../_modules/pyxu/util/misc.html#star_like_sample"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pyxu.util.misc.star_like_sample" title="Link to this definition">#</a></dt>
@@ -509,52 +687,70 @@ <h1>pyxu.util.misc<a class="headerlink" href="#pyxu-util-misc" title="Link to th
 </dd>
 </dl>
 <p class="rubric">Examples</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/pyplot_summary.html#module-matplotlib.pyplot" title="matplotlib.pyplot"><span class="nn">matplotlib.pyplot</span></a> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.star_like_sample" title="pyxu.util.misc.star_like_sample"><span class="n">star_like_sample</span></a>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">pyxu.util.misc</span> <span class="kn">import</span> <span class="n">star_like_sample</span>
 
-<span class="n">star</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../../api/util/misc.html#pyxu.util.misc.star_like_sample" title="pyxu.util.misc.star_like_sample"><span class="n">star_like_sample</span></a><span class="p">(</span><span class="n">N</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mi">8</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">po</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">()</span>
-<a class="sphinx-codeautolink-a" href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">star</span><span class="p">)</span>
+<span class="n">star</span> <span class="o">=</span> <span class="n">star_like_sample</span><span class="p">(</span><span class="n">N</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span> <span class="n">w</span><span class="o">=</span><span class="mi">8</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">po</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">x0</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">star</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>(<a class="reference download internal" download="" href="../../_downloads/382f1aebcc11e28238e392f33afc5648/misc-2.py"><code class="xref download docutils literal notranslate"><span class="pre">Source</span> <span class="pre">code</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/3eb5f1c9b5d6c13bf16aab3a100d09ad/misc-2.png"><code class="xref download docutils literal notranslate"><span class="pre">png</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/07525e45c4a11f5c1ae9fa67095152b3/misc-2.hires.png"><code class="xref download docutils literal notranslate"><span class="pre">hires.png</span></code></a>, <a class="reference download internal" download="" href="../../_downloads/2e7add4265c7fc537212f569e3f61c7f/misc-2.pdf"><code class="xref download docutils literal notranslate"><span class="pre">pdf</span></code></a>)</p>
 <figure class="align-default">
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+<li aria-current="page" class="breadcrumb-item active">Using Contributed Plugins in Pyxu</li>
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+<article class="bd-article" role="main">
+<section id="Using-Contributed-Plugins-in-Pyxu">
+<h1>Using Contributed Plugins in Pyxu<a class="headerlink" href="#Using-Contributed-Plugins-in-Pyxu" title="Link to this heading">#</a></h1>
+<p>In this notebook, we will explore how to use contributed plugins in the Pyxu software framework. We will focus on the <code class="docutils literal notranslate"><span class="pre">pyxu-gradient-descent</span></code> plugin.</p>
+<section id="Step-1:-Attempting-to-Import-Before-Installation">
+<h2>Step 1: Attempting to Import Before Installation<a class="headerlink" href="#Step-1:-Attempting-to-Import-Before-Installation" title="Link to this heading">#</a></h2>
+<p>Before installing the plugin, let’s try importing an object from the <code class="docutils literal notranslate"><span class="pre">pyxu-gradient-descent</span></code> namespace to see what happens.</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
+    <span class="kn">from</span> <span class="nn">pyxu.opt.solver</span> <span class="kn">import</span> <span class="n">GradientDescent</span>
+<span class="k">except</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/exceptions.html#ImportError" title="ImportError"><span class="ne">ImportError</span></a> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
+    <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#print" title="print"><span class="nb">print</span></a><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</pre></div>
+</div>
+<div style="border:1px solid #ccc; padding: 10px; background-color: #f9f9f9; font-family: monospace;"><p>cannot import name ‘GradientDescent’ from ‘pyxu.opt.solver’ (pyxu/opt/solver/<strong>init</strong>.py)</p>
+</div><p>You should see an <em>ImportError</em>, indicating that the objects are not available because the plugin is not installed yet.</p>
+</section>
+<section id="Step-2:-Installing-the-Plugin">
+<h2>Step 2: Installing the Plugin<a class="headerlink" href="#Step-2:-Installing-the-Plugin" title="Link to this heading">#</a></h2>
+<p>To install the pyxu-gradient-descent plugin, use the following magic command:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="err">!</span><span class="n">pip</span> <span class="n">install</span> <span class="n">pyxu</span><span class="o">-</span><span class="n">gradient</span><span class="o">-</span><span class="n">descent</span>
+</pre></div>
+</div>
+</section>
+<section id="Step-3:-Importing-the-Necessary-Objects">
+<h2>Step 3: Importing the Necessary Objects<a class="headerlink" href="#Step-3:-Importing-the-Necessary-Objects" title="Link to this heading">#</a></h2>
+<p>Now that we have installed the plugin, let’s import the necessary objects:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.operator</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.SquaredL2Norm" title="pyxu.operator.func.norm.SquaredL2Norm"><span class="n">SquaredL2Norm</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.opt.solver</span> <span class="kn">import</span> <span class="n">GradientDescent</span>
+<span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
+</pre></div>
+</div>
+<div style=" padding: 10px; background-color: #ffe6e6;"><p>pyxu/info/plugin.py:69: ContributionWarning: Plugin <code class="docutils literal notranslate"><span class="pre">GradientDescent</span></code> loaded, use with caution. warnings.warn(f”Plugin <code class="docutils literal notranslate"><span class="pre">{name}</span></code> loaded, use with caution.”, pxw.ContributionWarning)</p>
+</div><p>The warning signals that a class or function has been imported from external code into the core Pyxu codebase, and should be used with caution.</p>
+</section>
+<section id="Step-4:-Using-the-Gradient-Descent-Algorithm">
+<h2>Step 4: Using the Gradient Descent Algorithm<a class="headerlink" href="#Step-4:-Using-the-Gradient-Descent-Algorithm" title="Link to this heading">#</a></h2>
+<p>In this step, we will use the gradient descent algorithm to minimize a function defined by the squared L2 norm. Here is how you can do it:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Define the dimension</span>
+<span class="n">N</span> <span class="o">=</span> <span class="mi">100</span>
+
+<span class="c1"># Generate random data</span>
+<span class="n">rng</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/random/generator.html#numpy.random.default_rng" title="numpy.random.default_rng"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span></a><span class="p">(</span><span class="n">seed</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">N</span><span class="p">)</span>
+
+<span class="c1"># Define the loss function</span>
+<span class="n">loss</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator/func.html#pyxu.operator.SquaredL2Norm" title="pyxu.operator.func.norm.SquaredL2Norm"><span class="n">SquaredL2Norm</span></a><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="n">N</span><span class="p">)</span><span class="o">.</span><span class="n">asloss</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
+
+<span class="c1"># Initialize the gradient descent algorithm</span>
+<span class="n">gd</span> <span class="o">=</span> <span class="n">GradientDescent</span><span class="p">(</span><span class="n">f</span><span class="o">=</span><span class="n">loss</span><span class="p">)</span>
+
+<span class="c1"># Define the initial point</span>
+<span class="n">x0</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><span class="n">N</span><span class="p">)</span>
+
+<span class="c1"># Run the gradient descent algorithm</span>
+<span class="n">gd</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">x0</span><span class="o">=</span><span class="n">x0</span><span class="p">,</span> <span class="n">acceleration</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+
+<span class="c1"># Check the solution</span>
+<span class="k">assert</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.allclose.html#numpy.allclose" title="numpy.allclose"><span class="n">np</span><span class="o">.</span><span class="n">allclose</span></a><span class="p">(</span><span class="n">gd</span><span class="o">.</span><span class="n">solution</span><span class="p">(),</span> <span class="n">y</span><span class="p">)</span>
+</pre></div>
+</div>
+<div style="border:1px solid #ccc; padding: 10px; background-color: #f9f9f9; font-family: monospace;"><p>INFO – [2023-09-13 09:28:52.933466] Iteration 0</p>
+<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>iteration: 0
+RelError[x]: 0.0
+</pre></div>
+</div>
+<p>INFO – [2023-09-13 09:28:52.934287] Iteration 1</p>
+<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>iteration: 1
+RelError[x]: 1.1798071385920126
+</pre></div>
+</div>
+<p>INFO – [2023-09-13 09:28:52.934882] Iteration 2</p>
+<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>iteration: 2
+RelError[x]: 9.55411637565644e-17
+</pre></div>
+</div>
+<p>INFO – [2023-09-13 09:28:52.935515] Stopping Criterion satisfied -&gt; END</p>
+</div><p>If everything runs without errors, it means that the gradient descent algorithm has successfully found a solution that is close to the input data.</p>
+</section>
+<section id="Conclusion">
+<h2>Conclusion<a class="headerlink" href="#Conclusion" title="Link to this heading">#</a></h2>
+<p>In this notebook, we have seen how to use contributed plugins in the Pyxu software framework. We learned how to install a plugin and use it to run a gradient descent algorithm. We hope this guide has been helpful, and encourage you to explore other plugins available for the Pyxu framework.</p>
+</section>
+</section>
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+<ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Step-1:-Attempting-to-Import-Before-Installation">Step 1: Attempting to Import Before Installation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Step-2:-Installing-the-Plugin">Step 2: Installing the Plugin</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Step-3:-Importing-the-Necessary-Objects">Step 3: Importing the Necessary Objects</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Step-4:-Using-the-Gradient-Descent-Algorithm">Step 4: Using the Gradient Descent Algorithm</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Conclusion">Conclusion</a></li>
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+      © Copyright 2023, M. Simeoni, S. Kashani, J. Rué-Queralt &amp; Pyxu Developers.
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+<div class="footer-item">
+<p class="sphinx-version">
+     Created with <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5, with some help from <a href="https://chat.openai.com/"> ChatGPT</a> (GPT 4).
+    <br/>
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+<div class="footer-item"><p class="theme-version">
+  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
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diff --git a/examples/contributing.ipynb b/examples/contributing.ipynb
new file mode 100644
index 00000000..817f3fd3
--- /dev/null
+++ b/examples/contributing.ipynb
@@ -0,0 +1,134 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "92ed2e98",
+   "metadata": {},
+   "source": [
+    "# Using Contributed Plugins in Pyxu\n",
+    "\n",
+    "In this notebook, we will explore how to use contributed plugins in the Pyxu software framework. We will focus on the `pyxu-gradient-descent` plugin. \n",
+    "\n",
+    "## Step 1: Attempting to Import Before Installation\n",
+    "\n",
+    "Before installing the plugin, let's try importing an object from the `pyxu-gradient-descent` namespace to see what happens.\n",
+    "```python\n",
+    "try:\n",
+    "    from pyxu.opt.solver import GradientDescent\n",
+    "except ImportError as e:\n",
+    "    print(e)\n",
+    "```\n",
+    "\n",
+    "<div style=\"border:1px solid #ccc; padding: 10px; background-color: #f9f9f9; font-family: monospace;\">\n",
+    "\n",
+    "cannot import name 'GradientDescent' from 'pyxu.opt.solver' (pyxu/opt/solver/__init__.py)\n",
+    "\n",
+    "    \n",
+    "</div>\n",
+    "\n",
+    "\n",
+    "You should see an *ImportError*, indicating that the objects are not available because the plugin is not installed yet.\n",
+    "\n",
+    "## Step 2: Installing the Plugin\n",
+    "\n",
+    "To install the pyxu-gradient-descent plugin, use the following magic command:\n",
+    "\n",
+    "```python\n",
+    "!pip install pyxu-gradient-descent\n",
+    "```\n",
+    "\n",
+    "## Step 3: Importing the Necessary Objects\n",
+    "\n",
+    "Now that we have installed the plugin, let's import the necessary objects:\n",
+    "\n",
+    "```python\n",
+    "from pyxu.operator import SquaredL2Norm\n",
+    "from pyxu.opt.solver import GradientDescent\n",
+    "import numpy as np\n",
+    "```\n",
+    "<div style=\" padding: 10px; background-color: #ffe6e6;\">\n",
+    "pyxu/info/plugin.py:69: ContributionWarning: Plugin `GradientDescent` loaded, use with caution.\n",
+    "  warnings.warn(f\"Plugin `{name}` loaded, use with caution.\", pxw.ContributionWarning)\n",
+    "</div>\n",
+    "\n",
+    "The warning signals that a class or function has been imported from external code into the core Pyxu codebase, and should be used with caution. \n",
+    "\n",
+    "## Step 4: Using the Gradient Descent Algorithm\n",
+    "\n",
+    "In this step, we will use the gradient descent algorithm to minimize a function defined by the squared L2 norm. Here is how you can do it:\n",
+    "\n",
+    "```python\n",
+    "# Define the dimension\n",
+    "N = 100\n",
+    "\n",
+    "# Generate random data\n",
+    "rng = np.random.default_rng(seed=0)\n",
+    "y = rng.uniform(size=N)\n",
+    "\n",
+    "# Define the loss function\n",
+    "loss = SquaredL2Norm(dim=N).asloss(y)\n",
+    "\n",
+    "# Initialize the gradient descent algorithm\n",
+    "gd = GradientDescent(f=loss)\n",
+    "\n",
+    "# Define the initial point\n",
+    "x0 = np.random.randn(N)\n",
+    "\n",
+    "# Run the gradient descent algorithm\n",
+    "gd.fit(x0=x0, acceleration=True)\n",
+    "\n",
+    "# Check the solution\n",
+    "assert np.allclose(gd.solution(), y)\n",
+    "```\n",
+    "<div style=\"border:1px solid #ccc; padding: 10px; background-color: #f9f9f9; font-family: monospace;\">\n",
+    "\n",
+    "INFO -- [2023-09-13 09:28:52.933466] Iteration 0\n",
+    "    \n",
+    "\titeration: 0\n",
+    "    RelError[x]: 0.0\n",
+    "\n",
+    "INFO -- [2023-09-13 09:28:52.934287] Iteration 1\n",
+    "\n",
+    "    iteration: 1\n",
+    "    RelError[x]: 1.1798071385920126\n",
+    "\n",
+    "INFO -- [2023-09-13 09:28:52.934882] Iteration 2\n",
+    "\n",
+    "    iteration: 2\n",
+    "    RelError[x]: 9.55411637565644e-17\n",
+    "\n",
+    "INFO -- [2023-09-13 09:28:52.935515] Stopping Criterion satisfied -> END\n",
+    "\n",
+    "</div>\n",
+    "\n",
+    "\n",
+    "If everything runs without errors, it means that the gradient descent algorithm has successfully found a solution that is close to the input data.\n",
+    "\n",
+    "## Conclusion\n",
+    "\n",
+    "In this notebook, we have seen how to use contributed plugins in the Pyxu software framework. We learned how to install a plugin and use it to run a gradient descent algorithm. We hope this guide has been helpful, and encourage you to explore other plugins available for the Pyxu framework."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/examples/index.html b/examples/index.html
index 7abdc067..68c9c467 100644
--- a/examples/index.html
+++ b/examples/index.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -39,13 +39,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
     <link rel="stylesheet" type="text/css" href="../_static/nbsphinx-gallery.css?v=26227f6e" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -62,8 +62,8 @@
     <link rel="icon" href="../_static/favicon.png"/>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
-    <link rel="next" title="Convolution with Pyxu" href="Stencils.html" />
-    <link rel="prev" title="High Performance Computing Features" href="../guide/hpc.html" />
+    <link rel="next" title="Using Contributed Plugins in Pyxu" href="contributing.html" />
+    <link rel="prev" title="Differential Operators in Pyxu" href="../guide/diff_ops.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
   <meta name="docsearch:language" content="en"/>
   </head>
@@ -407,8 +407,8 @@
      aria-label="Section Navigation">
   <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
   <div class="bd-toc-item navbar-nav"><ul class="nav bd-sidenav">
-<li class="toctree-l1"><a class="reference internal" href="Stencils.html">Convolution with Pyxu</a></li>
-<li class="toctree-l1"><a class="reference internal" href="DifferentialOperators.html">Differential operators in Pyxu</a></li>
+<li class="toctree-l1"><a class="reference internal" href="contributing.html">Using Contributed Plugins in Pyxu</a></li>
+<li class="toctree-l1"><a class="reference internal" href="stencils.html">Convolution with Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
@@ -467,14 +467,10 @@
 <h1>Example Gallery<a class="headerlink" href="#example-gallery" title="Link to this heading">#</a></h1>
 <div class="toctree-wrapper compound" id="rst-link-gallery">
 <div class="nbsphinx-gallery">
-<a class="reference internal" href="Stencils.html">
-  <div><img alt="" src="../_images/examples_Stencils_28_0.png"></div>
+<a class="reference internal" href="stencils.html">
+  <div><img alt="" src="../_images/examples_stencils_28_0.png"></div>
   <div>Convolution with Pyxu</div>
 </a>
-<a class="reference internal" href="DifferentialOperators.html">
-  <div><img alt="" src="../_images/examples_DifferentialOperators_34_0.png"></div>
-  <div>Differential operators in Pyxu</div>
-</a>
 </div>
 </div>
 <div class="toctree-wrapper compound">
@@ -493,20 +489,20 @@ <h1>Example Gallery<a class="headerlink" href="#example-gallery" title="Link to
     <div class="footer-article-item"><!-- Previous / next buttons -->
 <div class="prev-next-area">
     <a class="left-prev"
-       href="../guide/hpc.html"
+       href="../guide/diff_ops.html"
        title="previous page">
       <i class="fa-solid fa-angle-left"></i>
       <div class="prev-next-info">
         <p class="prev-next-subtitle">previous</p>
-        <p class="prev-next-title">High Performance Computing Features</p>
+        <p class="prev-next-title">Differential Operators in Pyxu</p>
       </div>
     </a>
     <a class="right-next"
-       href="Stencils.html"
+       href="contributing.html"
        title="next page">
       <div class="prev-next-info">
         <p class="prev-next-subtitle">next</p>
-        <p class="prev-next-title">Convolution with Pyxu</p>
+        <p class="prev-next-title">Using Contributed Plugins in Pyxu</p>
       </div>
       <i class="fa-solid fa-angle-right"></i>
     </a>
diff --git a/examples/Stencils.html b/examples/stencils.html
similarity index 94%
rename from examples/Stencils.html
rename to examples/stencils.html
index 56561365..b4eed9bb 100644
--- a/examples/Stencils.html
+++ b/examples/stencils.html
@@ -18,7 +18,7 @@
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" rel="preload" type="font/woff2"/>
-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
 <link href="../_static/sphinx-codeautolink.css?v=125d5c1c" rel="stylesheet" type="text/css"/>
 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -29,11 +29,11 @@
 <link href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" rel="stylesheet" type="text/css"/>
 <link href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" rel="stylesheet" type="text/css"/>
 <link href="../_static/nbsphinx-code-cells.css?v=2aa19091" rel="stylesheet" type="text/css"/>
-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
 <!-- Pre-loaded scripts that we'll load fully later -->
 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
 <link as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" rel="preload"/>
-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
 <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -48,12 +48,12 @@
 <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
 <script>window.MathJax = {"tex": {"inlineMath": [["$", "$"], ["\\(", "\\)"]], "processEscapes": true}, "options": {"ignoreHtmlClass": "tex2jax_ignore|mathjax_ignore|document", "processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
 <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
-<script>DOCUMENTATION_OPTIONS.pagename = 'examples/Stencils';</script>
+<script>DOCUMENTATION_OPTIONS.pagename = 'examples/stencils';</script>
 <link href="../_static/favicon.png" rel="icon"/>
 <link href="../genindex.html" rel="index" title="Index"/>
 <link href="../search.html" rel="search" title="Search"/>
-<link href="DifferentialOperators.html" rel="next" title="Differential operators in Pyxu"/>
-<link href="index.html" rel="prev" title="Example Gallery"/>
+<link href="../api/index.html" rel="next" title="API Reference"/>
+<link href="contributing.html" rel="prev" title="Using Contributed Plugins in Pyxu"/>
 <meta content="width=device-width, initial-scale=1" name="viewport"/>
 <meta content="en" name="docsearch:language"/>
 </head>
@@ -226,8 +226,8 @@
 <div class="sidebar-primary-item"><nav aria-label="Section Navigation" class="bd-docs-nav bd-links">
 <p aria-level="1" class="bd-links__title" role="heading">Section Navigation</p>
 <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="contributing.html">Using Contributed Plugins in Pyxu</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">Convolution with Pyxu</a></li>
-<li class="toctree-l1"><a class="reference internal" href="DifferentialOperators.html">Differential operators in Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
@@ -343,7 +343,7 @@ <h3>Create blurring kernel<a class="headerlink" href="#Create-blurring-kernel" t
 <div class="prompt empty docutils container">
 </div>
 <div class="output_area docutils container">
-<img alt="../_images/examples_Stencils_9_0.png" src="../_images/examples_Stencils_9_0.png"/>
+<img alt="../_images/examples_stencils_9_0.png" src="../_images/examples_stencils_9_0.png"/>
 </div>
 </div>
 </section>
@@ -429,7 +429,7 @@ <h3>PyLops<a class="headerlink" href="#PyLops" title="Link to this heading">#</a
 
 <span class="c1"># 2d convolution</span>
 <span class="n">conv_pylops</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.interop.html#pyxu.operator.interop.from_sciop" title="pyxu.operator.interop.from_sciop"><span class="n">from_sciop</span></a><span class="p">(</span>
-    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
+    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
     <span class="n">sp_op</span><span class="o">=</span><span class="n">Convolve2D</span><span class="p">(</span>
         <span class="n">dims</span><span class="o">=</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
         <span class="n">h</span><span class="o">=</span><span class="n">kernel_2d</span><span class="p">,</span>
@@ -449,7 +449,7 @@ <h3>PyLops<a class="headerlink" href="#PyLops" title="Link to this heading">#</a
 </div>
 <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Separable convolution</span>
 <span class="n">conv_pylops_rows</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.interop.html#pyxu.operator.interop.from_sciop" title="pyxu.operator.interop.from_sciop"><span class="n">from_sciop</span></a><span class="p">(</span>
-    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
+    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
     <span class="n">sp_op</span><span class="o">=</span><span class="n">Convolve2D</span><span class="p">(</span>
         <span class="n">dims</span><span class="o">=</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
         <span class="n">h</span><span class="o">=</span><span class="n">kernel_1d</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:],</span>
@@ -459,7 +459,7 @@ <h3>PyLops<a class="headerlink" href="#PyLops" title="Link to this heading">#</a
     <span class="p">),</span>
 <span class="p">)</span>
 <span class="n">conv_pylops_cols</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.interop.html#pyxu.operator.interop.from_sciop" title="pyxu.operator.interop.from_sciop"><span class="n">from_sciop</span></a><span class="p">(</span>
-    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
+    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
     <span class="n">sp_op</span><span class="o">=</span><span class="n">Convolve2D</span><span class="p">(</span>
         <span class="n">dims</span><span class="o">=</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
         <span class="n">h</span><span class="o">=</span><span class="n">kernel_1d</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span>
@@ -488,19 +488,19 @@ <h3>Scico<a class="headerlink" href="#Scico" title="Link to this heading">#</a><
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/jax.numpy.html#module-jax.numpy" title="jax.numpy"><span class="nn">jax.numpy</span></a> <span class="k">as</span> <span class="nn">jnp</span>
 
 <span class="c1"># Convert data and kernel from Numpy to Jax</span>
-<span class="n">data_jax</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">data</span><span class="p">)</span>
-<span class="n">k2d_jax</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">kernel_2d</span><span class="p">)</span>
+<a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">data_jax</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+<a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">k2d_jax</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">kernel_2d</span><span class="p">)</span>
 <span class="n">config</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="s2">"jax_enable_x64"</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
 
 <span class="c1"># 2d convolution</span>
 <span class="n">conv_scico</span> <span class="o">=</span> <span class="n">Conv_scico</span><span class="p">(</span>
-    <span class="n">k2d_jax</span><span class="p">,</span>
+    <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">k2d_jax</span></a><span class="p">,</span>
     <span class="n">input_shape</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
     <span class="n">input_dtype</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span>
     <span class="n">mode</span><span class="o">=</span><span class="s2">"same"</span><span class="p">,</span>
     <span class="n">jit</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
 <span class="p">)</span>
-<span class="n">y_scico</span> <span class="o">=</span> <span class="n">conv_scico</span><span class="p">(</span><span class="n">data_jax</span><span class="p">)</span>
+<span class="n">y_scico</span> <span class="o">=</span> <span class="n">conv_scico</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">data_jax</span></a><span class="p">)</span>
 <span class="k">assert</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.allclose.html#numpy.allclose" title="numpy.allclose"><span class="n">np</span><span class="o">.</span><span class="n">allclose</span></a><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">y_scico</span><span class="p">)</span>
 </pre></div>
 </div>
@@ -510,23 +510,23 @@ <h3>Scico<a class="headerlink" href="#Scico" title="Link to this heading">#</a><
 </pre></div>
 </div>
 <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Separable convolution</span>
-<span class="n">k1d_jax</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">kernel_1d</span><span class="p">)</span>
+<a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">k1d_jax</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">kernel_1d</span><span class="p">)</span>
 
 <span class="n">conv_scico_rows</span> <span class="o">=</span> <span class="n">Conv_scico</span><span class="p">(</span>
-    <span class="n">k1d_jax</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:],</span>
+    <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">k1d_jax</span></a><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:],</span>
     <span class="n">input_shape</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
     <span class="n">input_dtype</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span>
     <span class="n">mode</span><span class="o">=</span><span class="s2">"same"</span><span class="p">,</span>
     <span class="n">jit</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
 <span class="p">)</span>
 <span class="n">conv_scico_cols</span> <span class="o">=</span> <span class="n">Conv_scico</span><span class="p">(</span>
-    <span class="n">k1d_jax</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span>
+    <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">k1d_jax</span></a><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span>
     <span class="n">input_shape</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
     <span class="n">input_dtype</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span>
     <span class="n">mode</span><span class="o">=</span><span class="s2">"same"</span><span class="p">,</span>
     <span class="n">jit</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
 <span class="p">)</span>
-<span class="n">y_scico</span> <span class="o">=</span> <span class="n">conv_scico_cols</span><span class="p">(</span><span class="n">conv_scico_rows</span><span class="p">(</span><span class="n">data_jax</span><span class="p">))</span>
+<span class="n">y_scico</span> <span class="o">=</span> <span class="n">conv_scico_cols</span><span class="p">(</span><span class="n">conv_scico_rows</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">data_jax</span></a><span class="p">))</span>
 <span class="k">assert</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.allclose.html#numpy.allclose" title="numpy.allclose"><span class="n">np</span><span class="o">.</span><span class="n">allclose</span></a><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">y_scico</span><span class="p">)</span>
 </pre></div>
 </div>
@@ -567,8 +567,8 @@ <h3>Separable 1d convolution<a class="headerlink" href="#Separable-1d-convolutio
         <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">width</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#enumerate" title="enumerate"><span class="nb">enumerate</span></a><span class="p">(</span><span class="n">nwidths</span><span class="p">):</span>
             <span class="k">if</span> <span class="n">npix</span> <span class="o">&gt;</span> <span class="p">(</span><span class="n">width</span> <span class="o">*</span> <span class="mi">2</span><span class="p">):</span>
                 <span class="n">kernel</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.fromfunction.html#numpy.fromfunction" title="numpy.fromfunction"><span class="n">np</span><span class="o">.</span><span class="n">fromfunction</span></a><span class="p">(</span><span class="n">gauss</span><span class="p">,</span> <span class="p">(</span><span class="n">width</span><span class="p">,))</span>
-                <span class="n">data_jax</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">data</span><span class="p">)</span>
-                <span class="n">k1d_jax</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">kernel_1d</span><span class="p">)</span>
+                <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">data_jax</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+                <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">k1d_jax</span></a> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.asarray.html#jax.numpy.asarray" title="jax.numpy.asarray"><span class="n">jnp</span><span class="o">.</span><span class="n">asarray</span></a><span class="p">(</span><span class="n">kernel_1d</span><span class="p">)</span>
 
                 <span class="c1">## PYXU</span>
 
@@ -631,7 +631,7 @@ <h3>Separable 1d convolution<a class="headerlink" href="#Separable-1d-convolutio
                 <span class="c1"># Instantation + first run time</span>
                 <span class="n">tic</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/time.html#time.perf_counter" title="time.perf_counter"><span class="n">time</span><span class="o">.</span><span class="n">perf_counter</span></a><span class="p">()</span>
                 <span class="n">conv_pylops_rows</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.interop.html#pyxu.operator.interop.from_sciop" title="pyxu.operator.interop.from_sciop"><span class="n">from_sciop</span></a><span class="p">(</span>
-                    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
+                    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
                     <span class="n">sp_op</span><span class="o">=</span><span class="n">Convolve2D</span><span class="p">(</span>
                         <span class="n">dims</span><span class="o">=</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
                         <span class="n">h</span><span class="o">=</span><span class="n">kernel_1d</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:],</span>
@@ -641,7 +641,7 @@ <h3>Separable 1d convolution<a class="headerlink" href="#Separable-1d-convolutio
                     <span class="p">),</span>
                 <span class="p">)</span>
                 <span class="n">conv_pylops_cols</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.interop.html#pyxu.operator.interop.from_sciop" title="pyxu.operator.interop.from_sciop"><span class="n">from_sciop</span></a><span class="p">(</span>
-                    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
+                    <span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
                     <span class="n">sp_op</span><span class="o">=</span><span class="n">Convolve2D</span><span class="p">(</span>
                         <span class="n">dims</span><span class="o">=</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
                         <span class="n">h</span><span class="o">=</span><span class="n">kernel_1d</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span>
@@ -674,27 +674,27 @@ <h3>Separable 1d convolution<a class="headerlink" href="#Separable-1d-convolutio
                 <span class="n">config</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="s2">"jax_enable_x64"</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
 
                 <span class="n">conv_scico_rows</span> <span class="o">=</span> <span class="n">Conv_scico</span><span class="p">(</span>
-                    <span class="n">k1d_jax</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:],</span>
+                    <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">k1d_jax</span></a><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:],</span>
                     <span class="n">input_shape</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
                     <span class="n">input_dtype</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span>
                     <span class="n">mode</span><span class="o">=</span><span class="s2">"same"</span><span class="p">,</span>
                     <span class="n">jit</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
                 <span class="p">)</span>
                 <span class="n">conv_scico_cols</span> <span class="o">=</span> <span class="n">Conv_scico</span><span class="p">(</span>
-                    <span class="n">k1d_jax</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span>
+                    <a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">k1d_jax</span></a><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">],</span>
                     <span class="n">input_shape</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span>
                     <span class="n">input_dtype</span><span class="o">=</span><span class="n">data_jax</span><span class="o">.</span><span class="n">dtype</span><span class="p">,</span>
                     <span class="n">mode</span><span class="o">=</span><span class="s2">"same"</span><span class="p">,</span>
                     <span class="n">jit</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
                 <span class="p">)</span>
-                <span class="n">y_scico</span> <span class="o">=</span> <span class="n">conv_scico_cols</span><span class="p">(</span><span class="n">conv_scico_rows</span><span class="p">(</span><span class="n">data_jax</span><span class="p">))</span>
+                <span class="n">y_scico</span> <span class="o">=</span> <span class="n">conv_scico_cols</span><span class="p">(</span><span class="n">conv_scico_rows</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">data_jax</span></a><span class="p">))</span>
                 <span class="n">t_scico</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/time.html#time.perf_counter" title="time.perf_counter"><span class="n">time</span><span class="o">.</span><span class="n">perf_counter</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">tic</span>
 
                 <span class="c1"># Run time</span>
                 <span class="n">times</span> <span class="o">=</span> <span class="mi">0</span>
                 <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#range" title="range"><span class="nb">range</span></a><span class="p">(</span><span class="n">nreps</span><span class="p">):</span>
                     <span class="n">tic</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/time.html#time.perf_counter" title="time.perf_counter"><span class="n">time</span><span class="o">.</span><span class="n">perf_counter</span></a><span class="p">()</span>
-                    <span class="n">y_scico</span> <span class="o">=</span> <span class="n">conv_scico_cols</span><span class="p">(</span><span class="n">conv_scico_rows</span><span class="p">(</span><span class="n">data_jax</span><span class="p">))</span>
+                    <span class="n">y_scico</span> <span class="o">=</span> <span class="n">conv_scico_cols</span><span class="p">(</span><span class="n">conv_scico_rows</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://jax.readthedocs.io/en/latest/_autosummary/jax.Array.html#jax.Array" title="jax.Array"><span class="n">data_jax</span></a><span class="p">))</span>
                     <span class="n">times</span> <span class="o">+=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/time.html#time.perf_counter" title="time.perf_counter"><span class="n">time</span><span class="o">.</span><span class="n">perf_counter</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">tic</span>
                 <span class="n">t_scico</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">times</span> <span class="o">/</span> <span class="n">nreps</span>
             <span class="n">pbar</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
@@ -766,7 +766,7 @@ <h3>Separable 1d convolution<a class="headerlink" href="#Separable-1d-convolutio
 <div class="prompt empty docutils container">
 </div>
 <div class="output_area docutils container">
-<img alt="../_images/examples_Stencils_26_0.png" src="../_images/examples_Stencils_26_0.png"/>
+<img alt="../_images/examples_stencils_26_0.png" src="../_images/examples_stencils_26_0.png"/>
 </div>
 </div>
 </section>
@@ -830,7 +830,7 @@ <h3>Direct 2d convolution<a class="headerlink" href="#Direct-2d-convolution" tit
 <div class="prompt empty docutils container">
 </div>
 <div class="output_area docutils container">
-<img alt="../_images/examples_Stencils_28_0.png" src="../_images/examples_Stencils_28_0.png"/>
+<img alt="../_images/examples_stencils_28_0.png" src="../_images/examples_stencils_28_0.png"/>
 </div>
 </div>
 </section>
@@ -841,17 +841,17 @@ <h3>Direct 2d convolution<a class="headerlink" href="#Direct-2d-convolution" tit
 <div class="footer-article-items footer-article__inner">
 <div class="footer-article-item"><!-- Previous / next buttons -->
 <div class="prev-next-area">
-<a class="left-prev" href="index.html" title="previous page">
+<a class="left-prev" href="contributing.html" title="previous page">
 <i class="fa-solid fa-angle-left"></i>
 <div class="prev-next-info">
 <p class="prev-next-subtitle">previous</p>
-<p class="prev-next-title">Example Gallery</p>
+<p class="prev-next-title">Using Contributed Plugins in Pyxu</p>
 </div>
 </a>
-<a class="right-next" href="DifferentialOperators.html" title="next page">
+<a class="right-next" href="../api/index.html" title="next page">
 <div class="prev-next-info">
 <p class="prev-next-subtitle">next</p>
-<p class="prev-next-title">Differential operators in Pyxu</p>
+<p class="prev-next-title">API Reference</p>
 </div>
 <i class="fa-solid fa-angle-right"></i>
 </a>
@@ -890,7 +890,7 @@ <h3>Direct 2d convolution<a class="headerlink" href="#Direct-2d-convolution" tit
 <div id="searchbox"></div></div>
 <div class="sidebar-secondary-item">
 <div class="tocsection editthispage">
-<a href="https://github.com/matthieumeo/pyxu/edit/main/doc/examples/Stencils.ipynb">
+<a href="https://github.com/matthieumeo/pyxu/edit/main/doc/examples/stencils.ipynb">
 <i class="fa-solid fa-pencil"></i>
       
       
@@ -903,7 +903,7 @@ <h3>Direct 2d convolution<a class="headerlink" href="#Direct-2d-convolution" tit
 </div>
 <div class="sidebar-secondary-item">
 <div class="tocsection sourcelink">
-<a href="../_sources/examples/Stencils.ipynb">
+<a href="../_sources/examples/stencils.ipynb">
 <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
 </div>
diff --git a/examples/Stencils.ipynb b/examples/stencils.ipynb
similarity index 100%
rename from examples/Stencils.ipynb
rename to examples/stencils.ipynb
diff --git a/fair/.DS_Store b/fair/.DS_Store
deleted file mode 100644
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GIT binary patch
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diff --git a/fair/contribute.html b/fair/contribute.html
index 897ffbcc..e6b9c540 100644
--- a/fair/contribute.html
+++ b/fair/contribute.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -410,24 +410,29 @@
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Plugin Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="plugins/CSEEG.html">CSEEG</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/DSP-Notebooks.html">DSP-Notebooks</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/EnvironTracker.html">EnvironTracker</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HoughDetector.html">HoughDetector</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HVOX.html">HVOX</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/OrientationPy.html">OrientationPy</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/Palentologist.html">Palentologist</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PhaseRet.html">PhaseRet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycGSP.html">PycGSP</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycNUFFT.html">pycNUFFT</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycSphere.html">PycSphere</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycWavelet.html">pycWavelet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PYFW.html">PYFW</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TokemakRec.html">TokemakRec</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TVDenoiser.html">TVDenoiser</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/UncertaintyQuant.html">UncertaintyQuant</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/WaveProp.html">WaveProp</a></li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins_preview/index.html">Plugin Preview Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/CSEEG.html">CSEEG</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/DSP-Notebooks.html">DSP-Notebooks</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/EnvironTracker.html">EnvironTracker</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HoughDetector.html">HoughDetector</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HVOX.html">HVOX</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/OrientationPy.html">OrientationPy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/Palentologist.html">Palentologist</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PhaseRet.html">PhaseRet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycGSP.html">PycGSP</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycNUFFT.html">pycNUFFT</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycSphere.html">PycSphere</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycWavelet.html">pycWavelet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PYFW.html">PYFW</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TokemakRec.html">TokemakRec</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TVDenoiser.html">TVDenoiser</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/UncertaintyQuant.html">UncertaintyQuant</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/WaveProp.html">WaveProp</a></li>
 </ul>
 </li>
 </ul>
diff --git a/fair/dev_notes.html b/fair/dev_notes.html
index 4b6b923f..a259943d 100644
--- a/fair/dev_notes.html
+++ b/fair/dev_notes.html
@@ -28,7 +28,7 @@
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-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
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     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -410,24 +410,29 @@
 <li class="toctree-l1"><a class="reference internal" href="contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Plugin Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="plugins/CSEEG.html">CSEEG</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/DSP-Notebooks.html">DSP-Notebooks</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/EnvironTracker.html">EnvironTracker</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HoughDetector.html">HoughDetector</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HVOX.html">HVOX</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/OrientationPy.html">OrientationPy</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/Palentologist.html">Palentologist</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PhaseRet.html">PhaseRet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycGSP.html">PycGSP</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycNUFFT.html">pycNUFFT</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycSphere.html">PycSphere</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycWavelet.html">pycWavelet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PYFW.html">PYFW</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TokemakRec.html">TokemakRec</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TVDenoiser.html">TVDenoiser</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/UncertaintyQuant.html">UncertaintyQuant</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/WaveProp.html">WaveProp</a></li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins_preview/index.html">Plugin Preview Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/CSEEG.html">CSEEG</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/DSP-Notebooks.html">DSP-Notebooks</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/EnvironTracker.html">EnvironTracker</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HoughDetector.html">HoughDetector</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HVOX.html">HVOX</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/OrientationPy.html">OrientationPy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/Palentologist.html">Palentologist</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PhaseRet.html">PhaseRet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycGSP.html">PycGSP</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycNUFFT.html">pycNUFFT</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycSphere.html">PycSphere</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycWavelet.html">pycWavelet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PYFW.html">PYFW</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TokemakRec.html">TokemakRec</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TVDenoiser.html">TVDenoiser</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/UncertaintyQuant.html">UncertaintyQuant</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/WaveProp.html">WaveProp</a></li>
 </ul>
 </li>
 </ul>
@@ -492,9 +497,9 @@ <h1>Developer Notes<a class="headerlink" href="#developer-notes" title="Link to
 <section id="api-rules">
 <h2>API Rules<a class="headerlink" href="#api-rules" title="Link to this heading">#</a></h2>
 <p>To implement novel operators or algorithms, users must subclass an abstract base class from Pyxu’s
-<a class="reference internal" href="../api/abc/operator.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> hierarchy. Doing so requires defining the fundamental methods attached to the subclass
-(e.g. <a class="reference internal" href="../api/abc/operator.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>, <a class="reference internal" href="../api/abc/operator.html#pyxu.abc.DiffFunc.grad" title="pyxu.abc.DiffFunc.grad"><code class="xref py py-meth docutils literal notranslate"><span class="pre">grad()</span></code></a>, <a class="reference internal" href="../api/abc/operator.html#pyxu.abc.ProxFunc.prox" title="pyxu.abc.ProxFunc.prox"><code class="xref py py-meth docutils literal notranslate"><span class="pre">prox()</span></code></a>,
-<a class="reference internal" href="../api/abc/operator.html#pyxu.abc.LinOp.adjoint" title="pyxu.abc.LinOp.adjoint"><code class="xref py py-meth docutils literal notranslate"><span class="pre">adjoint()</span></code></a>, …). When marked as such in the documentation, such a user-defined method should
+<a class="reference internal" href="../api/abc.html#pyxu.abc.Operator" title="pyxu.abc.Operator"><code class="xref py py-class docutils literal notranslate"><span class="pre">Operator</span></code></a> hierarchy. Doing so requires defining the fundamental methods attached to the subclass
+(e.g. <a class="reference internal" href="../api/abc.html#pyxu.abc.Map.apply" title="pyxu.abc.Map.apply"><code class="xref py py-meth docutils literal notranslate"><span class="pre">apply()</span></code></a>, <a class="reference internal" href="../api/abc.html#pyxu.abc.DiffFunc.grad" title="pyxu.abc.DiffFunc.grad"><code class="xref py py-meth docutils literal notranslate"><span class="pre">grad()</span></code></a>, <a class="reference internal" href="../api/abc.html#pyxu.abc.ProxFunc.prox" title="pyxu.abc.ProxFunc.prox"><code class="xref py py-meth docutils literal notranslate"><span class="pre">prox()</span></code></a>,
+<a class="reference internal" href="../api/abc.html#pyxu.abc.LinOp.adjoint" title="pyxu.abc.LinOp.adjoint"><code class="xref py py-meth docutils literal notranslate"><span class="pre">adjoint()</span></code></a>, …). When marked as such in the documentation, such a user-defined method should
 abide by the following set of rules:</p>
 <ul class="simple">
 <li><p>It must handle properly the case where the input array is a 1-D or N-D array. In the latter case, the  first N-1
@@ -506,7 +511,7 @@ <h2>API Rules<a class="headerlink" href="#api-rules" title="Link to this heading
 <em>double</em>) of the inputs/outputs. If possible, the computation performed by the method itself should also be carried
 out at the user-specified precision, accessible via <a class="reference internal" href="../api/runtime.html#pyxu.runtime.getPrecision" title="pyxu.runtime.getPrecision"><code class="xref py py-func docutils literal notranslate"><span class="pre">getPrecision()</span></code></a>.</p></li>
 <li><p>Whenever possible, it should be compatible with the array modules supported by Pyxu. (Use
-<a class="reference internal" href="../api/info.deps.html#pyxu.info.deps.supported_array_modules" title="pyxu.info.deps.supported_array_modules"><code class="xref py py-func docutils literal notranslate"><span class="pre">supported_array_modules()</span></code></a> for an up-to-date list).  <a class="reference internal" href="../api/util/array_module.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><code class="xref py py-func docutils literal notranslate"><span class="pre">get_array_module()</span></code></a>
+<a class="reference internal" href="../api/info.deps.html#pyxu.info.deps.supported_array_modules" title="pyxu.info.deps.supported_array_modules"><code class="xref py py-func docutils literal notranslate"><span class="pre">supported_array_modules()</span></code></a> for an up-to-date list).  <a class="reference internal" href="../api/util.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><code class="xref py py-func docutils literal notranslate"><span class="pre">get_array_module()</span></code></a>
 can be used to write <a class="reference external" href="https://docs.cupy.dev/en/stable/user_guide/basic.html#how-to-write-cpu-gpu-agnostic-code">module-agnostic</a> code easily.</p></li>
 </ul>
 </section>
diff --git a/fair/howto.html b/fair/howto.html
index bcc25496..b53812bf 100644
--- a/fair/howto.html
+++ b/fair/howto.html
@@ -18,7 +18,7 @@
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" rel="preload" type="font/woff2"/>
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 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" rel="preload" type="font/woff2"/>
-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
 <link href="../_static/sphinx-codeautolink.css?v=125d5c1c" rel="stylesheet" type="text/css"/>
 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -28,11 +28,11 @@
 <link href="../_static/sg_gallery-dataframe.css?v=2082cf3c" rel="stylesheet" type="text/css"/>
 <link href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" rel="stylesheet" type="text/css"/>
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-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
 <!-- Pre-loaded scripts that we'll load fully later -->
 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
 <link as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" rel="preload"/>
-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
 <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -227,24 +227,29 @@
 <li class="toctree-l1"><a class="reference internal" href="contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Plugin Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="plugins/CSEEG.html">CSEEG</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/DSP-Notebooks.html">DSP-Notebooks</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/EnvironTracker.html">EnvironTracker</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HoughDetector.html">HoughDetector</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HVOX.html">HVOX</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/OrientationPy.html">OrientationPy</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/Palentologist.html">Palentologist</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PhaseRet.html">PhaseRet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycGSP.html">PycGSP</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycNUFFT.html">pycNUFFT</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycSphere.html">PycSphere</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycWavelet.html">pycWavelet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PYFW.html">PYFW</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TokemakRec.html">TokemakRec</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TVDenoiser.html">TVDenoiser</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/UncertaintyQuant.html">UncertaintyQuant</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/WaveProp.html">WaveProp</a></li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins_preview/index.html">Plugin Preview Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/CSEEG.html">CSEEG</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/DSP-Notebooks.html">DSP-Notebooks</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/EnvironTracker.html">EnvironTracker</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HoughDetector.html">HoughDetector</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HVOX.html">HVOX</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/OrientationPy.html">OrientationPy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/Palentologist.html">Palentologist</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PhaseRet.html">PhaseRet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycGSP.html">PycGSP</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycNUFFT.html">pycNUFFT</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycSphere.html">PycSphere</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycWavelet.html">pycWavelet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PYFW.html">PYFW</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TokemakRec.html">TokemakRec</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TVDenoiser.html">TVDenoiser</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/UncertaintyQuant.html">UncertaintyQuant</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/WaveProp.html">WaveProp</a></li>
 </ul>
 </li>
 </ul>
@@ -300,7 +305,7 @@ <h2>For Pyxu Users<a class="headerlink" href="#for-pyxu-users" title="Link to th
 </div>
 </li>
 <li><p>Once installed, you can import the <code class="docutils literal notranslate"><span class="pre">GradientDescent</span></code> class in your Python scripts as if it was part of Pyxu’s <a class="reference external" href="../api/opt.html#pyxu-opt-solver">solver</a> module, using the following line of code:</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pyxu.opt.solver.GradientDescent</span>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.opt.solver</span> <span class="kn">import</span> <span class="n">GradientDescent</span>
 </pre></div>
 </div>
 </li>
@@ -330,9 +335,22 @@ <h2>For Developers<a class="headerlink" href="#for-developers" title="Link to th
 <li><p><a class="reference external" href="../api/math.html">pyxu.math</a></p></li>
 <li><p>pyxu.contrib: for any other contribution</p></li>
 </ul>
+<p>To override a class or function in the core Pyxu framework, simply use the identical name as the target you wish to override.
+This process involves a critical step: specifying your intention in the setup.cfg file by prefixing the new entry point
+with an underscore (<code class="docutils literal notranslate"><span class="pre">_</span></code>).</p>
+<p>For example, to override the <code class="docutils literal notranslate"><span class="pre">NullFunc</span></code> class housed within the <code class="docutils literal notranslate"><span class="pre">pyxu.operator.func</span></code> namespace, insert the following
+directive in your setup.cfg file:</p>
+<div class="highlight-ini notranslate"><div class="highlight"><pre><span></span><span class="k">[options.entry_points]</span>
+<span class="w">   </span><span class="na">pyxu.operator.func</span><span class="w"> </span><span class="o">=</span>
+<span class="w">    </span><span class="na">_NullFunc</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">your_module_name:NullFunc</span>
+</pre></div>
+</div>
 <p>Once ready, publish your plugin on <a class="reference external" href="https://pypi.org/">PyPI</a>. The Pyxu-FAIR periodically scans PyPI for new plugins and
 <a class="reference external" href="./score.html">scores</a> them based on their popularity and quality. The higher the score, the higher the chances of your
 plugin being discovered by Pyxu users.</p>
+<p>If you believe your plugin enhances the Pyxu core codebase, we encourage you to reach out so we can evaluate the possibility
+of incorporating it. Even if you’re uncertain, don’t hesitate to open an issue on the <a class="reference external" href="https://github.com/matthieumeo/pyxu">Pyxu GitHub repository</a>
+for feedback and guidance.</p>
 <p>🌟 No matter your expertise level, the Pyxu-FAIR ensures a smooth experience. Dive in, and may your Pyxu journey be
 FAIR and fantastic! 🌟</p>
 </section>
diff --git a/fair/index.html b/fair/index.html
index 6febad3e..e19ee23b 100644
--- a/fair/index.html
+++ b/fair/index.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -410,24 +410,29 @@
 <li class="toctree-l1"><a class="reference internal" href="contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Plugin Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="plugins/CSEEG.html">CSEEG</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/DSP-Notebooks.html">DSP-Notebooks</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/EnvironTracker.html">EnvironTracker</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HoughDetector.html">HoughDetector</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HVOX.html">HVOX</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/OrientationPy.html">OrientationPy</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/Palentologist.html">Palentologist</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PhaseRet.html">PhaseRet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycGSP.html">PycGSP</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycNUFFT.html">pycNUFFT</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycSphere.html">PycSphere</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycWavelet.html">pycWavelet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PYFW.html">PYFW</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TokemakRec.html">TokemakRec</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TVDenoiser.html">TVDenoiser</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/UncertaintyQuant.html">UncertaintyQuant</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/WaveProp.html">WaveProp</a></li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins_preview/index.html">Plugin Preview Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/CSEEG.html">CSEEG</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/DSP-Notebooks.html">DSP-Notebooks</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/EnvironTracker.html">EnvironTracker</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HoughDetector.html">HoughDetector</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HVOX.html">HVOX</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/OrientationPy.html">OrientationPy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/Palentologist.html">Palentologist</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PhaseRet.html">PhaseRet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycGSP.html">PycGSP</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycNUFFT.html">pycNUFFT</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycSphere.html">PycSphere</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycWavelet.html">pycWavelet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PYFW.html">PYFW</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TokemakRec.html">TokemakRec</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TVDenoiser.html">TVDenoiser</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/UncertaintyQuant.html">UncertaintyQuant</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/WaveProp.html">WaveProp</a></li>
 </ul>
 </li>
 </ul>
diff --git a/fair/plugins/index.html b/fair/plugins/index.html
index 9e7b7f37..ed6b9471 100644
--- a/fair/plugins/index.html
+++ b/fair/plugins/index.html
@@ -8,7 +8,7 @@
     <meta charset="utf-8" />
     <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
 
-    <title>Plugin Catalog &#8212; Pyxu Documentation</title>
+    <title>Catalogue &#8212; Pyxu Documentation</title>
   
   
   
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -61,7 +61,7 @@
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
-    <link rel="next" title="CSEEG" href="CSEEG.html" />
+    <link rel="next" title="pyxu-eigh" href="pyxu-eigh.html" />
     <link rel="prev" title="Pyxu Score Explained" href="../score.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
   <meta name="docsearch:language" content="en"/>
@@ -406,24 +406,29 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="current reference internal" href="#">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
-<li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
-<li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
-<li class="toctree-l2"><a class="reference internal" href="HoughDetector.html">HoughDetector</a></li>
-<li class="toctree-l2"><a class="reference internal" href="HVOX.html">HVOX</a></li>
-<li class="toctree-l2"><a class="reference internal" href="OrientationPy.html">OrientationPy</a></li>
-<li class="toctree-l2"><a class="reference internal" href="Palentologist.html">Palentologist</a></li>
-<li class="toctree-l2"><a class="reference internal" href="PhaseRet.html">PhaseRet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="PycGSP.html">PycGSP</a></li>
-<li class="toctree-l2"><a class="reference internal" href="pycNUFFT.html">pycNUFFT</a></li>
-<li class="toctree-l2"><a class="reference internal" href="PycSphere.html">PycSphere</a></li>
-<li class="toctree-l2"><a class="reference internal" href="pycWavelet.html">pycWavelet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="PYFW.html">PYFW</a></li>
-<li class="toctree-l2"><a class="reference internal" href="TokemakRec.html">TokemakRec</a></li>
-<li class="toctree-l2"><a class="reference internal" href="TVDenoiser.html">TVDenoiser</a></li>
-<li class="toctree-l2"><a class="reference internal" href="UncertaintyQuant.html">UncertaintyQuant</a></li>
-<li class="toctree-l2"><a class="reference internal" href="WaveProp.html">WaveProp</a></li>
+<li class="toctree-l1 current active has-children"><a class="current reference internal" href="#">Catalogue</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins_preview/index.html">Plugin Preview Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/CSEEG.html">CSEEG</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/DSP-Notebooks.html">DSP-Notebooks</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/EnvironTracker.html">EnvironTracker</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/HoughDetector.html">HoughDetector</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/HVOX.html">HVOX</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/OrientationPy.html">OrientationPy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/Palentologist.html">Palentologist</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/PhaseRet.html">PhaseRet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/PycGSP.html">PycGSP</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/pycNUFFT.html">pycNUFFT</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/PycSphere.html">PycSphere</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/pycWavelet.html">pycWavelet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/PYFW.html">PYFW</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/TokemakRec.html">TokemakRec</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/TVDenoiser.html">TVDenoiser</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/UncertaintyQuant.html">UncertaintyQuant</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/WaveProp.html">WaveProp</a></li>
 </ul>
 </li>
 </ul>
@@ -466,7 +471,7 @@
     
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
-    <li class="breadcrumb-item active" aria-current="page">Plugin Catalog</li>
+    <li class="breadcrumb-item active" aria-current="page">Catalogue</li>
   </ul>
 </nav>
 </div>
@@ -655,900 +660,110 @@
 .tooltip:hover .tooltiptext {
     visibility: visible;
 }
-</style><section id="plugin-catalog">
-<h1 class="sd-d-none">Plugin Catalog<a class="headerlink" href="#plugin-catalog" title="Link to this heading">#</a></h1>
-<h2 style="font-size: 60px; font-weight: bold; display: inline"><span>Plugin Catalogue</span></h2><p><strong>Total Registered Plugin Packages: 17</strong></p>
+</style><section id="catalogue">
+<h1 class="sd-d-none">Catalogue<a class="headerlink" href="#catalogue" title="Link to this heading">#</a></h1>
+<h2 style="font-size: 60px; font-weight: bold; display: inline"><span>Catalogue</span></h2><p><strong>Total Registered Plugin Packages: 2</strong></p>
 <div class='globalsummary-box'>
      <div style="display: table;">
 
          <span class="badge" style="display: table-row; line-height: 2;">
              <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left blue" style="float: none; display: inline; text-align: right; border: none">Operator</span></span>
-             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">17 plugins in 12 packages </span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">0 plugins in 0 packages </span></span>
          </span>
 
          <span class="badge" style="display: table-row; line-height: 2;">
              <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left brown" style="float: none; display: inline; text-align: right; border: none">Solver</span></span>
-             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">14 plugins in 10 packages </span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">1 plugin in 1 package </span></span>
          </span>
 
          <span class="badge" style="display: table-row; line-height: 2;">
              <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left purple" style="float: none; display: inline; text-align: right; border: none">Stop</span></span>
-             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">18 plugins in 11 packages </span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">0 plugins in 0 packages </span></span>
          </span>
 
          <span class="badge" style="display: table-row; line-height: 2;">
              <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left green" style="float: none; display: inline; text-align: right; border: none">Math</span></span>
-             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">16 plugins in 10 packages </span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">1 plugin in 1 package </span></span>
          </span>
 
          <span class="badge" style="display: table-row; line-height: 2;">
              <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left orange" style="float: none; display: inline; text-align: right; border: none">Contrib</span></span>
-             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">20 plugins in 12 packages </span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">0 plugins in 0 packages </span></span>
          </span>
 
      </div>
- </div><p><strong>Plugin in alphabetical order:</strong></p>
+ </div><p><strong>Plugin list in alphabetical order</strong></p>
 <div class="sd-container-fluid sd-sphinx-override sd-mb-4 docutils">
 <div class="sd-row sd-row-cols-2 sd-row-cols-xs-2 sd-row-cols-sm-2 sd-row-cols-md-3 sd-row-cols-lg-3 sd-g-3 sd-g-xs-3 sd-g-sm-3 sd-g-md-3 sd-g-lg-3 docutils">
 <div class="sd-col sd-d-flex-row docutils">
 <div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
 <div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="CSEEG.html">CSEEG</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/lbrooks/CSEEG" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://lbrooks.github.io/CSEEG/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 69.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left brown">Solver</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="DSP-Notebooks.html">DSP-Notebooks</a></h2>
+<h2 style="font-size: 30px;"><a href="pyxu-eigh.html">pyxu-eigh</a></h2>
 
 <p class="currentstate">
 
-    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-1-007ec6.svg?logo=data:image/png;base64,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"></p>
 
 <ul class="plugin-info">
 
 
     <li>
-        <a href="https://github.com/sdunn/DSP-Notebooks" target="_blank">Home page</a>
+        <a href="https://github.com/AIR-Hub/pyxu-eigh" target="_blank">Home page</a>
     </li>
 
 
 
-    <li>
-        <a href="https://sdunn.github.io/DSP-Notebooks/html/index" target="_blank">Documentation</a>
-    </li>
-
 
 
     <li>
-        <a> Score: 83.0 % </a>
+        <a> Score: 1 % </a>
     </li>
 
 </ul>
 
 <p class="summaryinfo">
 
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">2</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">2</span>
-    </span>
-
     <span class="badge">
         <span class="badge-left green">Math</span>
-        <span class="badge-right">3</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="EnvironTracker.html">EnvironTracker</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/cedwards/EnvironTracker" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://cedwards.github.io/EnvironTracker/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 79.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="HoughDetector.html">HoughDetector</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/abrick/HoughDetector" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://abrick.github.io/HoughDetector/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 56.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left brown">Solver</span>
         <span class="badge-right">1</span>
     </span>
 
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">4</span>
-    </span>
-
 </p></div>
 </div>
 </div>
 <div class="sd-col sd-d-flex-row docutils">
 <div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
 <div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="HVOX.html">HVOX</a></h2>
+<h2 style="font-size: 30px;"><a href="pyxu-gradient-descent.html">pyxu-gradient-descent</a></h2>
 
 <p class="currentstate">
 
-    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Pre-alpha: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-1-007ec6.svg?logo=data:image/png;base64,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"></p>
 
 <ul class="plugin-info">
 
 
     <li>
-        <a href="https://github.com/snassar/HVOX" target="_blank">Home page</a>
+        <a href="https://github.com/joanrue/pyxu-gradient-descent" target="_blank">Home page</a>
     </li>
 
 
 
-    <li>
-        <a href="https://snassar.github.io/HVOX/html/index" target="_blank">Documentation</a>
-    </li>
-
 
 
     <li>
-        <a> Score: 80.0 % </a>
+        <a> Score: 1 % </a>
     </li>
 
 </ul>
 
 <p class="summaryinfo">
 
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">1</span>
-    </span>
-
     <span class="badge">
         <span class="badge-left brown">Solver</span>
         <span class="badge-right">1</span>
     </span>
 
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="OrientationPy.html">OrientationPy</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Mature: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/mmonteith/OrientationPy" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://mmonteith.github.io/OrientationPy/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 77.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">2</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="Palentologist.html">Palentologist</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAZCAYAAADE6YVjAAAACXBIWXMAAAHpAAAB6QHzJ3XIAAAAGXRFWHRTb2Z0d2FyZQB3d3cuaW5rc2NhcGUub3Jnm+48GgAAAzpJREFUSImtlU1oXFUUx3/nzVemWq1pbQXXIpSaEiPUtiCSTdK4qAhVLFh0VXChKAbSVbCiUFFxoSAB3ZmKH2C0aivigBpR/AJxERS1hGATg9F2JhN999x7XMx7Ly/TaQmZHvhzLoc793e+eCNmxuVsYXT/9vLmwhNRNXqUqpSlGiFVSRQhFWldNAY2DZ7+vtMbUafgWx9/dt/cYt3mFutWFFkwz2jwVsYD3mj55JzmKHzXrA3bSm1oz2UhJ0/Vnvl5dtH29ve/AVAZHyb/sHnDMr96zpshX63UDsx1hEyeqtmeW3cf21TtYX7+XCs5b7nM233u3GaG3ZgHRQlgvlgoUC6VODh8Jw/efw+//n42ybStAgXUEiXn0BnUrA0NABST2I59t/UDcGz8ae69e4Tfzs6yM30oFkLdQwEoCVISpJIoXYCeVjzaWkCqkg7qW0Ciyfdr7+YzuH3vfmYXzlMulSASzEFoBsxoDTlVyPlcJeGCJyz5bFaNz0eujxAOXlws7Np58+rEDEhX3SwREJJWWW7L0p80WzHR8EsUQsA5pd5YXnNpZmaGl2463N7ovOasINNW4SMry5SU+JrSWpT9ZwhcK6+9fdpCCIQQODB4R3bhi+lpAJaW/uHv8xfYtvU6jh45JKzTlj+86wZEz0lFKKoqKSSOHeVyKemKIUBv7xZ6e7fgnM6vFwBw1cgH84CsfDq0L1JVVBV1yntnPskuRVGEmWHJDFTjuUs/eWmrDp75MvJeH1CnuAQ2+c4U3/zwI7v7+hARSEA9PdWBjUAAxMx4buJkMhdP8K3W+RCIm3VEJNPxsUfWPZO8FQFU3Z8h2PbgfQZIt04EQBK/MYsAxh4+skNdq10uNyPnHLFzOOdwsdswJP2s4FR/CsHvCiFkLVNVDOiiiNVKAJ4aPXpLWkG6cS6rSHHOxruGAGisY2sA6nHaatsrL4wfvyKQ5598/EQKWFluZBVpsL82CoDcTFJzzrsQfCmOYywEzIzXJ57d1g3kov94r3pYVfHqUe/p8cVrugFAh0qi5h9TjXA13nsolvtfnThRv+KQRqG3z7t/oeo2v/nyi41uAQDZRzDVoYcea7bHutX/c3lfgmmbsZoAAAAASUVORK5CYII="></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/knaiman/Palentologist" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://knaiman.github.io/Palentologist/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 73.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left green">Math</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="PhaseRet.html">PhaseRet</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-inactive-bbbbbb.svg" title="Inactive: No longer maintained.">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/esequeira/PhaseRet" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://esequeira.github.io/PhaseRet/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">2</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">3</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">3</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="PycGSP.html">PycGSP</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/doliphant/PycGSP" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://doliphant.github.io/PycGSP/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 77.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">2</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left brown">Solver</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left green">Math</span>
-        <span class="badge-right">3</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="pycNUFFT.html">pycNUFFT</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/csincell/pycNUFFT" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://csincell.github.io/pycNUFFT/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 78.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left brown">Solver</span>
-        <span class="badge-right">2</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left green">Math</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="PycSphere.html">PycSphere</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Pre-alpha: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/jhawk/PycSphere" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://jhawk.github.io/PycSphere/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 79.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left brown">Solver</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">2</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="pycWavelet.html">pycWavelet</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/cpark/pycWavelet" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://cpark.github.io/pycWavelet/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 68.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left brown">Solver</span>
-        <span class="badge-right">2</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">3</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left green">Math</span>
-        <span class="badge-right">3</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="PYFW.html">PYFW</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Mature: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/rshelton/PYFW" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://rshelton.github.io/PYFW/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 95.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">2</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left green">Math</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">2</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="TokemakRec.html">TokemakRec</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-beta-d6af23.svg" title="Beta: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/msmith/TokemakRec" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://msmith.github.io/TokemakRec/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 91.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left brown">Solver</span>
-        <span class="badge-right">3</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">2</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left green">Math</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">1</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
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-<h2 style="font-size: 30px;"><a href="TVDenoiser.html">TVDenoiser</a></h2>
-
-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-inactive-bbbbbb.svg" title="Inactive: No longer maintained.">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/dbrown/TVDenoiser" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://dbrown.github.io/TVDenoiser/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left brown">Solver</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left green">Math</span>
-        <span class="badge-right">1</span>
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-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">3</span>
-    </span>
-
-</p></div>
-</div>
-</div>
-<div class="sd-col sd-d-flex-row docutils">
-<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
-<div class="sd-card-body docutils">
-<h2 style="font-size: 30px;"><a href="UncertaintyQuant.html">UncertaintyQuant</a></h2>
-
-<p class="currentstate">
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-    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
-
-<ul class="plugin-info">
-
-
-    <li>
-        <a href="https://github.com/kdavis/UncertaintyQuant" target="_blank">Home page</a>
-    </li>
-
-
-
-    <li>
-        <a href="https://kdavis.github.io/UncertaintyQuant/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 88.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left green">Math</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">1</span>
-    </span>
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-</p></div>
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-</div>
-<div class="sd-col sd-d-flex-row docutils">
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-<div class="sd-card-body docutils">
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-<p class="currentstate">
-
-    <img class="svg-badge" src="../../_static/plugins/status/status-beta-d6af23.svg" title="Beta: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
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-<ul class="plugin-info">
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-
-    <li>
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-
-
-
-    <li>
-        <a href="https://knix.github.io/WaveProp/html/index" target="_blank">Documentation</a>
-    </li>
-
-
-
-    <li>
-        <a> Score: 76.0 % </a>
-    </li>
-
-</ul>
-
-<p class="summaryinfo">
-
-    <span class="badge">
-        <span class="badge-left blue">Operator</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left brown">Solver</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left purple">Stop</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left green">Math</span>
-        <span class="badge-right">1</span>
-    </span>
-
-    <span class="badge">
-        <span class="badge-left orange">Contrib</span>
-        <span class="badge-right">1</span>
-    </span>
-
 </p></div>
 </div>
 </div>
@@ -1579,11 +794,11 @@ <h2 style="font-size: 30px;"><a href="WaveProp.html">WaveProp</a></h2>
       </div>
     </a>
     <a class="right-next"
-       href="CSEEG.html"
+       href="pyxu-eigh.html"
        title="next page">
       <div class="prev-next-info">
         <p class="prev-next-subtitle">next</p>
-        <p class="prev-next-title">CSEEG</p>
+        <p class="prev-next-title">pyxu-eigh</p>
       </div>
       <i class="fa-solid fa-angle-right"></i>
     </a>
diff --git a/fair/plugins/pyxu-eigh.html b/fair/plugins/pyxu-eigh.html
new file mode 100644
index 00000000..a0a9c3da
--- /dev/null
+++ b/fair/plugins/pyxu-eigh.html
@@ -0,0 +1,839 @@
+
+<!DOCTYPE html>
+
+
+<html lang="en" data-theme="light">
+
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
+
+    <title>pyxu-eigh &#8212; Pyxu Documentation</title>
+  
+  
+  
+  <script data-cfasync="false">
+    document.documentElement.dataset.mode = localStorage.getItem("mode") || "light";
+    document.documentElement.dataset.theme = localStorage.getItem("theme") || "light";
+  </script>
+  
+  <!-- Loaded before other Sphinx assets -->
+  <link href="../../_static/styles/theme.css?digest=e353d410970836974a52" rel="stylesheet" />
+<link href="../../_static/styles/bootstrap.css?digest=e353d410970836974a52" rel="stylesheet" />
+<link href="../../_static/styles/pydata-sphinx-theme.css?digest=e353d410970836974a52" rel="stylesheet" />
+
+  
+  <link href="../../_static/vendor/fontawesome/6.1.2/css/all.min.css?digest=e353d410970836974a52" rel="stylesheet" />
+  <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" />
+<link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
+<link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
+
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
+    <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
+    <link rel="stylesheet" type="text/css" href="../../_static/togglebutton.css?v=13237357" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery.css?v=61a4c737" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-binder.css?v=f4aeca0c" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
+    <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
+  
+  <!-- Pre-loaded scripts that we'll load fully later -->
+  <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
+<link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
+
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
+    <script src="../../_static/doctools.js?v=888ff710"></script>
+    <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
+    <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
+    <script src="../../_static/copybutton.js?v=30646c52"></script>
+    <script>let toggleHintShow = 'Click to show';</script>
+    <script>let toggleHintHide = 'Click to hide';</script>
+    <script>let toggleOpenOnPrint = 'true';</script>
+    <script src="../../_static/togglebutton.js?v=4a39c7ea"></script>
+    <script src="../../_static/design-tabs.js?v=36754332"></script>
+    <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
+    <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
+    <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/pyxu-eigh';</script>
+    <link rel="icon" href="../../_static/favicon.png"/>
+    <link rel="index" title="Index" href="../../genindex.html" />
+    <link rel="search" title="Search" href="../../search.html" />
+    <link rel="next" title="pyxu-gradient-descent" href="pyxu-gradient-descent.html" />
+    <link rel="prev" title="Catalogue" href="index.html" />
+  <meta name="viewport" content="width=device-width, initial-scale=1"/>
+  <meta name="docsearch:language" content="en"/>
+  </head>
+  
+  
+  <body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="light">
+
+  
+  
+  <a class="skip-link" href="#main-content">Skip to main content</a>
+  
+  <input type="checkbox"
+          class="sidebar-toggle"
+          name="__primary"
+          id="__primary"/>
+  <label class="overlay overlay-primary" for="__primary"></label>
+  
+  <input type="checkbox"
+          class="sidebar-toggle"
+          name="__secondary"
+          id="__secondary"/>
+  <label class="overlay overlay-secondary" for="__secondary"></label>
+  
+  <div class="search-button__wrapper">
+    <div class="search-button__overlay"></div>
+    <div class="search-button__search-container">
+<form class="bd-search d-flex align-items-center"
+      action="../../search.html"
+      method="get">
+  <i class="fa-solid fa-magnifying-glass"></i>
+  <input type="search"
+         class="form-control"
+         name="q"
+         id="search-input"
+         placeholder="Search the docs ..."
+         aria-label="Search the docs ..."
+         autocomplete="off"
+         autocorrect="off"
+         autocapitalize="off"
+         spellcheck="false"/>
+  <span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
+</form></div>
+  </div>
+  
+    <nav class="bd-header navbar navbar-expand-lg bd-navbar">
+<div class="bd-header__inner bd-page-width">
+  <label class="sidebar-toggle primary-toggle" for="__primary">
+    <span class="fa-solid fa-bars"></span>
+  </label>
+  
+  <div class="navbar-header-items__start">
+    
+      <div class="navbar-item">
+  
+
+<a class="navbar-brand logo" href="../../index.html">
+  
+  
+  
+  
+    
+    
+    
+    <img src="../../_static/logo.png" class="logo__image only-light" alt="Logo image"/>
+    <script>document.write(`<img src="../../_static/logo.png" class="logo__image only-dark" alt="Logo image"/>`);</script>
+  
+  
+</a></div>
+    
+  </div>
+  
+  
+  <div class="col-lg-9 navbar-header-items">
+    
+    <div class="me-auto navbar-header-items__center">
+      
+        <div class="navbar-item"><nav class="navbar-nav">
+  <p class="sidebar-header-items__title"
+     role="heading"
+     aria-level="1"
+     aria-label="Site Navigation">
+    Site Navigation
+  </p>
+  <ul class="bd-navbar-elements navbar-nav">
+    
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../intro/index.html">
+                        Getting Started
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../guide/index.html">
+                        User Guide
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../examples/index.html">
+                        Example Gallery
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../api/index.html">
+                        API Reference
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item current active">
+                      <a class="nav-link nav-internal" href="../index.html">
+                        Extending Pyxu
+                      </a>
+                    </li>
+                
+  </ul>
+</nav></div>
+      
+    </div>
+    
+    
+    <div class="navbar-header-items__end">
+      
+        <div class="navbar-item navbar-persistent--container">
+          
+<script>
+document.write(`
+  <button class="btn btn-sm navbar-btn search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
+    <i class="fa-solid fa-magnifying-glass"></i>
+  </button>
+`);
+</script>
+        </div>
+      
+      
+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
+      
+        <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
+    aria-label="Icon Links">
+        <li class="nav-item">
+          
+          
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+                <article class="bd-article" role="main">
+                  
+  <span class="target" id="plugins-page"></span><!-- CSS overrides on the pyxu-fair only -->
+<style>
+
+.summaryinfo {
+    color: #000;
+    font-size: 80%;
+    margin-bottom: 12px;
+    margin-top: 12px;
+}
+
+.entrypointraw {
+    color: #777;
+}
+.badge {
+    white-space: nowrap;
+    display: inline-block;
+    vertical-align: middle;
+    /*vertical-align: baseline;*/
+    font-family: "DejaVu Sans", Verdana, Geneva, sans-serif;
+    /*font-size: 90%;*/
+}
+.currentstate {
+    color: #666;
+    font-size: 90%;
+    margin-bottom: 12px;
+}
+span.badge-left {
+    border-radius: .25rem;
+    border-top-right-radius: 0;
+    border-bottom-right-radius: 0;
+    color: #212529;
+    background-color: #A2CBFF;
+    /* color: #ffffff; */
+    text-shadow: 1px 1px 1px rgba(0,0,0,0.3);
+
+    padding: .25em .4em;
+    line-height: 1;
+    text-align: center;
+    white-space: nowrap;
+    float: left;
+    display: block;
+}
+
+span.badge-right {
+    border-radius: .25rem;
+    border-top-left-radius: 0;
+    border-bottom-left-radius: 0;
+
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+    background-color: #343a40;
+
+    padding: .25em .4em;
+    line-height: 1;
+    text-align: center;
+    white-space: nowrap;
+    float: left;
+    display: block;
+}
+
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+    background-color: rgb(255, 162, 162);
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+    background-color: #e41a1c;
+    color: #fff;
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+
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+    background-color: #377eb8;
+    color: #fff;
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+
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+    background-color: #4daf4a;
+    color: #fff;
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+
+.badge-right.purple, .badge-left.purple {
+    background-color: #984ea3;
+    color: #fff;
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+
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+    color: #fff;
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+    color: #fff;
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+
+.badge-right.dark-gray, .badge-left.dark-gray {
+    color: #fff;
+    background-color: #343a40;
+}
+
+
+.badge a {
+    text-decoration: none;
+    padding: 0;
+    border: 0;
+    color: inherit;
+}
+
+.badge a:visited, .badge a:active {
+    color: inherit;
+  }
+
+.badge a:focus, .badge a:hover {
+    color: rgba(255,255,255,0.5);
+    mix-blend-mode: difference;
+    text-decoration: none;
+    /* background-color: rgb(192, 219, 255); */
+}
+
+
+.svg-badge {
+    vertical-align: middle;
+}
+
+.tooltiptext {
+    visibility: hidden;
+    /* width: 120px; */
+    background-color: rgb(255, 247, 175);
+    color: #000;
+    text-align: center;
+    border-radius: 6px;
+    padding: 5px;
+
+    /* Position the tooltip */
+    position: absolute;
+    z-index: 1;
+}
+
+.tooltip:hover .tooltiptext {
+    visibility: visible;
+}
+</style><section id="pyxu-eigh">
+<h1>pyxu-eigh<a class="headerlink" href="#pyxu-eigh" title="Link to this heading">#</a></h1>
+<section id="description">
+<h2>Description<a class="headerlink" href="#description" title="Link to this heading">#</a></h2>
+</section>
+<section id="general-information">
+<h2>General information<a class="headerlink" href="#general-information" title="Link to this heading">#</a></h2>
+<p>
+    <strong>Short description</strong>: Pyxu plugin to compute the eigenvectors and eigenvalues of a real symmetric matrix
+</p>
+
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!"></p>
+
+
+<p>
+    <strong>Source code</strong>: <a href="https://github.com/AIR-Hub/pyxu-eigh" target="_blank">Go to the source code repository</a>
+</p>
+
+
+<p>
+    <strong>Documentation</strong>: No documentation provided by the package author
+<p></section>
+<section id="detailed-information">
+<h2>Detailed information<a class="headerlink" href="#detailed-information" title="Link to this heading">#</a></h2>
+<p>
+    <strong>Author(s)</strong>: Joan Rue Queralt
+</p>
+
+
+<p>
+    <strong>Contact</strong>: <a href="mailto:joan.rue.q@gmail.com">joan.rue.q@gmail.com</a>
+</p>
+
+
+<p>
+    <strong>Most recent version</strong>: 0.1.0
+</p>
+<p>
+    <strong>Compatibility</strong>:
+    <img class="svg-badge" title="Compatible with Pyxu 1" src="https://img.shields.io/badge/Pyxu-1-007ec6.svg?logo=data:image/png;base64,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">
+</p></section>
+<section id="components-contributed">
+<h2>Components contributed<a class="headerlink" href="#components-contributed" title="Link to this heading">#</a></h2>
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p>
+
+
+
+  Math <span class="entrypointraw">(pyxu.math)</span>
+
+<ul>
+
+<li><code>eigh</code>
+
+</ul></section>
+</section>
+
+
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#detailed-information">Detailed information</a></li>
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+      
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+        
+          Edit on GitHub
+        
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+  </body>
+</html>
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new file mode 100644
index 00000000..fd687d91
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+
+<!DOCTYPE html>
+
+
+<html lang="en" data-theme="light">
+
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
+
+    <title>pyxu-gradient-descent &#8212; Pyxu Documentation</title>
+  
+  
+  
+  <script data-cfasync="false">
+    document.documentElement.dataset.mode = localStorage.getItem("mode") || "light";
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+  <link href="../../_static/styles/theme.css?digest=e353d410970836974a52" rel="stylesheet" />
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+  <link href="../../_static/vendor/fontawesome/6.1.2/css/all.min.css?digest=e353d410970836974a52" rel="stylesheet" />
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+
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
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+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-binder.css?v=f4aeca0c" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
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+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
+  
+  <!-- Pre-loaded scripts that we'll load fully later -->
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+    <script src="../../_static/copybutton.js?v=30646c52"></script>
+    <script>let toggleHintShow = 'Click to show';</script>
+    <script>let toggleHintHide = 'Click to hide';</script>
+    <script>let toggleOpenOnPrint = 'true';</script>
+    <script src="../../_static/togglebutton.js?v=4a39c7ea"></script>
+    <script src="../../_static/design-tabs.js?v=36754332"></script>
+    <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
+    <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
+    <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/pyxu-gradient-descent';</script>
+    <link rel="icon" href="../../_static/favicon.png"/>
+    <link rel="index" title="Index" href="../../genindex.html" />
+    <link rel="search" title="Search" href="../../search.html" />
+    <link rel="next" title="Plugin Preview Catalog" href="../plugins_preview/index.html" />
+    <link rel="prev" title="pyxu-eigh" href="pyxu-eigh.html" />
+  <meta name="viewport" content="width=device-width, initial-scale=1"/>
+  <meta name="docsearch:language" content="en"/>
+  </head>
+  
+  
+  <body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="light">
+
+  
+  
+  <a class="skip-link" href="#main-content">Skip to main content</a>
+  
+  <input type="checkbox"
+          class="sidebar-toggle"
+          name="__primary"
+          id="__primary"/>
+  <label class="overlay overlay-primary" for="__primary"></label>
+  
+  <input type="checkbox"
+          class="sidebar-toggle"
+          name="__secondary"
+          id="__secondary"/>
+  <label class="overlay overlay-secondary" for="__secondary"></label>
+  
+  <div class="search-button__wrapper">
+    <div class="search-button__overlay"></div>
+    <div class="search-button__search-container">
+<form class="bd-search d-flex align-items-center"
+      action="../../search.html"
+      method="get">
+  <i class="fa-solid fa-magnifying-glass"></i>
+  <input type="search"
+         class="form-control"
+         name="q"
+         id="search-input"
+         placeholder="Search the docs ..."
+         aria-label="Search the docs ..."
+         autocomplete="off"
+         autocorrect="off"
+         autocapitalize="off"
+         spellcheck="false"/>
+  <span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
+</form></div>
+  </div>
+  
+    <nav class="bd-header navbar navbar-expand-lg bd-navbar">
+<div class="bd-header__inner bd-page-width">
+  <label class="sidebar-toggle primary-toggle" for="__primary">
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+  </label>
+  
+  <div class="navbar-header-items__start">
+    
+      <div class="navbar-item">
+  
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+  
+  
+  
+  
+    
+    
+    
+    <img src="../../_static/logo.png" class="logo__image only-light" alt="Logo image"/>
+    <script>document.write(`<img src="../../_static/logo.png" class="logo__image only-dark" alt="Logo image"/>`);</script>
+  
+  
+</a></div>
+    
+  </div>
+  
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+  <div class="col-lg-9 navbar-header-items">
+    
+    <div class="me-auto navbar-header-items__center">
+      
+        <div class="navbar-item"><nav class="navbar-nav">
+  <p class="sidebar-header-items__title"
+     role="heading"
+     aria-level="1"
+     aria-label="Site Navigation">
+    Site Navigation
+  </p>
+  <ul class="bd-navbar-elements navbar-nav">
+    
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../intro/index.html">
+                        Getting Started
+                      </a>
+                    </li>
+                
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+                      <a class="nav-link nav-internal" href="../../guide/index.html">
+                        User Guide
+                      </a>
+                    </li>
+                
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+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../examples/index.html">
+                        Example Gallery
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../api/index.html">
+                        API Reference
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item current active">
+                      <a class="nav-link nav-internal" href="../index.html">
+                        Extending Pyxu
+                      </a>
+                    </li>
+                
+  </ul>
+</nav></div>
+      
+    </div>
+    
+    
+    <div class="navbar-header-items__end">
+      
+        <div class="navbar-item navbar-persistent--container">
+          
+<script>
+document.write(`
+  <button class="btn btn-sm navbar-btn search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
+    <i class="fa-solid fa-magnifying-glass"></i>
+  </button>
+`);
+</script>
+        </div>
+      
+      
+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
+      
+        <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
+    aria-label="Icon Links">
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://github.com/matthieumeo/pyxu" title="GitHub" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-github"></i></span>
+            <label class="sr-only">GitHub</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://pypi.org/project/pyxu/" title="PyPI" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-python"></i></span>
+            <label class="sr-only">PyPI</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+            <label class="sr-only">Contact</label></a>
+        </li>
+        <li class="nav-item">
+          
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+          
+          
+          
+          
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+          
+          <a href="https://imaging.epfl.ch/" title="EPFL Center for Imaging" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><img src="../../_static/imaging.png" class="icon-link-image" alt="EPFL Center for Imaging"/></a>
+        </li>
+</ul></div>
+      
+    </div>
+    
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+  
+  
+    <div class="navbar-persistent--mobile">
+<script>
+document.write(`
+  <button class="btn btn-sm navbar-btn search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
+    <i class="fa-solid fa-magnifying-glass"></i>
+  </button>
+`);
+</script>
+    </div>
+  
+
+  
+    <label class="sidebar-toggle secondary-toggle" for="__secondary">
+      <span class="fa-solid fa-outdent"></span>
+    </label>
+  
+</div>
+
+    </nav>
+  
+  <div class="bd-container">
+    <div class="bd-container__inner bd-page-width">
+      
+      <div class="bd-sidebar-primary bd-sidebar">
+        
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+  <div class="sidebar-header-items sidebar-primary__section">
+    
+    
+      <div class="sidebar-header-items__center">
+        
+          <div class="navbar-item"><nav class="navbar-nav">
+  <p class="sidebar-header-items__title"
+     role="heading"
+     aria-level="1"
+     aria-label="Site Navigation">
+    Site Navigation
+  </p>
+  <ul class="bd-navbar-elements navbar-nav">
+    
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../intro/index.html">
+                        Getting Started
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../guide/index.html">
+                        User Guide
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../examples/index.html">
+                        Example Gallery
+                      </a>
+                    </li>
+                
+
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+                      <a class="nav-link nav-internal" href="../../api/index.html">
+                        API Reference
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item current active">
+                      <a class="nav-link nav-internal" href="../index.html">
+                        Extending Pyxu
+                      </a>
+                    </li>
+                
+  </ul>
+</nav></div>
+        
+      </div>
+    
+    
+    
+      <div class="sidebar-header-items__end">
+        
+          <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
+        
+          <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
+    aria-label="Icon Links">
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://github.com/matthieumeo/pyxu" title="GitHub" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-github"></i></span>
+            <label class="sr-only">GitHub</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://pypi.org/project/pyxu/" title="PyPI" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-python"></i></span>
+            <label class="sr-only">PyPI</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
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+          
+          
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+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+            <label class="sr-only">Contact</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
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+          
+          <a href="https://imaging.epfl.ch/" title="EPFL Center for Imaging" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><img src="../../_static/imaging.png" class="icon-link-image" alt="EPFL Center for Imaging"/></a>
+        </li>
+</ul></div>
+        
+      </div>
+    
+  </div>
+  
+    <div class="sidebar-primary-items__start sidebar-primary__section">
+        <div class="sidebar-primary-item"><nav class="bd-docs-nav bd-links"
+     aria-label="Section Navigation">
+  <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
+  <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="../howto.html">How to use plugins in Pyxu?</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Catalogue</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2 current active"><a class="current reference internal" href="#">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins_preview/index.html">Plugin Preview Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/CSEEG.html">CSEEG</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/EnvironTracker.html">EnvironTracker</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/HVOX.html">HVOX</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/OrientationPy.html">OrientationPy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/Palentologist.html">Palentologist</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/PhaseRet.html">PhaseRet</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/pycNUFFT.html">pycNUFFT</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/PycSphere.html">PycSphere</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/pycWavelet.html">pycWavelet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/PYFW.html">PYFW</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/TokemakRec.html">TokemakRec</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/TVDenoiser.html">TVDenoiser</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/UncertaintyQuant.html">UncertaintyQuant</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins_preview/WaveProp.html">WaveProp</a></li>
+</ul>
+</li>
+</ul>
+</div>
+</nav></div>
+    </div>
+  
+  
+  <div class="sidebar-primary-items__end sidebar-primary__section">
+  </div>
+  
+  <div id="rtd-footer-container"></div>
+
+
+      </div>
+      
+      <main id="main-content" class="bd-main">
+        
+        
+          <div class="bd-content">
+            <div class="bd-article-container">
+              
+              <div class="bd-header-article">
+<div class="header-article-items header-article__inner">
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+      
+        <div class="header-article-item">
+
+
+
+<nav aria-label="Breadcrumbs">
+  <ul class="bd-breadcrumbs" role="navigation" aria-label="Breadcrumb">
+    
+    <li class="breadcrumb-item breadcrumb-home">
+      <a href="../../index.html" class="nav-link" aria-label="Home">
+        <i class="fa-solid fa-home"></i>
+      </a>
+    </li>
+    
+    <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
+    
+    
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Catalogue</a></li>
+    
+    <li class="breadcrumb-item active" aria-current="page">pyxu-gradient-descent</li>
+  </ul>
+</nav>
+</div>
+      
+    </div>
+  
+  
+</div>
+</div>
+              
+              
+              
+                
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <span class="target" id="plugins-page"></span><!-- CSS overrides on the pyxu-fair only -->
+<style>
+
+.summaryinfo {
+    color: #000;
+    font-size: 80%;
+    margin-bottom: 12px;
+    margin-top: 12px;
+}
+
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+}
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+}
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+}
+span.badge-left {
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+
+    padding: .25em .4em;
+    line-height: 1;
+    text-align: center;
+    white-space: nowrap;
+    float: left;
+    display: block;
+}
+
+span.badge-right {
+    border-radius: .25rem;
+    border-top-left-radius: 0;
+    border-bottom-left-radius: 0;
+
+    color: #fff;
+    background-color: #343a40;
+
+    padding: .25em .4em;
+    line-height: 1;
+    text-align: center;
+    white-space: nowrap;
+    float: left;
+    display: block;
+}
+
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+    background-color: #A2CBFF;
+    color: #212529;
+}
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+}
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+    background-color: #e41a1c;
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+}
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+    color: #fff;
+}
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+    color: #fff;
+}
+
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+    background-color: #a65628;
+    color: #fff;
+}
+
+.badge-right.dark-gray, .badge-left.dark-gray {
+    color: #fff;
+    background-color: #343a40;
+}
+
+
+.badge a {
+    text-decoration: none;
+    padding: 0;
+    border: 0;
+    color: inherit;
+}
+
+.badge a:visited, .badge a:active {
+    color: inherit;
+  }
+
+.badge a:focus, .badge a:hover {
+    color: rgba(255,255,255,0.5);
+    mix-blend-mode: difference;
+    text-decoration: none;
+    /* background-color: rgb(192, 219, 255); */
+}
+
+
+.svg-badge {
+    vertical-align: middle;
+}
+
+.tooltiptext {
+    visibility: hidden;
+    /* width: 120px; */
+    background-color: rgb(255, 247, 175);
+    color: #000;
+    text-align: center;
+    border-radius: 6px;
+    padding: 5px;
+
+    /* Position the tooltip */
+    position: absolute;
+    z-index: 1;
+}
+
+.tooltip:hover .tooltiptext {
+    visibility: visible;
+}
+</style><section id="pyxu-gradient-descent">
+<h1>pyxu-gradient-descent<a class="headerlink" href="#pyxu-gradient-descent" title="Link to this heading">#</a></h1>
+<section id="description">
+<h2>Description<a class="headerlink" href="#description" title="Link to this heading">#</a></h2>
+</section>
+<section id="general-information">
+<h2>General information<a class="headerlink" href="#general-information" title="Link to this heading">#</a></h2>
+<p>
+    <strong>Short description</strong>: An accelerated gradient descent optimizer for Pyxu
+</p>
+
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!"></p>
+
+
+<p>
+    <strong>Source code</strong>: <a href="https://github.com/joanrue/pyxu-gradient-descent" target="_blank">Go to the source code repository</a>
+</p>
+
+
+<p>
+    <strong>Documentation</strong>: No documentation provided by the package author
+<p></section>
+<section id="detailed-information">
+<h2>Detailed information<a class="headerlink" href="#detailed-information" title="Link to this heading">#</a></h2>
+<p>
+    <strong>Author(s)</strong>: Joan Rue Queralt
+</p>
+
+
+<p>
+    <strong>Contact</strong>: <a href="mailto:joan.rue.q@gmail.com">joan.rue.q@gmail.com</a>
+</p>
+
+
+<p>
+    <strong>Most recent version</strong>: 0.1.0
+</p>
+<p>
+    <strong>Compatibility</strong>:
+    <img class="svg-badge" title="Compatible with Pyxu 1" src="https://img.shields.io/badge/Pyxu-1-007ec6.svg?logo=data:image/png;base64,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">
+</p></section>
+<section id="components-contributed">
+<h2>Components contributed<a class="headerlink" href="#components-contributed" title="Link to this heading">#</a></h2>
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p>
+
+
+
+  Solver <span class="entrypointraw">(pyxu.solver)</span>
+
+<ul>
+
+<li><code>GradientDescent</code>
+
+</ul></section>
+</section>
+
+
+                </article>
+              
+              
+              
+                <footer class="bd-footer-article">
+                  
+<div class="footer-article-items footer-article__inner">
+  
+    <div class="footer-article-item"><!-- Previous / next buttons -->
+<div class="prev-next-area">
+    <a class="left-prev"
+       href="pyxu-eigh.html"
+       title="previous page">
+      <i class="fa-solid fa-angle-left"></i>
+      <div class="prev-next-info">
+        <p class="prev-next-subtitle">previous</p>
+        <p class="prev-next-title">pyxu-eigh</p>
+      </div>
+    </a>
+    <a class="right-next"
+       href="../plugins_preview/index.html"
+       title="next page">
+      <div class="prev-next-info">
+        <p class="prev-next-subtitle">next</p>
+        <p class="prev-next-title">Plugin Preview Catalog</p>
+      </div>
+      <i class="fa-solid fa-angle-right"></i>
+    </a>
+</div></div>
+  
+</div>
+
+                </footer>
+              
+            </div>
+            
+            
+              
+                <div class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
+
+  <div class="sidebar-secondary-item">
+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> On this page
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#description">Description</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#general-information">General information</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#detailed-information">Detailed information</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#components-contributed">Components contributed</a></li>
+</ul>
+  </nav></div>
+
+  <div class="sidebar-secondary-item">
+<div id="searchbox"></div></div>
+
+  <div class="sidebar-secondary-item">
+  
+  <div class="tocsection editthispage">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/pyxu-gradient-descent.rst">
+      <i class="fa-solid fa-pencil"></i>
+      
+      
+        
+          Edit on GitHub
+        
+      
+    </a>
+  </div>
+</div>
+
+  <div class="sidebar-secondary-item">
+  <div class="tocsection sourcelink">
+    <a href="../../_sources/fair/plugins/pyxu-gradient-descent.rst">
+      <i class="fa-solid fa-file-lines"></i> Show Source
+    </a>
+  </div>
+</div>
+
+</div></div>
+              
+            
+          </div>
+          <footer class="bd-footer-content">
+            
+          </footer>
+        
+      </main>
+    </div>
+  </div>
+  
+  <!-- Scripts loaded after <body> so the DOM is not blocked -->
+  <script src="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52"></script>
+<script src="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52"></script>
+
+  <footer class="bd-footer">
+<div class="bd-footer__inner bd-page-width">
+  
+    <div class="footer-items__start">
+      
+        <div class="footer-item">
+  <p class="copyright">
+    
+      © Copyright 2023, M. Simeoni, S. Kashani, J. Rué-Queralt &amp; Pyxu Developers.
+      <br/>
+    
+  </p>
+</div>
+      
+        <div class="footer-item">
+  <p class="sphinx-version">
+     Created with <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5, with some help from <a href="https://chat.openai.com/"> ChatGPT</a> (GPT 4).
+    <br/>
+  </p>
+</div>
+      
+    </div>
+  
+  
+    <div class="footer-items__end">
+      
+        <div class="footer-item"><p class="theme-version">
+  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
+</p></div>
+      
+    </div>
+  
+</div>
+
+  </footer>
+  </body>
+</html>
\ No newline at end of file
diff --git a/fair/plugins/CSEEG.html b/fair/plugins_preview/CSEEG.html
similarity index 95%
rename from fair/plugins/CSEEG.html
rename to fair/plugins_preview/CSEEG.html
index 32f25230..33bc039d 100644
--- a/fair/plugins/CSEEG.html
+++ b/fair/plugins_preview/CSEEG.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
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     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,12 +57,12 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/CSEEG';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/CSEEG';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
     <link rel="next" title="DSP-Notebooks" href="DSP-Notebooks.html" />
-    <link rel="prev" title="Plugin Catalog" href="index.html" />
+    <link rel="prev" title="Plugin Preview Catalog" href="index.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
   <meta name="docsearch:language" content="en"/>
   </head>
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2 current active"><a class="current reference internal" href="#">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">CSEEG</li>
   </ul>
@@ -718,7 +723,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
       <i class="fa-solid fa-angle-left"></i>
       <div class="prev-next-info">
         <p class="prev-next-subtitle">previous</p>
-        <p class="prev-next-title">Plugin Catalog</p>
+        <p class="prev-next-title">Plugin Preview Catalog</p>
       </div>
     </a>
     <a class="right-next"
@@ -761,7 +766,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/CSEEG.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/CSEEG.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -775,7 +780,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/CSEEG.rst">
+    <a href="../../_sources/fair/plugins_preview/CSEEG.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/DSP-Notebooks.html b/fair/plugins_preview/DSP-Notebooks.html
similarity index 95%
rename from fair/plugins/DSP-Notebooks.html
rename to fair/plugins_preview/DSP-Notebooks.html
index 80bc1e14..f5d0ffe8 100644
--- a/fair/plugins/DSP-Notebooks.html
+++ b/fair/plugins_preview/DSP-Notebooks.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/DSP-Notebooks';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/DSP-Notebooks';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2 current active"><a class="current reference internal" href="#">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">DSP-Notebooks</li>
   </ul>
@@ -817,7 +822,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/DSP-Notebooks.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/DSP-Notebooks.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -831,7 +836,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/DSP-Notebooks.rst">
+    <a href="../../_sources/fair/plugins_preview/DSP-Notebooks.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/EnvironTracker.html b/fair/plugins_preview/EnvironTracker.html
similarity index 95%
rename from fair/plugins/EnvironTracker.html
rename to fair/plugins_preview/EnvironTracker.html
index bc86100a..08cef884 100644
--- a/fair/plugins/EnvironTracker.html
+++ b/fair/plugins_preview/EnvironTracker.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/EnvironTracker';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/EnvironTracker';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2 current active"><a class="current reference internal" href="#">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">EnvironTracker</li>
   </ul>
@@ -765,7 +770,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/EnvironTracker.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/EnvironTracker.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -779,7 +784,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/EnvironTracker.rst">
+    <a href="../../_sources/fair/plugins_preview/EnvironTracker.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/HVOX.html b/fair/plugins_preview/HVOX.html
similarity index 95%
rename from fair/plugins/HVOX.html
rename to fair/plugins_preview/HVOX.html
index 1ad8a6ab..0528d24c 100644
--- a/fair/plugins/HVOX.html
+++ b/fair/plugins_preview/HVOX.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/HVOX';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/HVOX';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">HVOX</li>
   </ul>
@@ -791,7 +796,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/HVOX.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/HVOX.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -805,7 +810,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/HVOX.rst">
+    <a href="../../_sources/fair/plugins_preview/HVOX.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/HoughDetector.html b/fair/plugins_preview/HoughDetector.html
similarity index 95%
rename from fair/plugins/HoughDetector.html
rename to fair/plugins_preview/HoughDetector.html
index b7bca00b..ebc3bc1a 100644
--- a/fair/plugins/HoughDetector.html
+++ b/fair/plugins_preview/HoughDetector.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/HoughDetector';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/HoughDetector';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">HoughDetector</li>
   </ul>
@@ -797,7 +802,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/HoughDetector.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/HoughDetector.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -811,7 +816,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/HoughDetector.rst">
+    <a href="../../_sources/fair/plugins_preview/HoughDetector.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/OrientationPy.html b/fair/plugins_preview/OrientationPy.html
similarity index 95%
rename from fair/plugins/OrientationPy.html
rename to fair/plugins_preview/OrientationPy.html
index c835e896..023cf690 100644
--- a/fair/plugins/OrientationPy.html
+++ b/fair/plugins_preview/OrientationPy.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/OrientationPy';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/OrientationPy';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">OrientationPy</li>
   </ul>
@@ -795,7 +800,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/OrientationPy.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/OrientationPy.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -809,7 +814,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/OrientationPy.rst">
+    <a href="../../_sources/fair/plugins_preview/OrientationPy.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/PYFW.html b/fair/plugins_preview/PYFW.html
similarity index 96%
rename from fair/plugins/PYFW.html
rename to fair/plugins_preview/PYFW.html
index ff572e23..01bdb77a 100644
--- a/fair/plugins/PYFW.html
+++ b/fair/plugins_preview/PYFW.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/PYFW';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/PYFW';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">PYFW</li>
   </ul>
@@ -811,7 +816,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/PYFW.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/PYFW.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -825,7 +830,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/PYFW.rst">
+    <a href="../../_sources/fair/plugins_preview/PYFW.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/Palentologist.html b/fair/plugins_preview/Palentologist.html
similarity index 95%
rename from fair/plugins/Palentologist.html
rename to fair/plugins_preview/Palentologist.html
index 226abefe..43e24e61 100644
--- a/fair/plugins/Palentologist.html
+++ b/fair/plugins_preview/Palentologist.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/Palentologist';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/Palentologist';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">Palentologist</li>
   </ul>
@@ -781,7 +786,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/Palentologist.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/Palentologist.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -795,7 +800,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/Palentologist.rst">
+    <a href="../../_sources/fair/plugins_preview/Palentologist.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/PhaseRet.html b/fair/plugins_preview/PhaseRet.html
similarity index 95%
rename from fair/plugins/PhaseRet.html
rename to fair/plugins_preview/PhaseRet.html
index 83c93062..b70e8113 100644
--- a/fair/plugins/PhaseRet.html
+++ b/fair/plugins_preview/PhaseRet.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/PhaseRet';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/PhaseRet';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">PhaseRet</li>
   </ul>
@@ -799,7 +804,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/PhaseRet.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/PhaseRet.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -813,7 +818,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/PhaseRet.rst">
+    <a href="../../_sources/fair/plugins_preview/PhaseRet.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/PycGSP.html b/fair/plugins_preview/PycGSP.html
similarity index 96%
rename from fair/plugins/PycGSP.html
rename to fair/plugins_preview/PycGSP.html
index b7bca024..14b13f50 100644
--- a/fair/plugins/PycGSP.html
+++ b/fair/plugins_preview/PycGSP.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/PycGSP';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/PycGSP';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">PycGSP</li>
   </ul>
@@ -815,7 +820,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/PycGSP.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/PycGSP.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -829,7 +834,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/PycGSP.rst">
+    <a href="../../_sources/fair/plugins_preview/PycGSP.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/PycSphere.html b/fair/plugins_preview/PycSphere.html
similarity index 95%
rename from fair/plugins/PycSphere.html
rename to fair/plugins_preview/PycSphere.html
index 28809a2d..bbb9236d 100644
--- a/fair/plugins/PycSphere.html
+++ b/fair/plugins_preview/PycSphere.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/PycSphere';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/PycSphere';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">PycSphere</li>
   </ul>
@@ -793,7 +798,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/PycSphere.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/PycSphere.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -807,7 +812,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/PycSphere.rst">
+    <a href="../../_sources/fair/plugins_preview/PycSphere.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/TVDenoiser.html b/fair/plugins_preview/TVDenoiser.html
similarity index 96%
rename from fair/plugins/TVDenoiser.html
rename to fair/plugins_preview/TVDenoiser.html
index 741fe0a3..6f77f2d5 100644
--- a/fair/plugins/TVDenoiser.html
+++ b/fair/plugins_preview/TVDenoiser.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/TVDenoiser';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/TVDenoiser';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">TVDenoiser</li>
   </ul>
@@ -825,7 +830,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/TVDenoiser.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/TVDenoiser.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -839,7 +844,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/TVDenoiser.rst">
+    <a href="../../_sources/fair/plugins_preview/TVDenoiser.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/TokemakRec.html b/fair/plugins_preview/TokemakRec.html
similarity index 95%
rename from fair/plugins/TokemakRec.html
rename to fair/plugins_preview/TokemakRec.html
index 634b6a2a..fbbed4c3 100644
--- a/fair/plugins/TokemakRec.html
+++ b/fair/plugins_preview/TokemakRec.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/TokemakRec';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/TokemakRec';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">TokemakRec</li>
   </ul>
@@ -825,7 +830,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/TokemakRec.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/TokemakRec.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -839,7 +844,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/TokemakRec.rst">
+    <a href="../../_sources/fair/plugins_preview/TokemakRec.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/UncertaintyQuant.html b/fair/plugins_preview/UncertaintyQuant.html
similarity index 95%
rename from fair/plugins/UncertaintyQuant.html
rename to fair/plugins_preview/UncertaintyQuant.html
index 9b02da52..96c0c83d 100644
--- a/fair/plugins/UncertaintyQuant.html
+++ b/fair/plugins_preview/UncertaintyQuant.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/UncertaintyQuant';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/UncertaintyQuant';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">UncertaintyQuant</li>
   </ul>
@@ -781,7 +786,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/UncertaintyQuant.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/UncertaintyQuant.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -795,7 +800,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/UncertaintyQuant.rst">
+    <a href="../../_sources/fair/plugins_preview/UncertaintyQuant.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/WaveProp.html b/fair/plugins_preview/WaveProp.html
similarity index 96%
rename from fair/plugins/WaveProp.html
rename to fair/plugins_preview/WaveProp.html
index 8ff52c1c..22427636 100644
--- a/fair/plugins/WaveProp.html
+++ b/fair/plugins_preview/WaveProp.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/WaveProp';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/WaveProp';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -409,7 +409,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -470,7 +475,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">WaveProp</li>
   </ul>
@@ -813,7 +818,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/WaveProp.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/WaveProp.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -827,7 +832,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/WaveProp.rst">
+    <a href="../../_sources/fair/plugins_preview/WaveProp.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins_preview/index.html b/fair/plugins_preview/index.html
new file mode 100644
index 00000000..b5d41798
--- /dev/null
+++ b/fair/plugins_preview/index.html
@@ -0,0 +1,1655 @@
+
+<!DOCTYPE html>
+
+
+<html lang="en" data-theme="light">
+
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />
+
+    <title>Plugin Preview Catalog &#8212; Pyxu Documentation</title>
+  
+  
+  
+  <script data-cfasync="false">
+    document.documentElement.dataset.mode = localStorage.getItem("mode") || "light";
+    document.documentElement.dataset.theme = localStorage.getItem("theme") || "light";
+  </script>
+  
+  <!-- Loaded before other Sphinx assets -->
+  <link href="../../_static/styles/theme.css?digest=e353d410970836974a52" rel="stylesheet" />
+<link href="../../_static/styles/bootstrap.css?digest=e353d410970836974a52" rel="stylesheet" />
+<link href="../../_static/styles/pydata-sphinx-theme.css?digest=e353d410970836974a52" rel="stylesheet" />
+
+  
+  <link href="../../_static/vendor/fontawesome/6.1.2/css/all.min.css?digest=e353d410970836974a52" rel="stylesheet" />
+  <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" />
+<link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
+<link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
+
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
+    <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
+    <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
+    <link rel="stylesheet" type="text/css" href="../../_static/togglebutton.css?v=13237357" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery.css?v=61a4c737" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-binder.css?v=f4aeca0c" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
+    <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
+    <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
+  
+  <!-- Pre-loaded scripts that we'll load fully later -->
+  <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
+<link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
+
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
+    <script src="../../_static/doctools.js?v=888ff710"></script>
+    <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
+    <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
+    <script src="../../_static/copybutton.js?v=30646c52"></script>
+    <script>let toggleHintShow = 'Click to show';</script>
+    <script>let toggleHintHide = 'Click to hide';</script>
+    <script>let toggleOpenOnPrint = 'true';</script>
+    <script src="../../_static/togglebutton.js?v=4a39c7ea"></script>
+    <script src="../../_static/design-tabs.js?v=36754332"></script>
+    <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
+    <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
+    <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/index';</script>
+    <link rel="icon" href="../../_static/favicon.png"/>
+    <link rel="index" title="Index" href="../../genindex.html" />
+    <link rel="search" title="Search" href="../../search.html" />
+    <link rel="next" title="CSEEG" href="CSEEG.html" />
+    <link rel="prev" title="pyxu-gradient-descent" href="../plugins/pyxu-gradient-descent.html" />
+  <meta name="viewport" content="width=device-width, initial-scale=1"/>
+  <meta name="docsearch:language" content="en"/>
+  </head>
+  
+  
+  <body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="light">
+
+  
+  
+  <a class="skip-link" href="#main-content">Skip to main content</a>
+  
+  <input type="checkbox"
+          class="sidebar-toggle"
+          name="__primary"
+          id="__primary"/>
+  <label class="overlay overlay-primary" for="__primary"></label>
+  
+  <input type="checkbox"
+          class="sidebar-toggle"
+          name="__secondary"
+          id="__secondary"/>
+  <label class="overlay overlay-secondary" for="__secondary"></label>
+  
+  <div class="search-button__wrapper">
+    <div class="search-button__overlay"></div>
+    <div class="search-button__search-container">
+<form class="bd-search d-flex align-items-center"
+      action="../../search.html"
+      method="get">
+  <i class="fa-solid fa-magnifying-glass"></i>
+  <input type="search"
+         class="form-control"
+         name="q"
+         id="search-input"
+         placeholder="Search the docs ..."
+         aria-label="Search the docs ..."
+         autocomplete="off"
+         autocorrect="off"
+         autocapitalize="off"
+         spellcheck="false"/>
+  <span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
+</form></div>
+  </div>
+  
+    <nav class="bd-header navbar navbar-expand-lg bd-navbar">
+<div class="bd-header__inner bd-page-width">
+  <label class="sidebar-toggle primary-toggle" for="__primary">
+    <span class="fa-solid fa-bars"></span>
+  </label>
+  
+  <div class="navbar-header-items__start">
+    
+      <div class="navbar-item">
+  
+
+<a class="navbar-brand logo" href="../../index.html">
+  
+  
+  
+  
+    
+    
+    
+    <img src="../../_static/logo.png" class="logo__image only-light" alt="Logo image"/>
+    <script>document.write(`<img src="../../_static/logo.png" class="logo__image only-dark" alt="Logo image"/>`);</script>
+  
+  
+</a></div>
+    
+  </div>
+  
+  
+  <div class="col-lg-9 navbar-header-items">
+    
+    <div class="me-auto navbar-header-items__center">
+      
+        <div class="navbar-item"><nav class="navbar-nav">
+  <p class="sidebar-header-items__title"
+     role="heading"
+     aria-level="1"
+     aria-label="Site Navigation">
+    Site Navigation
+  </p>
+  <ul class="bd-navbar-elements navbar-nav">
+    
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../intro/index.html">
+                        Getting Started
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../guide/index.html">
+                        User Guide
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../examples/index.html">
+                        Example Gallery
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../api/index.html">
+                        API Reference
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item current active">
+                      <a class="nav-link nav-internal" href="../index.html">
+                        Extending Pyxu
+                      </a>
+                    </li>
+                
+  </ul>
+</nav></div>
+      
+    </div>
+    
+    
+    <div class="navbar-header-items__end">
+      
+        <div class="navbar-item navbar-persistent--container">
+          
+<script>
+document.write(`
+  <button class="btn btn-sm navbar-btn search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
+    <i class="fa-solid fa-magnifying-glass"></i>
+  </button>
+`);
+</script>
+        </div>
+      
+      
+        <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
+      
+        <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
+    aria-label="Icon Links">
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://github.com/matthieumeo/pyxu" title="GitHub" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-github"></i></span>
+            <label class="sr-only">GitHub</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://pypi.org/project/pyxu/" title="PyPI" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-python"></i></span>
+            <label class="sr-only">PyPI</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+            <label class="sr-only">Contact</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://imaging.epfl.ch/" title="EPFL Center for Imaging" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><img src="../../_static/imaging.png" class="icon-link-image" alt="EPFL Center for Imaging"/></a>
+        </li>
+</ul></div>
+      
+    </div>
+    
+  </div>
+  
+  
+    <div class="navbar-persistent--mobile">
+<script>
+document.write(`
+  <button class="btn btn-sm navbar-btn search-button search-button__button" title="Search" aria-label="Search" data-bs-placement="bottom" data-bs-toggle="tooltip">
+    <i class="fa-solid fa-magnifying-glass"></i>
+  </button>
+`);
+</script>
+    </div>
+  
+
+  
+</div>
+
+    </nav>
+  
+  <div class="bd-container">
+    <div class="bd-container__inner bd-page-width">
+      
+      <div class="bd-sidebar-primary bd-sidebar">
+        
+
+  
+  <div class="sidebar-header-items sidebar-primary__section">
+    
+    
+      <div class="sidebar-header-items__center">
+        
+          <div class="navbar-item"><nav class="navbar-nav">
+  <p class="sidebar-header-items__title"
+     role="heading"
+     aria-level="1"
+     aria-label="Site Navigation">
+    Site Navigation
+  </p>
+  <ul class="bd-navbar-elements navbar-nav">
+    
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../intro/index.html">
+                        Getting Started
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../guide/index.html">
+                        User Guide
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../examples/index.html">
+                        Example Gallery
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item">
+                      <a class="nav-link nav-internal" href="../../api/index.html">
+                        API Reference
+                      </a>
+                    </li>
+                
+
+                    <li class="nav-item current active">
+                      <a class="nav-link nav-internal" href="../index.html">
+                        Extending Pyxu
+                      </a>
+                    </li>
+                
+  </ul>
+</nav></div>
+        
+      </div>
+    
+    
+    
+      <div class="sidebar-header-items__end">
+        
+          <div class="navbar-item"><strong> Pyxu v1.0.1 </strong></div>
+        
+          <div class="navbar-item"><ul class="navbar-icon-links navbar-nav"
+    aria-label="Icon Links">
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://github.com/matthieumeo/pyxu" title="GitHub" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-github"></i></span>
+            <label class="sr-only">GitHub</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://pypi.org/project/pyxu/" title="PyPI" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-python"></i></span>
+            <label class="sr-only">PyPI</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="mailto: contact@pyxu.org" title="Contact" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><span><i class="fa-brands fa-telegram"></i></span>
+            <label class="sr-only">Contact</label></a>
+        </li>
+        <li class="nav-item">
+          
+          
+          
+          
+          
+          
+          
+          
+          <a href="https://imaging.epfl.ch/" title="EPFL Center for Imaging" class="nav-link" rel="noopener" target="_blank" data-bs-toggle="tooltip" data-bs-placement="bottom"><img src="../../_static/imaging.png" class="icon-link-image" alt="EPFL Center for Imaging"/></a>
+        </li>
+</ul></div>
+        
+      </div>
+    
+  </div>
+  
+    <div class="sidebar-primary-items__start sidebar-primary__section">
+        <div class="sidebar-primary-item"><nav class="bd-docs-nav bd-links"
+     aria-label="Section Navigation">
+  <p class="bd-links__title" role="heading" aria-level="1">Section Navigation</p>
+  <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="../howto.html">How to use plugins in Pyxu?</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="current reference internal" href="#">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
+<li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
+<li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
+<li class="toctree-l2"><a class="reference internal" href="HoughDetector.html">HoughDetector</a></li>
+<li class="toctree-l2"><a class="reference internal" href="HVOX.html">HVOX</a></li>
+<li class="toctree-l2"><a class="reference internal" href="OrientationPy.html">OrientationPy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Palentologist.html">Palentologist</a></li>
+<li class="toctree-l2"><a class="reference internal" href="PhaseRet.html">PhaseRet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="PycGSP.html">PycGSP</a></li>
+<li class="toctree-l2"><a class="reference internal" href="pycNUFFT.html">pycNUFFT</a></li>
+<li class="toctree-l2"><a class="reference internal" href="PycSphere.html">PycSphere</a></li>
+<li class="toctree-l2"><a class="reference internal" href="pycWavelet.html">pycWavelet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="PYFW.html">PYFW</a></li>
+<li class="toctree-l2"><a class="reference internal" href="TokemakRec.html">TokemakRec</a></li>
+<li class="toctree-l2"><a class="reference internal" href="TVDenoiser.html">TVDenoiser</a></li>
+<li class="toctree-l2"><a class="reference internal" href="UncertaintyQuant.html">UncertaintyQuant</a></li>
+<li class="toctree-l2"><a class="reference internal" href="WaveProp.html">WaveProp</a></li>
+</ul>
+</li>
+</ul>
+</div>
+</nav></div>
+    </div>
+  
+  
+  <div class="sidebar-primary-items__end sidebar-primary__section">
+  </div>
+  
+  <div id="rtd-footer-container"></div>
+
+
+      </div>
+      
+      <main id="main-content" class="bd-main">
+        
+        
+          <div class="bd-content">
+            <div class="bd-article-container">
+              
+              <div class="bd-header-article">
+<div class="header-article-items header-article__inner">
+  
+    <div class="header-article-items__start">
+      
+        <div class="header-article-item">
+
+
+
+<nav aria-label="Breadcrumbs">
+  <ul class="bd-breadcrumbs" role="navigation" aria-label="Breadcrumb">
+    
+    <li class="breadcrumb-item breadcrumb-home">
+      <a href="../../index.html" class="nav-link" aria-label="Home">
+        <i class="fa-solid fa-home"></i>
+      </a>
+    </li>
+    
+    <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
+    
+    <li class="breadcrumb-item active" aria-current="page">Plugin Preview Catalog</li>
+  </ul>
+</nav>
+</div>
+      
+    </div>
+  
+  
+</div>
+</div>
+              
+              
+              
+                
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <!-- CSS overrides on the pyxu-fair only -->
+<style>
+.globalsummary-box {
+    width:95%;
+    padding:10px;
+    margin: 20px;
+    padding-left: 40px;
+    padding-right: 40px;
+    background-color: rgba(255,255,255,0.19);
+    border:1px solid rgba(50,50,50,0.4);
+    border-radius:4px;
+    -webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,.05);
+    box-shadow:inset 0 1px 1px rgba(0,0,0,.05);
+    line-height: 1.5;
+}
+.summaryinfo {
+    color: #000;
+    font-size: 80%;
+    margin-bottom: 12px;
+    margin-top: 12px;
+}
+.submenu-entry {
+    width:90%;
+    min-height:140px;
+    padding:10px;
+    margin: 20px;
+    padding-left: 40px;
+    padding-right: 40px;
+    background-color:rgba(245,245,245,.19);
+    border:1px solid rgba(227,227,227,.31);
+    border-radius:4px;
+    -webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,.05);
+    box-shadow:inset 0 1px 1px rgba(0,0,0,.05);
+}
+.badge {
+    white-space: nowrap;
+    display: inline-block;
+    vertical-align: middle;
+    /*vertical-align: baseline;*/
+    font-family: "DejaVu Sans", Verdana, Geneva, sans-serif;
+    /*font-size: 90%;*/
+}
+.currentstate {
+    color: #666;
+    font-size: 90%;
+    margin-bottom: 12px;
+}
+span.badge-left {
+    border-radius: .25rem;
+    border-top-right-radius: 0;
+    border-bottom-right-radius: 0;
+    color: #212529;
+    background-color: #A2CBFF;
+    /* color: #ffffff; */
+    text-shadow: 1px 1px 1px rgba(0,0,0,0.3);
+
+    padding: .25em .4em;
+    line-height: 1;
+    text-align: center;
+    white-space: nowrap;
+    float: left;
+    display: block;
+}
+
+span.badge-right {
+    border-radius: .25rem;
+    border-top-left-radius: 0;
+    border-bottom-left-radius: 0;
+
+    color: #fff;
+    background-color: #343a40;
+
+    padding: .25em .4em;
+    line-height: 1;
+    text-align: center;
+    white-space: nowrap;
+    float: left;
+    display: block;
+}
+
+.badge-right.light-blue, .badge-left.light-blue {
+    background-color: #A2CBFF;
+    color: #212529;
+}
+
+.badge-right.light-red, .badge-left.light-red {
+    background-color: rgb(255, 162, 162);
+    color: rgb(43, 14, 14);
+}
+
+.badge-right.red, .badge-left.red {
+    background-color: #e41a1c;
+    color: #fff;
+}
+
+.badge-right.blue, .badge-left.blue {
+    background-color: #377eb8;
+    color: #fff;
+}
+
+.badge-right.green, .badge-left.green {
+    background-color: #4daf4a;
+    color: #fff;
+}
+
+.badge-right.purple, .badge-left.purple {
+    background-color: #984ea3;
+    color: #fff;
+}
+
+.badge-right.orange, .badge-left.orange {
+    background-color: #ff7f00;
+    color: #fff;
+}
+
+.badge-right.brown, .badge-left.brown {
+    background-color: #a65628;
+    color: #fff;
+}
+
+.badge-right.dark-gray, .badge-left.dark-gray {
+    color: #fff;
+    background-color: #343a40;
+}
+
+
+.badge a {
+    text-decoration: none;
+    padding: 0;
+    border: 0;
+    color: inherit;
+}
+
+.badge a:visited, .badge a:active {
+    color: inherit;
+  }
+
+.badge a:focus, .badge a:hover {
+    color: rgba(255,255,255,0.5);
+    mix-blend-mode: difference;
+    text-decoration: none;
+    /* background-color: rgb(192, 219, 255); */
+}
+
+
+.svg-badge {
+    vertical-align: middle;
+}
+
+.tooltip {
+    position: relative;
+    display: inline-block;
+    border-bottom: 1px dotted black;
+}
+
+.tooltip .tooltiptext {
+    visibility: hidden;
+    /* width: 120px; */
+    background-color: rgb(255, 247, 175);
+    color: #000;
+    text-align: center;
+    border-radius: 6px;
+    padding: 5px;
+
+    /* Position the tooltip */
+    position: absolute;
+    z-index: 1;
+}
+
+.tooltip:hover .tooltiptext {
+    visibility: visible;
+}
+</style><section id="plugin-preview-catalog">
+<h1 class="sd-d-none">Plugin Preview Catalog<a class="headerlink" href="#plugin-preview-catalog" title="Link to this heading">#</a></h1>
+<h2 style="font-size: 60px; font-weight: bold; display: inline"><span>Plugin Catalogue</span></h2><p><strong>Total Registered Plugin Packages: 17</strong></p>
+<div class='globalsummary-box'>
+     <div style="display: table;">
+
+         <span class="badge" style="display: table-row; line-height: 2;">
+             <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left blue" style="float: none; display: inline; text-align: right; border: none">Operator</span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">17 plugins in 12 packages </span></span>
+         </span>
+
+         <span class="badge" style="display: table-row; line-height: 2;">
+             <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left brown" style="float: none; display: inline; text-align: right; border: none">Solver</span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">14 plugins in 10 packages </span></span>
+         </span>
+
+         <span class="badge" style="display: table-row; line-height: 2;">
+             <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left purple" style="float: none; display: inline; text-align: right; border: none">Stop</span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">18 plugins in 11 packages </span></span>
+         </span>
+
+         <span class="badge" style="display: table-row; line-height: 2;">
+             <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left green" style="float: none; display: inline; text-align: right; border: none">Math</span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">16 plugins in 10 packages </span></span>
+         </span>
+
+         <span class="badge" style="display: table-row; line-height: 2;">
+             <span style="display: table-cell; float: none; text-align: right;"><span class="badge-left orange" style="float: none; display: inline; text-align: right; border: none">Contrib</span></span>
+             <span style="display: table-cell; float: none; text-align: left;"><span class="badge-right" style="float: none; display: inline; text-align: left; border: none">20 plugins in 12 packages </span></span>
+         </span>
+
+     </div>
+ </div><p><strong>Plugin in alphabetical order:</strong></p>
+<div class="sd-container-fluid sd-sphinx-override sd-mb-4 docutils">
+<div class="sd-row sd-row-cols-2 sd-row-cols-xs-2 sd-row-cols-sm-2 sd-row-cols-md-3 sd-row-cols-lg-3 sd-g-3 sd-g-xs-3 sd-g-sm-3 sd-g-md-3 sd-g-lg-3 docutils">
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="CSEEG.html">CSEEG</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Planning: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/lbrooks/CSEEG" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://lbrooks.github.io/CSEEG/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 69.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="DSP-Notebooks.html">DSP-Notebooks</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/sdunn/DSP-Notebooks" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://sdunn.github.io/DSP-Notebooks/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 83.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">2</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">2</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">3</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="EnvironTracker.html">EnvironTracker</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/cedwards/EnvironTracker" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://cedwards.github.io/EnvironTracker/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 79.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="HoughDetector.html">HoughDetector</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/abrick/HoughDetector" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://abrick.github.io/HoughDetector/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 56.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">4</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="HVOX.html">HVOX</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Pre-alpha: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/snassar/HVOX" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://snassar.github.io/HVOX/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 80.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="OrientationPy.html">OrientationPy</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Mature: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/mmonteith/OrientationPy" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://mmonteith.github.io/OrientationPy/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 77.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">2</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="Palentologist.html">Palentologist</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/knaiman/Palentologist" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://knaiman.github.io/Palentologist/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 73.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="PhaseRet.html">PhaseRet</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-inactive-bbbbbb.svg" title="Inactive: No longer maintained.">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/esequeira/PhaseRet" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://esequeira.github.io/PhaseRet/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">2</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">3</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">3</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="PycGSP.html">PycGSP</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/doliphant/PycGSP" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://doliphant.github.io/PycGSP/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 77.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">2</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">3</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="pycNUFFT.html">pycNUFFT</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/csincell/pycNUFFT" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://csincell.github.io/pycNUFFT/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 78.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">2</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="PycSphere.html">PycSphere</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-planning-d9644d.svg" title="Pre-alpha: Not yet ready to use. Developers welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/jhawk/PycSphere" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://jhawk.github.io/PycSphere/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 79.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">2</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="pycWavelet.html">pycWavelet</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-alpha-d6af23.svg" title="Alpha: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/cpark/pycWavelet" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://cpark.github.io/pycWavelet/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 68.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">2</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">3</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">3</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="PYFW.html">PYFW</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Mature: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/rshelton/PYFW" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://rshelton.github.io/PYFW/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 95.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">2</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">2</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="TokemakRec.html">TokemakRec</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-beta-d6af23.svg" title="Beta: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/msmith/TokemakRec" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://msmith.github.io/TokemakRec/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 91.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">3</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">2</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="TVDenoiser.html">TVDenoiser</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-inactive-bbbbbb.svg" title="Inactive: No longer maintained.">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/dbrown/TVDenoiser" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://dbrown.github.io/TVDenoiser/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">3</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="UncertaintyQuant.html">UncertaintyQuant</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-stable-4cc61e.svg" title="Production/Stable: Ready for production calculations. Bug reports welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/kdavis/UncertaintyQuant" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://kdavis.github.io/UncertaintyQuant/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 88.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+<div class="sd-col sd-d-flex-row docutils">
+<div class="sd-card sd-sphinx-override sd-w-100 sd-shadow-sm docutils">
+<div class="sd-card-body docutils">
+<h2 style="font-size: 30px;"><a href="WaveProp.html">WaveProp</a></h2>
+
+<p class="currentstate">
+
+    <img class="svg-badge" src="../../_static/plugins/status/status-beta-d6af23.svg" title="Beta: Adds new functionality, not yet ready for production. Testing welcome!">&nbsp;<img class="svg-badge" title="Compatible with Pyxu plugin.pyxu_version }}" src="https://img.shields.io/badge/Pyxu-2.0.0-007ec6.svg?logo=data:image/png;base64,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"></p>
+
+<ul class="plugin-info">
+
+
+    <li>
+        <a href="https://github.com/knix/WaveProp" target="_blank">Home page</a>
+    </li>
+
+
+
+    <li>
+        <a href="https://knix.github.io/WaveProp/html/index" target="_blank">Documentation</a>
+    </li>
+
+
+
+    <li>
+        <a> Score: 76.0 % </a>
+    </li>
+
+</ul>
+
+<p class="summaryinfo">
+
+    <span class="badge">
+        <span class="badge-left blue">Operator</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left brown">Solver</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left purple">Stop</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left green">Math</span>
+        <span class="badge-right">1</span>
+    </span>
+
+    <span class="badge">
+        <span class="badge-left orange">Contrib</span>
+        <span class="badge-right">1</span>
+    </span>
+
+</p></div>
+</div>
+</div>
+</div>
+</div>
+<div class="toctree-wrapper compound">
+</div>
+</section>
+
+
+                </article>
+              
+              
+              
+                <footer class="bd-footer-article">
+                  
+<div class="footer-article-items footer-article__inner">
+  
+    <div class="footer-article-item"><!-- Previous / next buttons -->
+<div class="prev-next-area">
+    <a class="left-prev"
+       href="../plugins/pyxu-gradient-descent.html"
+       title="previous page">
+      <i class="fa-solid fa-angle-left"></i>
+      <div class="prev-next-info">
+        <p class="prev-next-subtitle">previous</p>
+        <p class="prev-next-title">pyxu-gradient-descent</p>
+      </div>
+    </a>
+    <a class="right-next"
+       href="CSEEG.html"
+       title="next page">
+      <div class="prev-next-info">
+        <p class="prev-next-subtitle">next</p>
+        <p class="prev-next-title">CSEEG</p>
+      </div>
+      <i class="fa-solid fa-angle-right"></i>
+    </a>
+</div></div>
+  
+</div>
+
+                </footer>
+              
+            </div>
+            
+            
+              
+            
+          </div>
+          <footer class="bd-footer-content">
+            
+          </footer>
+        
+      </main>
+    </div>
+  </div>
+  
+  <!-- Scripts loaded after <body> so the DOM is not blocked -->
+  <script src="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52"></script>
+<script src="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52"></script>
+
+  <footer class="bd-footer">
+<div class="bd-footer__inner bd-page-width">
+  
+    <div class="footer-items__start">
+      
+        <div class="footer-item">
+  <p class="copyright">
+    
+      © Copyright 2023, M. Simeoni, S. Kashani, J. Rué-Queralt &amp; Pyxu Developers.
+      <br/>
+    
+  </p>
+</div>
+      
+        <div class="footer-item">
+  <p class="sphinx-version">
+     Created with <a href="https://www.sphinx-doc.org/">Sphinx</a> 7.2.5, with some help from <a href="https://chat.openai.com/"> ChatGPT</a> (GPT 4).
+    <br/>
+  </p>
+</div>
+      
+    </div>
+  
+  
+    <div class="footer-items__end">
+      
+        <div class="footer-item"><p class="theme-version">
+  Built with the <a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">PyData Sphinx Theme</a> 0.13.3.
+</p></div>
+      
+    </div>
+  
+</div>
+
+  </footer>
+  </body>
+</html>
\ No newline at end of file
diff --git a/fair/plugins/pycNUFFT.html b/fair/plugins_preview/pycNUFFT.html
similarity index 95%
rename from fair/plugins/pycNUFFT.html
rename to fair/plugins_preview/pycNUFFT.html
index ace56dca..b7824e97 100644
--- a/fair/plugins/pycNUFFT.html
+++ b/fair/plugins_preview/pycNUFFT.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/pycNUFFT';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/pycNUFFT';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">pycNUFFT</li>
   </ul>
@@ -795,7 +800,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/pycNUFFT.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/pycNUFFT.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -809,7 +814,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/pycNUFFT.rst">
+    <a href="../../_sources/fair/plugins_preview/pycNUFFT.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/plugins/pycWavelet.html b/fair/plugins_preview/pycWavelet.html
similarity index 95%
rename from fair/plugins/pycWavelet.html
rename to fair/plugins_preview/pycWavelet.html
index 1ebf695e..458488bc 100644
--- a/fair/plugins/pycWavelet.html
+++ b/fair/plugins_preview/pycWavelet.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../../_static/doctools.js?v=888ff710"></script>
     <script src="../../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -57,7 +57,7 @@
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
     <script crossorigin="anonymous" integrity="sha256-Ae2Vz/4ePdIu6ZyI/5ZGsYnb+m0JlOmKPjt6XZ9JJkA=" src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js"></script>
     <script>var togglebuttonSelector = '.toggle, .admonition.dropdown';</script>
-    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins/pycWavelet';</script>
+    <script>DOCUMENTATION_OPTIONS.pagename = 'fair/plugins_preview/pycWavelet';</script>
     <link rel="icon" href="../../_static/favicon.png"/>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
@@ -410,7 +410,12 @@
 <li class="toctree-l1"><a class="reference internal" href="../contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../score.html">Pyxu Score Explained</a></li>
-<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
+<li class="toctree-l1 has-children"><a class="reference internal" href="../plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current active has-children"><a class="reference internal" href="index.html">Plugin Preview Catalog</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
 <li class="toctree-l2"><a class="reference internal" href="CSEEG.html">CSEEG</a></li>
 <li class="toctree-l2"><a class="reference internal" href="DSP-Notebooks.html">DSP-Notebooks</a></li>
 <li class="toctree-l2"><a class="reference internal" href="EnvironTracker.html">EnvironTracker</a></li>
@@ -471,7 +476,7 @@
     <li class="breadcrumb-item"><a href="../index.html" class="nav-link">Extending Pyxu</a></li>
     
     
-    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Catalog</a></li>
+    <li class="breadcrumb-item"><a href="index.html" class="nav-link">Plugin Preview Catalog</a></li>
     
     <li class="breadcrumb-item active" aria-current="page">pycWavelet</li>
   </ul>
@@ -815,7 +820,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
   <div class="sidebar-secondary-item">
   
   <div class="tocsection editthispage">
-    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins/pycWavelet.rst">
+    <a href="https://github.com/matthieumeo/pyxu/edit/main/doc/fair/plugins_preview/pycWavelet.rst">
       <i class="fa-solid fa-pencil"></i>
       
       
@@ -829,7 +834,7 @@ <h2>Components contributed<a class="headerlink" href="#components-contributed" t
 
   <div class="sidebar-secondary-item">
   <div class="tocsection sourcelink">
-    <a href="../../_sources/fair/plugins/pycWavelet.rst">
+    <a href="../../_sources/fair/plugins_preview/pycWavelet.rst">
       <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
   </div>
diff --git a/fair/score.html b/fair/score.html
index 4c028c8f..07d3e3c8 100644
--- a/fair/score.html
+++ b/fair/score.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -61,7 +61,7 @@
     <link rel="icon" href="../_static/favicon.png"/>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
-    <link rel="next" title="Plugin Catalog" href="plugins/index.html" />
+    <link rel="next" title="Catalogue" href="plugins/index.html" />
     <link rel="prev" title="Developer Notes" href="dev_notes.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
   <meta name="docsearch:language" content="en"/>
@@ -410,24 +410,29 @@
 <li class="toctree-l1"><a class="reference internal" href="contribute.html">Contributing to the Pyxu-FAIR</a></li>
 <li class="toctree-l1"><a class="reference internal" href="dev_notes.html">Developer Notes</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">Pyxu Score Explained</a></li>
-<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Plugin Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
-<li class="toctree-l2"><a class="reference internal" href="plugins/CSEEG.html">CSEEG</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/DSP-Notebooks.html">DSP-Notebooks</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/EnvironTracker.html">EnvironTracker</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HoughDetector.html">HoughDetector</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/HVOX.html">HVOX</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/OrientationPy.html">OrientationPy</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/Palentologist.html">Palentologist</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PhaseRet.html">PhaseRet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycGSP.html">PycGSP</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycNUFFT.html">pycNUFFT</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PycSphere.html">PycSphere</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/pycWavelet.html">pycWavelet</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/PYFW.html">PYFW</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TokemakRec.html">TokemakRec</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/TVDenoiser.html">TVDenoiser</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/UncertaintyQuant.html">UncertaintyQuant</a></li>
-<li class="toctree-l2"><a class="reference internal" href="plugins/WaveProp.html">WaveProp</a></li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins/index.html">Catalogue</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-eigh.html">pyxu-eigh</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins/pyxu-gradient-descent.html">pyxu-gradient-descent</a></li>
+</ul>
+</li>
+<li class="toctree-l1 has-children"><a class="reference internal" href="plugins_preview/index.html">Plugin Preview Catalog</a><input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-2"><i class="fa-solid fa-chevron-down"></i></label><ul>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/CSEEG.html">CSEEG</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/DSP-Notebooks.html">DSP-Notebooks</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/EnvironTracker.html">EnvironTracker</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HoughDetector.html">HoughDetector</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/HVOX.html">HVOX</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/OrientationPy.html">OrientationPy</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/Palentologist.html">Palentologist</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PhaseRet.html">PhaseRet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycGSP.html">PycGSP</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycNUFFT.html">pycNUFFT</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PycSphere.html">PycSphere</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/pycWavelet.html">pycWavelet</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/PYFW.html">PYFW</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TokemakRec.html">TokemakRec</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/TVDenoiser.html">TVDenoiser</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/UncertaintyQuant.html">UncertaintyQuant</a></li>
+<li class="toctree-l2"><a class="reference internal" href="plugins_preview/WaveProp.html">WaveProp</a></li>
 </ul>
 </li>
 </ul>
@@ -489,12 +494,17 @@
                   
   <section id="pyxu-score-explained">
 <h1>Pyxu Score Explained<a class="headerlink" href="#pyxu-score-explained" title="Link to this heading">#</a></h1>
-<p>The <strong>Pyxu Score</strong> is a quantitative measure we use to rank and evaluate Pyxu plugins. The score takes into account
-multiple criteria, ensuring you get a holistic understanding of a plugin’s standing. Here’s a breakdown:</p>
-<p>The Pyxu Score is calculated using the following criteria:</p>
+<p>The <strong>Pyxu Score</strong> is a quantitative measure we use to rank and evaluate <a class="reference external" href="./plugins/index.html">Pyxu plugins</a>.</p>
+<div class="admonition warning">
+<p class="admonition-title">Warning</p>
+<p>While the Pyxu Score offers insights into a plugin’s quality and popularity, it’s just one of many metrics.
+Users are encouraged to explore plugins individually and consider other factors before making a decision.</p>
+</div>
+<p>The score takes into account multiple criteria, ensuring you get a holistic understanding of a plugin’s standing. Here’s
+a breakdown:</p>
 <ol class="arabic">
-<li><p><strong>Version Matching</strong>: If a plugin’s version matches the latest Pyxu version, it gets a point.</p></li>
-<li><p><strong>Pyxu Principles Adherence</strong>: Plugins abiding by key Pyxu principles, namely:</p>
+<li><p><strong>Version Matching</strong>: If a plugin’s version matches the latest Pyxu version, and the latest Python version it gets a point.</p></li>
+<li><p><strong>Pyxu Principles Adherence</strong>: Plugins abiding by key <a class="reference external" href="./dev_notes.html">Pyxu principles</a>, namely:</p>
 <ul class="simple">
 <li><p>Input shape agnosticity (i.e., support for NDArrays),</p></li>
 <li><p>Complete backend-agnosticity (i.e., support for Numpy, Cupy and Dask arrays),</p></li>
@@ -504,22 +514,21 @@ <h1>Pyxu Score Explained<a class="headerlink" href="#pyxu-score-explained" title
 </li>
 <li><p><strong>Development Stage Weight</strong>:</p>
 <ul class="simple">
-<li><p><strong>Early stages</strong> (Planning 📑, Pre-Alpha 🌒, Alpha 🌓) contribute 0.5 points.</p></li>
-<li><p><strong>Advanced stages</strong> (Beta 🌔, Production/Stable ✔️, Mature 🌟) contribute 1 point.</p></li>
-<li><p><strong>Inactive 🚫</strong> plugins do not recieive a score.</p></li>
+<li><p><strong>Early stages</strong> (Planning, Pre-Alpha, Alpha) contribute 0.5 points.</p></li>
+<li><p><strong>Advanced stages</strong> (Beta, Production/Stable, Mature) contribute 1 point.</p></li>
+<li><p><strong>Inactive</strong> plugins do not recieive a score.</p></li>
 </ul>
+<p>See <a class="reference external" href="https://pypi.org/classifiers/">the PyPI classifiers</a> for more information on the development stages.</p>
 </li>
-<li><p><strong>Downloads ⬇️</strong>: Plugins get points based on the number of downloads in the last month, up to a maximum of 1 point
+<li><p><strong>Downloads</strong>: Plugins get points based on the number of downloads in the last month, up to a maximum of 1 point
 for 1000 downloads.</p></li>
 </ol>
 <p>The final score is then normalized by the number of criteria used (6 in this case) and presented as a percentage.</p>
-<p><strong>Note</strong>: While the Pyxu Score offers insights into a plugin’s quality and popularity, it’s just one of many metrics.
-Users are encouraged to explore plugins individually and consider other factors before making a decision.</p>
 <h3 style="margin-top: 0; font-weight: bold; text-align: left; ">Contribute to the Pyxu Score</h3><p>Your insights matter! If you’re a developer with ideas on how we can further refine the Pyxu Score, we’d love to hear
 from you. 💡</p>
-<p>We invite you to <strong>open an issue</strong> suggesting novel metrics or criteria that, in your opinion, would better represent
-the value and quality of Pyxu plugins. By contributing your thoughts, you play an integral role in refining and shaping
-the Pyxu community’s standards.</p>
+<p>We invite you to <a class="reference external" href="https://github.com/matthieumeo/pyxu/issues">open an issue</a> suggesting novel metrics or criteria
+that, in your opinion, would better represent the value and quality of Pyxu plugins. By contributing your thoughts, you
+play an integral role in refining and shaping the Pyxu community’s standards.</p>
 <p>Together, let’s make the Pyxu Score the best reflection of plugin excellence! 🌟</p>
 </section>
 
@@ -548,7 +557,7 @@ <h3 style="margin-top: 0; font-weight: bold; text-align: left; ">Contribute to t
        title="next page">
       <div class="prev-next-info">
         <p class="prev-next-subtitle">next</p>
-        <p class="prev-next-title">Plugin Catalog</p>
+        <p class="prev-next-title">Catalogue</p>
       </div>
       <i class="fa-solid fa-angle-right"></i>
     </a>
diff --git a/genindex.html b/genindex.html
index fbe4f178..29dd5fdf 100644
--- a/genindex.html
+++ b/genindex.html
@@ -27,7 +27,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
@@ -37,13 +37,13 @@
     <link rel="stylesheet" type="text/css" href="_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="_static/documentation_options.js?v=a4a8746c"></script>
     <script src="_static/doctools.js?v=888ff710"></script>
     <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="_static/clipboard.min.js?v=a7894cd8"></script>
@@ -454,9 +454,9 @@ <h1 id="index">Index</h1>
 <h2 id="_">_</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.__add__">__add__() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.__add__">__add__() (Operator method)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Map.__call__">__call__() (Map method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Map.__call__">__call__() (Map method)</a>
 </li>
       <li><a href="api/opt.stop.html#pyxu.opt.stop.AbsError.__init__">__init__() (AbsError method)</a>
 
@@ -485,17 +485,17 @@ <h2 id="_">_</h2>
 </li>
         <li><a href="api/experimental.sampler.html#pyxu.experimental.sampler.MYULA.__init__">(MYULA method)</a>
 </li>
-        <li><a href="api/abc/operator.html#pyxu.abc.Operator.__init__">(Operator method)</a>
+        <li><a href="api/abc.html#pyxu.abc.Operator.__init__">(Operator method)</a>
 </li>
         <li><a href="api/operator/linop.html#pyxu.operator.Pad.__init__">(Pad method)</a>
 </li>
-        <li><a href="api/abc/operator.html#pyxu.abc.QuadraticFunc.__init__">(QuadraticFunc method)</a>
+        <li><a href="api/abc.html#pyxu.abc.QuadraticFunc.__init__">(QuadraticFunc method)</a>
 </li>
         <li><a href="api/operator/func.html#pyxu.operator.RangeSet.__init__">(RangeSet method)</a>
 </li>
         <li><a href="api/opt.stop.html#pyxu.opt.stop.RelError.__init__">(RelError method)</a>
 </li>
-        <li><a href="api/abc/solver.html#pyxu.abc.Solver.__init__">(Solver method)</a>
+        <li><a href="api/abc.html#pyxu.abc.Solver.__init__">(Solver method)</a>
 </li>
         <li><a href="api/operator/func.html#pyxu.operator.SquaredL1Norm.__init__">(SquaredL1Norm method)</a>
 </li>
@@ -508,27 +508,27 @@ <h2 id="_">_</h2>
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.__mul__">__mul__() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.__mul__">__mul__() (Operator method)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.__neg__">__neg__() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.__neg__">__neg__() (Operator method)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.__pow__">__pow__() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.__pow__">__pow__() (Operator method)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.__sub__">__sub__() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.__sub__">__sub__() (Operator method)</a>
 </li>
-      <li><a href="api/util/operator.html#pyxu.util.operator._array_ize">_array_ize() (in module pyxu.util.operator)</a>
+      <li><a href="api/util.html#pyxu.util.operator._array_ize">_array_ize() (in module pyxu.util.operator)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver._astate">_astate (Solver attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver._astate">_astate (Solver attribute)</a>
 </li>
-      <li><a href="api/util/operator.html#pyxu.util.operator._dask_zip">_dask_zip() (in module pyxu.util.operator)</a>
+      <li><a href="api/util.html#pyxu.util.operator._dask_zip">_dask_zip() (in module pyxu.util.operator)</a>
 </li>
       <li><a href="api/operator.interop.html#pyxu.operator.interop.jax._from_jax">_from_jax() (in module pyxu.operator.interop.jax)</a>
 </li>
       <li><a href="api/operator.interop.html#pyxu.operator.interop.torch._from_torch">_from_torch() (in module pyxu.operator.interop.torch)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver._mstate">_mstate (Solver attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver._mstate">_mstate (Solver attribute)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.QuadraticFunc._quad_spec">_quad_spec() (QuadraticFunc method)</a>
+      <li><a href="api/abc.html#pyxu.abc.QuadraticFunc._quad_spec">_quad_spec() (QuadraticFunc method)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator._Stencil">_Stencil (class in pyxu.operator)</a>
 </li>
@@ -548,12 +548,12 @@ <h2 id="A">A</h2>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.Adam">Adam (class in pyxu.opt.solver)</a>
 </li>
-      <li><a href="api/abc/arithmetic.html#pyxu.abc.arithmetic.AddRule">AddRule (class in pyxu.abc.arithmetic)</a>
+      <li><a href="api/abc.html#pyxu.abc.arithmetic.AddRule">AddRule (class in pyxu.abc.arithmetic)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.FFT.adjoint">adjoint() (FFT method)</a>
 
       <ul>
-        <li><a href="api/abc/operator.html#pyxu.abc.LinOp.adjoint">(LinOp method)</a>
+        <li><a href="api/abc.html#pyxu.abc.LinOp.adjoint">(LinOp method)</a>
 </li>
         <li><a href="api/operator/linop.html#pyxu.operator.NUFFT.adjoint">(NUFFT method)</a>
 </li>
@@ -571,7 +571,7 @@ <h2 id="A">A</h2>
       <ul>
         <li><a href="api/operator/linop.html#pyxu.operator.FFT.apply">(FFT method)</a>
 </li>
-        <li><a href="api/abc/operator.html#pyxu.abc.Map.apply">(Map method)</a>
+        <li><a href="api/abc.html#pyxu.abc.Map.apply">(Map method)</a>
 </li>
         <li><a href="api/operator/linop.html#pyxu.operator.NUFFT.apply">(NUFFT method)</a>
 </li>
@@ -594,29 +594,29 @@ <h2 id="A">A</h2>
 </li>
       <li><a href="api/operator/map.html#pyxu.operator.arctanh">arctanh() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.argscale">argscale() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.argscale">argscale() (Operator method)</a>
 </li>
-      <li><a href="api/abc/arithmetic.html#pyxu.abc.arithmetic.ArgScaleRule">ArgScaleRule (class in pyxu.abc.arithmetic)</a>
+      <li><a href="api/abc.html#pyxu.abc.arithmetic.ArgScaleRule">ArgScaleRule (class in pyxu.abc.arithmetic)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.argshift">argshift() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.argshift">argshift() (Operator method)</a>
 </li>
-      <li><a href="api/abc/arithmetic.html#pyxu.abc.arithmetic.ArgShiftRule">ArgShiftRule (class in pyxu.abc.arithmetic)</a>
+      <li><a href="api/abc.html#pyxu.abc.arithmetic.ArgShiftRule">ArgShiftRule (class in pyxu.abc.arithmetic)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.arithmetic_methods">arithmetic_methods() (Property method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.arithmetic_methods">arithmetic_methods() (Property method)</a>
 </li>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.ArrayModule">ArrayModule (class in pyxu.info.ptype)</a>
 </li>
-      <li><a href="api/util/operator.html#pyxu.util.as_canonical_shape">as_canonical_shape() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.as_canonical_shape">as_canonical_shape() (in module pyxu.util)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.asarray">asarray() (LinOp method)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.asarray">asarray() (LinOp method)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.NUFFT.ascomplexarray">ascomplexarray() (NUFFT method)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Func.asloss">asloss() (Func method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Func.asloss">asloss() (Func method)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.asop">asop() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.asop">asop() (Operator method)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.SolverMode.ASYNC">ASYNC (SolverMode attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.SolverMode.ASYNC">ASYNC (SolverMode attribute)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.NUFFT.auto_chunk">auto_chunk() (NUFFT method)</a>
 </li>
@@ -632,7 +632,7 @@ <h2 id="B">B</h2>
 </li>
       <li><a href="api/math.html#pyxu.math.backtracking_linesearch">backtracking_linesearch() (in module pyxu.math)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.SolverMode.BLOCK">BLOCK (SolverMode attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.SolverMode.BLOCK">BLOCK (SolverMode attribute)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
@@ -640,7 +640,7 @@ <h2 id="B">B</h2>
 </li>
       <li><a href="api/operator/blocks.html#pyxu.operator.block_diag">block_diag() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.busy">busy() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.busy">busy() (Solver method)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -648,7 +648,7 @@ <h2 id="B">B</h2>
 <h2 id="C">C</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.CAN_EVAL">CAN_EVAL (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.CAN_EVAL">CAN_EVAL (Property attribute)</a>
 </li>
       <li><a href="api/operator/map.html#pyxu.operator.cbrt">cbrt() (in module pyxu.operator)</a>
 </li>
@@ -656,23 +656,23 @@ <h2 id="C">C</h2>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.CG">CG (class in pyxu.opt.solver)</a>
 </li>
-      <li><a href="api/abc/arithmetic.html#pyxu.abc.arithmetic.ChainRule">ChainRule (class in pyxu.abc.arithmetic)</a>
+      <li><a href="api/abc.html#pyxu.abc.arithmetic.ChainRule">ChainRule (class in pyxu.abc.arithmetic)</a>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.ChambollePock">ChambollePock() (in module pyxu.opt.solver)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.StoppingCriterion.clear">clear() (StoppingCriterion method)</a>
+      <li><a href="api/abc.html#pyxu.abc.StoppingCriterion.clear">clear() (StoppingCriterion method)</a>
 </li>
       <li><a href="api/operator/map.html#pyxu.operator.clip">clip() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.codim">codim (Operator property)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.codim">codim (Operator property)</a>
 </li>
       <li><a href="api/runtime.html#pyxu.runtime.coerce">coerce() (in module pyxu.runtime)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.cogram">cogram() (LinOp method)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.cogram">cogram() (LinOp method)</a>
 </li>
       <li><a href="api/runtime.html#pyxu.runtime.Width.complex">complex (Width property)</a>
 </li>
-      <li><a href="api/util/misc.html#pyxu.util.compute">compute() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.compute">compute() (in module pyxu.util)</a>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.CondatVu">CondatVu (class in pyxu.opt.solver)</a>
 </li>
@@ -680,8 +680,6 @@ <h2 id="C">C</h2>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/info.ptype.html#pyxu.info.ptype.Real.conjugate">conjugate() (Real method)</a>
-</li>
       <li><a href="api/operator/map.html#pyxu.operator.ConstantValued">ConstantValued() (in module pyxu.operator)</a>
 </li>
       <li><a href="api/info.warning.html#pyxu.info.warning.ContributionWarning">ContributionWarning</a>
@@ -692,7 +690,7 @@ <h2 id="C">C</h2>
 </li>
       <li><a href="api/operator/blocks.html#pyxu.operator.coo_block">coo_block() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/util/misc.html#pyxu.util.copy_if_unsafe">copy_if_unsafe() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.copy_if_unsafe">copy_if_unsafe() (in module pyxu.util)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.Correlate">Correlate (in module pyxu.operator)</a>
 </li>
@@ -718,11 +716,11 @@ <h2 id="C">C</h2>
 <h2 id="D">D</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.dagger">dagger() (LinOp method)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.dagger">dagger() (LinOp method)</a>
 </li>
       <li><a href="api/info.deps.html#pyxu.info.deps.NDArrayInfo.DASK">DASK (NDArrayInfo attribute)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.datafile">datafile (Solver property)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.datafile">datafile (Solver property)</a>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.DavisYin">DavisYin (class in pyxu.opt.solver)</a>
 </li>
@@ -732,7 +730,7 @@ <h2 id="D">D</h2>
         <li><a href="api/info.deps.html#pyxu.info.deps.SparseArrayInfo.default">(SparseArrayInfo class method)</a>
 </li>
       </ul></li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.default_stop_crit">default_stop_crit() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.default_stop_crit">default_stop_crit() (Solver method)</a>
 </li>
       <li><a href="api/info.warning.html#pyxu.info.warning.DenseWarning">DenseWarning</a>
 </li>
@@ -740,21 +738,21 @@ <h2 id="D">D</h2>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.DiagonalOp">DiagonalOp() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.DiffMap.diff_lipschitz">diff_lipschitz (DiffMap property)</a>
+      <li><a href="api/abc.html#pyxu.abc.DiffMap.diff_lipschitz">diff_lipschitz (DiffMap property)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.DifferenceOfGaussians">DifferenceOfGaussians() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.DIFFERENTIABLE">DIFFERENTIABLE (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.DIFFERENTIABLE">DIFFERENTIABLE (Property attribute)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.DIFFERENTIABLE_FUNCTION">DIFFERENTIABLE_FUNCTION (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.DIFFERENTIABLE_FUNCTION">DIFFERENTIABLE_FUNCTION (Property attribute)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.DiffFunc">DiffFunc (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.DiffFunc">DiffFunc (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.DiffMap">DiffMap (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.DiffMap">DiffMap (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.dim">dim (Operator property)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.dim">dim (Operator property)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.DirectionalDerivative">DirectionalDerivative() (in module pyxu.operator)</a>
 </li>
@@ -794,19 +792,19 @@ <h2 id="E">E</h2>
 </li>
       <li><a href="api/runtime.html#pyxu.runtime.Width.eps">eps() (Width method)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.DiffMap.estimate_diff_lipschitz">estimate_diff_lipschitz() (DiffMap method)</a>
+      <li><a href="api/abc.html#pyxu.abc.DiffMap.estimate_diff_lipschitz">estimate_diff_lipschitz() (DiffMap method)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.estimate_lipschitz">estimate_lipschitz() (LinOp method)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.estimate_lipschitz">estimate_lipschitz() (LinOp method)</a>
 
       <ul>
-        <li><a href="api/abc/operator.html#pyxu.abc.Map.estimate_lipschitz">(Map method)</a>
+        <li><a href="api/abc.html#pyxu.abc.Map.estimate_lipschitz">(Map method)</a>
 </li>
       </ul></li>
       <li><a href="api/operator/map.html#pyxu.operator.exp">exp() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.expr">expr() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.expr">expr() (Operator method)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -816,17 +814,17 @@ <h2 id="F">F</h2>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.FB">FB (in module pyxu.opt.solver)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.ProxFunc.fenchel_prox">fenchel_prox() (ProxFunc method)</a>
+      <li><a href="api/abc.html#pyxu.abc.ProxFunc.fenchel_prox">fenchel_prox() (ProxFunc method)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.FFT">FFT (class in pyxu.operator)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.PartialDerivative.finite_difference">finite_difference() (PartialDerivative static method)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.fit">fit() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.fit">fit() (Solver method)</a>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.ForwardBackward">ForwardBackward (class in pyxu.opt.solver)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.from_array">from_array() (LinOp class method)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.from_array">from_array() (LinOp class method)</a>
 </li>
       <li><a href="api/info.deps.html#pyxu.info.deps.NDArrayInfo.from_flag">from_flag() (NDArrayInfo class method)</a>
 </li>
@@ -846,9 +844,9 @@ <h2 id="F">F</h2>
 </li>
       <li><a href="api/operator.interop.html#pyxu.operator.interop.from_torch">from_torch() (in module pyxu.operator.interop)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Func">Func (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.Func">Func (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.FUNCTIONAL">FUNCTIONAL (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.FUNCTIONAL">FUNCTIONAL (Property attribute)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -862,7 +860,7 @@ <h2 id="G">G</h2>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.PartialDerivative.gaussian_derivative">gaussian_derivative() (PartialDerivative static method)</a>
 </li>
-      <li><a href="api/util/array_module.html#pyxu.util.get_array_module">get_array_module() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.get_array_module">get_array_module() (in module pyxu.util)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
@@ -870,11 +868,11 @@ <h2 id="G">G</h2>
 </li>
       <li><a href="api/runtime.html#pyxu.runtime.getPrecision">getPrecision() (in module pyxu.runtime)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.DiffFunc.grad">grad() (DiffFunc method)</a>
+      <li><a href="api/abc.html#pyxu.abc.DiffFunc.grad">grad() (DiffFunc method)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.Gradient">Gradient() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.gram">gram() (LinOp method)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.gram">gram() (LinOp method)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -882,7 +880,7 @@ <h2 id="G">G</h2>
 <h2 id="H">H</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.has">has() (Operator class method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.has">has() (Operator class method)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.Hessian">Hessian() (in module pyxu.operator)</a>
 </li>
@@ -904,9 +902,7 @@ <h2 id="I">I</h2>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/operator/linop.html#pyxu.operator.IdentityOp">IdentityOp (class in pyxu.operator)</a>
 </li>
-      <li><a href="api/info.ptype.html#pyxu.info.ptype.Real.imag">imag (Real property)</a>
-</li>
-      <li><a href="api/util/misc.html#pyxu.util.import_module">import_module() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.import_module">import_module() (in module pyxu.util)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator._Stencil.IndexSpec">IndexSpec (_Stencil attribute)</a>
 
@@ -916,11 +912,11 @@ <h2 id="I">I</h2>
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/util/misc.html#pyxu.util.infer_composition_shape">infer_composition_shape() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.infer_composition_shape">infer_composition_shape() (in module pyxu.util)</a>
 </li>
-      <li><a href="api/util/misc.html#pyxu.util.infer_sum_shape">infer_sum_shape() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.infer_sum_shape">infer_sum_shape() (in module pyxu.util)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.StoppingCriterion.info">info() (StoppingCriterion method)</a>
+      <li><a href="api/abc.html#pyxu.abc.StoppingCriterion.info">info() (StoppingCriterion method)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator._Stencil.init">init() (_Stencil static method)</a>
 </li>
@@ -932,7 +928,7 @@ <h2 id="I">I</h2>
 <h2 id="J">J</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.DiffMap.jacobian">jacobian() (DiffMap method)</a>
+      <li><a href="api/abc.html#pyxu.abc.DiffMap.jacobian">jacobian() (DiffMap method)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
@@ -978,35 +974,35 @@ <h2 id="L">L</h2>
 </li>
       <li><a href="api/operator/map.html#pyxu.operator.leakyrelu">leakyrelu() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.LINEAR">LINEAR (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.LINEAR">LINEAR (Property attribute)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.LINEAR_IDEMPOTENT">LINEAR_IDEMPOTENT (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.LINEAR_IDEMPOTENT">LINEAR_IDEMPOTENT (Property attribute)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.LINEAR_NORMAL">LINEAR_NORMAL (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.LINEAR_NORMAL">LINEAR_NORMAL (Property attribute)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.LINEAR_POSITIVE_DEFINITE">LINEAR_POSITIVE_DEFINITE (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.LINEAR_POSITIVE_DEFINITE">LINEAR_POSITIVE_DEFINITE (Property attribute)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.LINEAR_SELF_ADJOINT">LINEAR_SELF_ADJOINT (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.LINEAR_SELF_ADJOINT">LINEAR_SELF_ADJOINT (Property attribute)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.LINEAR_SQUARE">LINEAR_SQUARE (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.LINEAR_SQUARE">LINEAR_SQUARE (Property attribute)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.LINEAR_UNITARY">LINEAR_UNITARY (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.LINEAR_UNITARY">LINEAR_UNITARY (Property attribute)</a>
 </li>
       <li><a href="api/operator/func.html#pyxu.operator.LInfinityBall">LInfinityBall() (in module pyxu.operator)</a>
 </li>
       <li><a href="api/operator/func.html#pyxu.operator.LInfinityNorm">LInfinityNorm (class in pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinFunc">LinFunc (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinFunc">LinFunc (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp">LinOp (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp">LinOp (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Map.lipschitz">lipschitz (Map property)</a>
+      <li><a href="api/abc.html#pyxu.abc.Map.lipschitz">lipschitz (Map property)</a>
 </li>
       <li><a href="api/operator/map.html#pyxu.operator.log">log() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.logfile">logfile (Solver property)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.logfile">logfile (Solver property)</a>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.LorisVerhoeven">LorisVerhoeven (class in pyxu.opt.solver)</a>
 </li>
@@ -1018,15 +1014,15 @@ <h2 id="L">L</h2>
 <h2 id="M">M</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.m_init">m_init() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.m_init">m_init() (Solver method)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.m_step">m_step() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.m_step">m_step() (Solver method)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.SolverMode.MANUAL">MANUAL (SolverMode attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.SolverMode.MANUAL">MANUAL (SolverMode attribute)</a>
 </li>
       <li><a href="api/opt.stop.html#pyxu.opt.stop.ManualStop">ManualStop (class in pyxu.opt.stop)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Map">Map (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.Map">Map (class in pyxu.abc)</a>
 </li>
       <li><a href="api/opt.stop.html#pyxu.opt.stop.MaxCarbon">MaxCarbon (class in pyxu.opt.stop)</a>
 </li>
@@ -1065,7 +1061,7 @@ <h2 id="M">M</h2>
         <li><a href="api/info.deps.html#pyxu.info.deps.SparseArrayInfo.module">(SparseArrayInfo method)</a>
 </li>
       </ul></li>
-      <li><a href="api/abc/operator.html#pyxu.abc.ProxFunc.moreau_envelope">moreau_envelope() (ProxFunc method)</a>
+      <li><a href="api/abc.html#pyxu.abc.ProxFunc.moreau_envelope">moreau_envelope() (ProxFunc method)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.MovingAverage">MovingAverage() (in module pyxu.operator)</a>
 </li>
@@ -1085,7 +1081,7 @@ <h2 id="N">N</h2>
 </li>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.NDArrayShape">NDArrayShape (in module pyxu.info.ptype)</a>
 </li>
-      <li><a href="api/util/misc.html#pyxu.util.next_fast_len">next_fast_len() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.next_fast_len">next_fast_len() (in module pyxu.util)</a>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.NLCG">NLCG (class in pyxu.opt.solver)</a>
 </li>
@@ -1095,7 +1091,7 @@ <h2 id="N">N</h2>
 </li>
       <li><a href="api/math.html#pyxu.math.norm">norm() (in module pyxu.math)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.NormalOp">NormalOp (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.NormalOp">NormalOp (class in pyxu.abc)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.NUFFT">NUFFT (class in pyxu.operator)</a>
 </li>
@@ -1111,7 +1107,7 @@ <h2 id="N">N</h2>
 <h2 id="O">O</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.objective_func">objective_func() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.objective_func">objective_func() (Solver method)</a>
 
       <ul>
         <li><a href="api/experimental.sampler.html#pyxu.experimental.sampler.ULA.objective_func">(ULA method)</a>
@@ -1131,17 +1127,17 @@ <h2 id="O">O</h2>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/experimental.sampler.html#pyxu.experimental.sampler.OnlineVariance">OnlineVariance() (in module pyxu.experimental.sampler)</a>
 </li>
-      <li><a href="api/abc/arithmetic.html#pyxu.abc.arithmetic.Rule.op">op() (Rule method)</a>
+      <li><a href="api/abc.html#pyxu.abc.arithmetic.Rule.op">op() (Rule method)</a>
 </li>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.OpC">OpC (in module pyxu.info.ptype)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator">Operator (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator">Operator (class in pyxu.abc)</a>
 </li>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.OpShape">OpShape (in module pyxu.info.ptype)</a>
 </li>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.OpT">OpT (class in pyxu.info.ptype)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.OrthProjOp">OrthProjOp (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.OrthProjOp">OrthProjOp (class in pyxu.abc)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -1153,7 +1149,7 @@ <h2 id="P">P</h2>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.NUFFT.params">params() (NUFFT method)</a>
 </li>
-      <li><a href="api/util/misc.html#pyxu.util.parse_params">parse_params() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.parse_params">parse_params() (in module pyxu.util)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.PartialDerivative">PartialDerivative (class in pyxu.operator)</a>
 </li>
@@ -1161,23 +1157,23 @@ <h2 id="P">P</h2>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.PD3O">PD3O (class in pyxu.opt.solver)</a>
 </li>
-      <li><a href="api/util/misc.html#pyxu.util.misc.peaks">peaks() (in module pyxu.util.misc)</a>
+      <li><a href="api/util.html#pyxu.util.misc.peaks">peaks() (in module pyxu.util.misc)</a>
 </li>
       <li><a href="api/info.warning.html#pyxu.info.warning.PerformanceWarning">PerformanceWarning</a>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.PGD">PGD (class in pyxu.opt.solver)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.pinv">pinv() (LinOp method)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.pinv">pinv() (LinOp method)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.NUFFT.plot_kernel">plot_kernel() (NUFFT method)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.PosDefOp">PosDefOp (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.PosDefOp">PosDefOp (class in pyxu.abc)</a>
 </li>
       <li><a href="api/operator/func.html#pyxu.operator.PositiveL1Norm">PositiveL1Norm (class in pyxu.operator)</a>
 </li>
       <li><a href="api/operator/func.html#pyxu.operator.PositiveOrthant">PositiveOrthant (class in pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/arithmetic.html#pyxu.abc.arithmetic.PowerRule">PowerRule (class in pyxu.abc.arithmetic)</a>
+      <li><a href="api/abc.html#pyxu.abc.arithmetic.PowerRule">PowerRule (class in pyxu.abc.arithmetic)</a>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.PP">PP() (in module pyxu.opt.solver)</a>
 </li>
@@ -1187,17 +1183,17 @@ <h2 id="P">P</h2>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.Prewitt">Prewitt() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.ProjOp">ProjOp (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.ProjOp">ProjOp (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Map.properties">properties() (Map class method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Map.properties">properties() (Map class method)</a>
 
       <ul>
-        <li><a href="api/abc/operator.html#pyxu.abc.Operator.properties">(Operator class method)</a>
+        <li><a href="api/abc.html#pyxu.abc.Operator.properties">(Operator class method)</a>
 </li>
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property">Property (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property">Property (class in pyxu.abc)</a>
 
       <ul>
         <li><a href="api/info.ptype.html#pyxu.info.ptype.Property">(in module pyxu.info.ptype)</a>
@@ -1206,16 +1202,16 @@ <h2 id="P">P</h2>
       <li><a href="api/operator/func.html#pyxu.operator.ConvexSetIntersection.prox">prox() (ConvexSetIntersection method)</a>
 
       <ul>
-        <li><a href="api/abc/operator.html#pyxu.abc.ProxFunc.prox">(ProxFunc method)</a>
+        <li><a href="api/abc.html#pyxu.abc.ProxFunc.prox">(ProxFunc method)</a>
 </li>
         <li><a href="api/operator/func.html#pyxu.operator.SquaredL1Norm.prox">(SquaredL1Norm method)</a>
 </li>
       </ul></li>
-      <li><a href="api/abc/operator.html#pyxu.abc.ProxDiffFunc">ProxDiffFunc (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.ProxDiffFunc">ProxDiffFunc (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.ProxFunc">ProxFunc (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.ProxFunc">ProxFunc (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.PROXIMABLE">PROXIMABLE (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.PROXIMABLE">PROXIMABLE (Property attribute)</a>
 </li>
       <li><a href="api/opt.solver.html#pyxu.opt.solver.ProximalPoint">ProximalPoint() (in module pyxu.opt.solver)</a>
 </li>
@@ -1271,11 +1267,11 @@ <h2 id="P">P</h2>
 <h2 id="Q">Q</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.Property.QUADRATIC">QUADRATIC (Property attribute)</a>
+      <li><a href="api/abc.html#pyxu.abc.Property.QUADRATIC">QUADRATIC (Property attribute)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.QuadraticFunc">QuadraticFunc (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.QuadraticFunc">QuadraticFunc (class in pyxu.abc)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -1287,19 +1283,15 @@ <h2 id="R">R</h2>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.StructureTensor.ravel">ravel() (StructureTensor method)</a>
 </li>
-      <li><a href="api/util/misc.html#pyxu.util.read_only">read_only() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.read_only">read_only() (in module pyxu.util)</a>
 </li>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.Real">Real (class in pyxu.info.ptype)</a>
 </li>
       <li><a href="api/runtime.html#pyxu.runtime.CWidth.real">real (CWidth property)</a>
-
-      <ul>
-        <li><a href="api/info.ptype.html#pyxu.info.ptype.Real.real">(Real property)</a>
 </li>
-      </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/util/array_module.html#pyxu.util.redirect">redirect() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.redirect">redirect() (in module pyxu.util)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.Stencil.relative_indices">relative_indices (Stencil property)</a>
 </li>
@@ -1307,7 +1299,7 @@ <h2 id="R">R</h2>
 </li>
       <li><a href="api/operator/map.html#pyxu.operator.relu">relu() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/arithmetic.html#pyxu.abc.arithmetic.Rule">Rule (class in pyxu.abc.arithmetic)</a>
+      <li><a href="api/abc.html#pyxu.abc.arithmetic.Rule">Rule (class in pyxu.abc.arithmetic)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -1315,15 +1307,15 @@ <h2 id="R">R</h2>
 <h2 id="S">S</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/arithmetic.html#pyxu.abc.arithmetic.ScaleRule">ScaleRule (class in pyxu.abc.arithmetic)</a>
+      <li><a href="api/abc.html#pyxu.abc.arithmetic.ScaleRule">ScaleRule (class in pyxu.abc.arithmetic)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.Scharr">Scharr() (in module pyxu.operator)</a>
 </li>
       <li><a href="api/info.deps.html#pyxu.info.deps.SparseArrayInfo.SCIPY_SPARSE">SCIPY_SPARSE (SparseArrayInfo attribute)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.SelfAdjointOp">SelfAdjointOp (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.SelfAdjointOp">SelfAdjointOp (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.shape">shape (Operator property)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.shape">shape (Operator property)</a>
 </li>
       <li><a href="api/operator/func.html#pyxu.operator.shift_loss">shift_loss() (in module pyxu.operator)</a>
 </li>
@@ -1349,15 +1341,15 @@ <h2 id="S">S</h2>
 </li>
       <li><a href="api/operator/map.html#pyxu.operator.softplus">softplus() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.solution">solution() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.solution">solution() (Solver method)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver">Solver (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver">Solver (class in pyxu.abc)</a>
 </li>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.SolverC">SolverC (in module pyxu.info.ptype)</a>
 </li>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.SolverM">SolverM (class in pyxu.info.ptype)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.SolverMode">SolverMode (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.SolverMode">SolverMode (class in pyxu.abc)</a>
 </li>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.SolverT">SolverT (class in pyxu.info.ptype)</a>
 </li>
@@ -1377,31 +1369,31 @@ <h2 id="S">S</h2>
 </li>
       <li><a href="api/operator/func.html#pyxu.operator.SquaredL2Norm">SquaredL2Norm (class in pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.SquareOp">SquareOp (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.SquareOp">SquareOp (class in pyxu.abc)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.Operator.squeeze">squeeze() (Operator method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Operator.squeeze">squeeze() (Operator method)</a>
 </li>
       <li><a href="api/operator/blocks.html#pyxu.operator.stack">stack() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/util/misc.html#pyxu.util.misc.star_like_sample">star_like_sample() (in module pyxu.util.misc)</a>
+      <li><a href="api/util.html#pyxu.util.misc.star_like_sample">star_like_sample() (in module pyxu.util.misc)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.NUFFT.stats">stats() (NUFFT method)</a>
 
       <ul>
-        <li><a href="api/abc/solver.html#pyxu.abc.Solver.stats">(Solver method)</a>
+        <li><a href="api/abc.html#pyxu.abc.Solver.stats">(Solver method)</a>
 </li>
       </ul></li>
       <li><a href="api/operator/linop.html#pyxu.operator.Stencil">Stencil (class in pyxu.operator)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.steps">steps() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.steps">steps() (Solver method)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.stop">stop() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.stop">stop() (Solver method)</a>
 
       <ul>
-        <li><a href="api/abc/solver.html#pyxu.abc.StoppingCriterion.stop">(StoppingCriterion method)</a>
+        <li><a href="api/abc.html#pyxu.abc.StoppingCriterion.stop">(StoppingCriterion method)</a>
 </li>
       </ul></li>
-      <li><a href="api/abc/solver.html#pyxu.abc.StoppingCriterion">StoppingCriterion (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.StoppingCriterion">StoppingCriterion (class in pyxu.abc)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.StructureTensor">StructureTensor (class in pyxu.operator)</a>
 </li>
@@ -1417,7 +1409,7 @@ <h2 id="S">S</h2>
 </li>
       <li><a href="api/info.deps.html#pyxu.info.deps.supported_sparse_types">supported_sparse_types() (in module pyxu.info.deps)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.svdvals">svdvals() (LinOp method)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.svdvals">svdvals() (LinOp method)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -1425,25 +1417,25 @@ <h2 id="S">S</h2>
 <h2 id="T">T</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.T">T (LinOp property)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.T">T (LinOp property)</a>
 </li>
       <li><a href="api/operator/map.html#pyxu.operator.tan">tan() (in module pyxu.operator)</a>
 </li>
       <li><a href="api/operator/map.html#pyxu.operator.tanh">tanh() (in module pyxu.operator)</a>
 </li>
-      <li><a href="api/util/misc.html#pyxu.util.to_NUMPY">to_NUMPY() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.to_NUMPY">to_NUMPY() (in module pyxu.util)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.LinOp.to_sciop">to_sciop() (LinOp method)</a>
+      <li><a href="api/abc.html#pyxu.abc.LinOp.to_sciop">to_sciop() (LinOp method)</a>
 </li>
       <li><a href="api/math.html#pyxu.math.trace">trace() (in module pyxu.math)</a>
 
       <ul>
-        <li><a href="api/abc/operator.html#pyxu.abc.SquareOp.trace">(SquareOp method)</a>
+        <li><a href="api/abc.html#pyxu.abc.SquareOp.trace">(SquareOp method)</a>
 </li>
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/arithmetic.html#pyxu.abc.arithmetic.TransposeRule">TransposeRule (class in pyxu.abc.arithmetic)</a>
+      <li><a href="api/abc.html#pyxu.abc.arithmetic.TransposeRule">TransposeRule (class in pyxu.abc.arithmetic)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.Trim">Trim() (in module pyxu.operator)</a>
 </li>
@@ -1469,7 +1461,7 @@ <h2 id="U">U</h2>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/experimental.sampler.html#pyxu.experimental.sampler.ULA">ULA (class in pyxu.experimental.sampler)</a>
 </li>
-      <li><a href="api/abc/operator.html#pyxu.abc.UnitOp">UnitOp (class in pyxu.abc)</a>
+      <li><a href="api/abc.html#pyxu.abc.UnitOp">UnitOp (class in pyxu.abc)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
@@ -1489,17 +1481,17 @@ <h2 id="V">V</h2>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="api/info.ptype.html#pyxu.info.ptype.VarName">VarName (in module pyxu.info.ptype)</a>
 </li>
-      <li><a href="api/util/operator.html#pyxu.util.vectorize">vectorize() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.vectorize">vectorize() (in module pyxu.util)</a>
 </li>
-      <li><a href="api/util/complex.html#pyxu.util.view_as_complex">view_as_complex() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.view_as_complex">view_as_complex() (in module pyxu.util)</a>
 </li>
-      <li><a href="api/util/complex.html#pyxu.util.view_as_complex_mat">view_as_complex_mat() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.view_as_complex_mat">view_as_complex_mat() (in module pyxu.util)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/util/complex.html#pyxu.util.view_as_real">view_as_real() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.view_as_real">view_as_real() (in module pyxu.util)</a>
 </li>
-      <li><a href="api/util/complex.html#pyxu.util.view_as_real_mat">view_as_real_mat() (in module pyxu.util)</a>
+      <li><a href="api/util.html#pyxu.util.view_as_real_mat">view_as_real_mat() (in module pyxu.util)</a>
 </li>
       <li><a href="api/operator/linop.html#pyxu.operator.Stencil.visualize">visualize() (Stencil method)</a>
 </li>
@@ -1517,9 +1509,9 @@ <h2 id="W">W</h2>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.workdir">workdir (Solver property)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.workdir">workdir (Solver property)</a>
 </li>
-      <li><a href="api/abc/solver.html#pyxu.abc.Solver.writeback">writeback() (Solver method)</a>
+      <li><a href="api/abc.html#pyxu.abc.Solver.writeback">writeback() (Solver method)</a>
 </li>
   </ul></td>
 </tr></table>
diff --git a/guide/algebra.html b/guide/algebra.html
index 047a308f..bc6171c7 100644
--- a/guide/algebra.html
+++ b/guide/algebra.html
@@ -18,7 +18,7 @@
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" rel="preload" type="font/woff2"/>
-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
 <link href="../_static/sphinx-codeautolink.css?v=125d5c1c" rel="stylesheet" type="text/css"/>
 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -28,11 +28,11 @@
 <link href="../_static/sg_gallery-dataframe.css?v=2082cf3c" rel="stylesheet" type="text/css"/>
 <link href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" rel="stylesheet" type="text/css"/>
 <link href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" rel="stylesheet" type="text/css"/>
-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
 <!-- Pre-loaded scripts that we'll load fully later -->
 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
 <link as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" rel="preload"/>
-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
 <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -231,6 +231,7 @@
 <li class="toctree-l1"><a class="reference internal" href="algorithms.html">Optimization Algorithms</a></li>
 <li class="toctree-l1"><a class="reference internal" href="lipschitz.html">Lipschitz Constants and Automatic Step Size Tuning</a></li>
 <li class="toctree-l1"><a class="reference internal" href="hpc.html">High Performance Computing Features</a></li>
+<li class="toctree-l1"><a class="reference internal" href="diff_ops.html">Differential Operators in Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
@@ -281,25 +282,26 @@ <h2>Arithmetic Operations on Operators<a class="headerlink" href="#Arithmetic-Op
 <section id="How-Does-it-Work?-🛠️">
 <h3>How Does it Work? 🛠️<a class="headerlink" href="#How-Does-it-Work?-🛠️" title="Link to this heading">#</a></h3>
 <p>Every time you perform an arithmetic operation, Pyxu automatically infers the output type based on the properties of the operators involved in the operation. This type inference is super convenient because it saves you from manual calculations!</p>
-<p>For example, Pyxu takes care of updating as needed methods like <code class="docutils literal notranslate"><span class="pre">apply()</span></code>, <code class="docutils literal notranslate"><span class="pre">jacobian()</span></code>, <code class="docutils literal notranslate"><span class="pre">grad()</span></code>, <code class="docutils literal notranslate"><span class="pre">prox()</span></code>, and <code class="docutils literal notranslate"><span class="pre">adjoint()</span></code> according to arithmetic rules. This means you can plug these composite operators directly into proximal gradient algorithms without sweating the details of implementing gradients or proximal steps.</p>
+<p>For example, Pyxu takes care of updating as needed methods like <code class="docutils literal notranslate"><span class="pre">apply()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Map.apply">🔗</a>, <code class="docutils literal notranslate"><span class="pre">jacobian()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffMap.jacobian">🔗</a>, <code class="docutils literal notranslate"><span class="pre">grad()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffFunc.grad">🔗</a>, <code class="docutils literal notranslate"><span class="pre">prox()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.ProxFunc.prox">🔗</a>, and <code class="docutils literal notranslate"><span class="pre">adjoint()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp.adjoint">🔗</a> according to arithmetic rules. This means you can plug these composite operators directly into proximal gradient
+algorithms without sweating the details of implementing gradients or proximal steps.</p>
 </section>
 </section>
 <section id="Behind-the-Scenes:-Arithmetic-Rules">
 <h2>Behind the Scenes: Arithmetic Rules<a class="headerlink" href="#Behind-the-Scenes:-Arithmetic-Rules" title="Link to this heading">#</a></h2>
-<p>For those who love to peek under the hood, Pyxu utilizes a set of arithmetic rules located in the <code class="docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic</span></code> module:</p>
+<p>For those who love to peek under the hood, Pyxu utilizes a set of arithmetic rules located in the <code class="docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic</span></code><a class="reference external" href="../api/abc/arithmetic.html">🔗</a> module:</p>
 <ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">Rule</span></code>: The base class for all arithmetic rules.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">ScaleRule</span></code>: Handles scaling of operators by scalars.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">ArgScaleRule</span></code>: Manages the dilation of the arguments of operators.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">ArgShiftRule</span></code>: Takes care of shifting the arguments of operators.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">AddRule</span></code>: Manages the addition of two operators.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">ChainRule</span></code>: Deals with the composition of two operators.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">PowerRule</span></code>: Handles exponentiation of an operator.</p></li>
-<li><p><code class="docutils literal notranslate"><span class="pre">TransposeRule</span></code>: Takes care of transposing a linear operator.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">Rule</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.arithmetic.Rule">🔗</a>: The base class for all arithmetic rules.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">ScaleRule</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.arithmetic.ScaleRule">🔗</a>: Handles scaling of operators by scalars.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">ArgScaleRule</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.arithmetic.ArgScaleRule">🔗</a>: Manages the dilation of the arguments of operators.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">ArgShiftRule</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.arithmetic.ArgShiftRule">🔗</a>: Takes care of shifting the arguments of operators.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">AddRule</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.arithmetic.AddRule">🔗</a>: Manages the addition of two operators.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">ChainRule</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.arithmetic.ChainRule">🔗</a>: Deals with the composition of two operators.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">PowerRule</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.arithmetic.PowerRule">🔗</a>: Handles exponentiation of an operator.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">TransposeRule</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.arithmetic.TransposeRule">🔗</a>: Takes care of transposing a linear operator.</p></li>
 </ul>
 <section id="Working-Example-🎯">
 <h3>Working Example 🎯<a class="headerlink" href="#Working-Example-🎯" title="Link to this heading">#</a></h3>
-<p>Consider the composition of a <code class="docutils literal notranslate"><span class="pre">DiffFunc</span></code> with a <code class="docutils literal notranslate"><span class="pre">DiffMap</span></code>. Let <code class="docutils literal notranslate"><span class="pre">f</span></code> be a <code class="docutils literal notranslate"><span class="pre">DiffFunc</span></code> and <code class="docutils literal notranslate"><span class="pre">L</span></code> be a <code class="docutils literal notranslate"><span class="pre">DiffMap</span></code>. Then their composition <code class="docutils literal notranslate"><span class="pre">h</span></code> is another <code class="docutils literal notranslate"><span class="pre">DiffFunc</span></code>, and the gradient is given by:</p>
+<p>Consider the composition of a <code class="docutils literal notranslate"><span class="pre">DiffFunc</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffFunc">🔗</a> with a <code class="docutils literal notranslate"><span class="pre">DiffMap</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffMap">🔗</a>. Let <code class="docutils literal notranslate"><span class="pre">f</span></code> be a <code class="docutils literal notranslate"><span class="pre">DiffFunc</span></code> and <code class="docutils literal notranslate"><span class="pre">L</span></code> be a <code class="docutils literal notranslate"><span class="pre">DiffMap</span></code>. Then their composition <code class="docutils literal notranslate"><span class="pre">h</span></code> is another <code class="docutils literal notranslate"><span class="pre">DiffFunc</span></code>, and the gradient is given by:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="o">&gt;&gt;</span> <span class="n">h</span> <span class="o">=</span> <span class="n">f</span> <span class="o">*</span> <span class="n">L</span>
 <span class="o">&gt;&gt;</span> <span class="n">h</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="n">L</span><span class="o">.</span><span class="n">jacobian</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">adjoint</span><span class="p">(</span><span class="n">f</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="n">L</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
 </pre></div>
@@ -337,7 +339,8 @@ <h3>Working Example 🎯<a class="headerlink" href="#Working-Example-🎯" title
 </section>
 <section id="Building-Block-Operators">
 <h2>Building Block-Operators<a class="headerlink" href="#Building-Block-Operators" title="Link to this heading">#</a></h2>
-<p>You can even define block-operators using the <code class="docutils literal notranslate"><span class="pre">coo_block</span></code> function. Alternatively, higher-level functions like <code class="docutils literal notranslate"><span class="pre">block</span></code>, <code class="docutils literal notranslate"><span class="pre">block_diag</span></code>, <code class="docutils literal notranslate"><span class="pre">stack</span></code>, <code class="docutils literal notranslate"><span class="pre">vstack</span></code>, and <code class="docutils literal notranslate"><span class="pre">hstack</span></code> can also be used.</p>
+<p>You can even define block-operators using the <code class="docutils literal notranslate"><span class="pre">coo_block</span></code><a class="reference external" href="../api/operator/blocks.html#pyxu.operator.coo_block">🔗</a> function. Alternatively, higher-level functions like <code class="docutils literal notranslate"><span class="pre">block</span></code><a class="reference external" href="../api/operator/blocks.html#pyxu.operator.block">🔗</a>, <code class="docutils literal notranslate"><span class="pre">block_diag</span></code><a class="reference external" href="../api/operator/blocks.html#pyxu.operator.block_diag">🔗</a>, <code class="docutils literal notranslate"><span class="pre">stack</span></code><a class="reference external" href="../api/operator/blocks.html#pyxu.operator.stack">🔗</a>, <code class="docutils literal notranslate"><span class="pre">vstack</span></code><a class="reference external" href="../api/operator/blocks.html#pyxu.operator.vstack">🔗</a>, and
+<code class="docutils literal notranslate"><span class="pre">hstack</span></code><a class="reference external" href="../api/operator/blocks.html#pyxu.operator.hstack">🔗</a> can also be used.</p>
 <p>For example, the following code snippet:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="o">&gt;&gt;</span> <span class="n">coo_block</span><span class="p">(([</span><span class="n">A</span><span class="p">(</span><span class="mi">500</span><span class="p">,</span><span class="mi">1000</span><span class="p">),</span> <span class="n">B</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1000</span><span class="p">),</span> <span class="n">C</span><span class="p">(</span><span class="mi">500</span><span class="p">,</span><span class="mi">500</span><span class="p">),</span> <span class="n">D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">)],</span>  <span class="c1"># data</span>
    <span class="o">...</span>      <span class="p">[[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span>  <span class="c1"># i</span>
diff --git a/guide/algebra.ipynb b/guide/algebra.ipynb
index f4d56d58..267c042a 100644
--- a/guide/algebra.ipynb
+++ b/guide/algebra.ipynb
@@ -27,24 +27,24 @@
     "\n",
     "Every time you perform an arithmetic operation, Pyxu automatically infers the output type based on the properties of the operators involved in the operation. This type inference is super convenient because it saves you from manual calculations! \n",
     "\n",
-    "For example, Pyxu takes care of updating as needed methods like `apply()`, `jacobian()`, `grad()`, `prox()`, and `adjoint()` according to arithmetic rules. This means you can plug these composite operators directly into proximal gradient algorithms without sweating the details of implementing gradients or proximal steps.\n",
+    "For example, Pyxu takes care of updating as needed methods like `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply), `jacobian()`[🔗](../api/abc.html#pyxu.abc.DiffMap.jacobian), `grad()`[🔗](../api/abc.html#pyxu.abc.DiffFunc.grad), `prox()`[🔗](../api/abc.html#pyxu.abc.ProxFunc.prox), and `adjoint()`[🔗](../api/abc.html#pyxu.abc.LinOp.adjoint) according to arithmetic rules. This means you can plug these composite operators directly into proximal gradient algorithms without sweating the details of implementing gradients or proximal steps.\n",
     "\n",
     "## Behind the Scenes: Arithmetic Rules\n",
     "\n",
-    "For those who love to peek under the hood, Pyxu utilizes a set of arithmetic rules located in the `pyxu.abc.arithmetic` module:\n",
+    "For those who love to peek under the hood, Pyxu utilizes a set of arithmetic rules located in the `pyxu.abc.arithmetic`[🔗](../api/abc/arithmetic.html) module:\n",
     "\n",
-    "- `Rule`: The base class for all arithmetic rules.\n",
-    "- `ScaleRule`: Handles scaling of operators by scalars.\n",
-    "- `ArgScaleRule`: Manages the dilation of the arguments of operators.\n",
-    "- `ArgShiftRule`: Takes care of shifting the arguments of operators.\n",
-    "- `AddRule`: Manages the addition of two operators.\n",
-    "- `ChainRule`: Deals with the composition of two operators.\n",
-    "- `PowerRule`: Handles exponentiation of an operator.\n",
-    "- `TransposeRule`: Takes care of transposing a linear operator.\n",
+    "- `Rule`[🔗](../api/abc.html#pyxu.abc.arithmetic.Rule): The base class for all arithmetic rules.\n",
+    "- `ScaleRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.ScaleRule): Handles scaling of operators by scalars.\n",
+    "- `ArgScaleRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.ArgScaleRule): Manages the dilation of the arguments of operators.\n",
+    "- `ArgShiftRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.ArgShiftRule): Takes care of shifting the arguments of operators.\n",
+    "- `AddRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.AddRule): Manages the addition of two operators.\n",
+    "- `ChainRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.ChainRule): Deals with the composition of two operators.\n",
+    "- `PowerRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.PowerRule): Handles exponentiation of an operator.\n",
+    "- `TransposeRule`[🔗](../api/abc.html#pyxu.abc.arithmetic.TransposeRule): Takes care of transposing a linear operator.\n",
     "\n",
     "### Working Example 🎯\n",
     "\n",
-    "Consider the composition of a `DiffFunc` with a `DiffMap`. Let `f` be a `DiffFunc` and `L` be a `DiffMap`. Then their composition `h` is another `DiffFunc`, and the gradient is given by:\n",
+    "Consider the composition of a `DiffFunc`[🔗](../api/abc.html#pyxu.abc.DiffFunc) with a `DiffMap`[🔗](../api/abc.html#pyxu.abc.DiffMap). Let `f` be a `DiffFunc` and `L` be a `DiffMap`. Then their composition `h` is another `DiffFunc`, and the gradient is given by:\n",
     "\n",
     "```python\n",
     ">> h = f * L\n",
@@ -85,7 +85,7 @@
     "\n",
     "## Building Block-Operators \n",
     "\n",
-    "You can even define block-operators using the `coo_block` function. Alternatively, higher-level functions like `block`, `block_diag`, `stack`, `vstack`, and `hstack` can also be used.\n",
+    "You can even define block-operators using the `coo_block`[🔗](../api/operator/blocks.html#pyxu.operator.coo_block) function. Alternatively, higher-level functions like `block`[🔗](../api/operator/blocks.html#pyxu.operator.block), `block_diag`[🔗](../api/operator/blocks.html#pyxu.operator.block_diag), `stack`[🔗](../api/operator/blocks.html#pyxu.operator.stack), `vstack`[🔗](../api/operator/blocks.html#pyxu.operator.vstack), and `hstack`[🔗](../api/operator/blocks.html#pyxu.operator.hstack) can also be used.\n",
     "\n",
     "For example, the following code snippet: \n",
     "\n",
diff --git a/guide/algorithms.html b/guide/algorithms.html
index bf1a46f2..5e6b9a14 100644
--- a/guide/algorithms.html
+++ b/guide/algorithms.html
@@ -18,7 +18,7 @@
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" rel="preload" type="font/woff2"/>
-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
 <link href="../_static/sphinx-codeautolink.css?v=125d5c1c" rel="stylesheet" type="text/css"/>
 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -28,11 +28,11 @@
 <link href="../_static/sg_gallery-dataframe.css?v=2082cf3c" rel="stylesheet" type="text/css"/>
 <link href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" rel="stylesheet" type="text/css"/>
 <link href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" rel="stylesheet" type="text/css"/>
-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
 <!-- Pre-loaded scripts that we'll load fully later -->
 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
 <link as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" rel="preload"/>
-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
 <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -231,6 +231,7 @@
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">Optimization Algorithms</a></li>
 <li class="toctree-l1"><a class="reference internal" href="lipschitz.html">Lipschitz Constants and Automatic Step Size Tuning</a></li>
 <li class="toctree-l1"><a class="reference internal" href="hpc.html">High Performance Computing Features</a></li>
+<li class="toctree-l1"><a class="reference internal" href="diff_ops.html">Differential Operators in Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
@@ -268,15 +269,15 @@ <h1>Optimization Algorithms<a class="headerlink" href="#Optimization-Algorithms"
 <p>Navigating the landscape of optimization algorithms can be overwhelming at times, especially when each algorithm comes with its own set of assumptions and applicability scope. Pyxu aims to simplify this by offering a comprehensive suite of algorithms tailored for solving Bayesian estimation problems. In this section, we’ll walk through the different algorithms available, discuss how to choose the most suitable ones for your problem, and show you how to flexibly configure them. 🎛️</p>
 <section id="Algorithms-Overview">
 <h2>Algorithms Overview<a class="headerlink" href="#Algorithms-Overview" title="Link to this heading">#</a></h2>
-<section id="Conjugate-Gradient-(CG)">
-<h3>Conjugate Gradient (CG)<a class="headerlink" href="#Conjugate-Gradient-(CG)" title="Link to this heading">#</a></h3>
+<section id="Conjugate-Gradient-(CG)-🔗">
+<h3>Conjugate Gradient (CG) <a class="reference external" href="../api/opt.solver.html#pyxu.opt.solver.CG">🔗</a><a class="headerlink" href="#Conjugate-Gradient-(CG)-🔗" title="Link to this heading">#</a></h3>
 <p>👉 <strong>Use case:</strong> Quadratic problems, particularly when you have a well-conditioned matrix <span class="math notranslate nohighlight">\(A\)</span>.</p>
 <p><strong>Mathematical Form:</strong></p>
 <div class="math notranslate nohighlight">
 \[\min_{x\in\mathbb{R}^{N}} \frac{1}{2} \mathbf{x}^{T} \mathbf{A} \mathbf{x} - \mathbf{x}^{T} \mathbf{b}\]</div>
 </section>
-<section id="Accelerated-Proximal-Gradient-Descent-(APGD)">
-<h3>Accelerated Proximal Gradient Descent (APGD)<a class="headerlink" href="#Accelerated-Proximal-Gradient-Descent-(APGD)" title="Link to this heading">#</a></h3>
+<section id="Accelerated-Proximal-Gradient-Descent-(APGD)-🔗">
+<h3>Accelerated Proximal Gradient Descent (APGD) <a class="reference external" href="../api/opt.solver.html#pyxu.opt.solver.PGD">🔗</a><a class="headerlink" href="#Accelerated-Proximal-Gradient-Descent-(APGD)-🔗" title="Link to this heading">#</a></h3>
 <p>👉 <strong>Use case:</strong> Problems that separate into smooth and non-smooth components.</p>
 <p><strong>Mathematical Form:</strong></p>
 <div class="math notranslate nohighlight">
@@ -293,7 +294,7 @@ <h3>Primal-Dual Splitting (PDS) Methods<a class="headerlink" href="#Primal-Dual-
 <div class="math notranslate nohighlight">
 \[\min_{\mathbf{x}\in\mathbb{R}^N} \;\mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{G}(\mathbf{x})\;\;+\;\;\mathcal{H}(K\mathbf{x})\]</div>
 <p>where <span class="math notranslate nohighlight">\(\mathcal{F}\)</span> is differentiable, <span class="math notranslate nohighlight">\(\mathcal{G}\)</span> and <span class="math notranslate nohighlight">\(\mathcal{H}\)</span> are proximable, and <span class="math notranslate nohighlight">\(K\)</span> is a linear operator.</p>
-<p>Methods under this category include <code class="docutils literal notranslate"><span class="pre">CondatVu</span></code>, <code class="docutils literal notranslate"><span class="pre">PD3O</span></code>, <code class="docutils literal notranslate"><span class="pre">ADMM</span></code>, <code class="docutils literal notranslate"><span class="pre">ChambollePock</span></code>, and more.</p>
+<p>Methods under this category include <code class="docutils literal notranslate"><span class="pre">CondatVu</span></code> <a class="reference external" href="../api/opt.solver.html#pyxu.opt.solver.CondatVu">🔗</a>, <code class="docutils literal notranslate"><span class="pre">PD3O</span></code> <a class="reference external" href="../api/opt.solver.html#pyxu.opt.solver.PD3O">🔗</a>, <code class="docutils literal notranslate"><span class="pre">ADMM</span></code> <a class="reference external" href="../api/opt.solver.html#pyxu.opt.solver.ADMM">🔗</a>, <code class="docutils literal notranslate"><span class="pre">ChambollePock</span></code> <a class="reference external" href="../api/opt.solver.html#pyxu.opt.solver.ChambollePock">🔗</a>, and more.</p>
 <p>Note that, although implemented for three-term objective functionals, PDS methods can easilybe generalized to objective functionals of the form:</p>
 <div class="math notranslate nohighlight">
 \[{\min_{\mathbf{x}\in\mathbb{R}^N} \;\mathcal{F}(\mathbf{x})\;\;+\;\;\mathcal{G}(\mathbf{x})\;\;+\;\;\sum_{i=1}^J\mathcal{H}_i(K_i\mathbf{x})}\]</div>
@@ -306,8 +307,8 @@ <h3>Primal-Dual Splitting (PDS) Methods<a class="headerlink" href="#Primal-Dual-
 </section>
 <section id="Choosing-the-Right-Algorithm">
 <h2>Choosing the Right Algorithm<a class="headerlink" href="#Choosing-the-Right-Algorithm" title="Link to this heading">#</a></h2>
-<p>The golden rule is to <strong>choose the most specific algorithm</strong> —i.e., the one that makes the most assumptions consistent with your problem. This often results in faster convergence. For example, if your objective functional has a gradient, a gradient-based method like <code class="docutils literal notranslate"><span class="pre">APGD</span></code> will generally be more efficient than a generic proximal-based method like <code class="docutils literal notranslate"><span class="pre">DouglasRachford</span></code>.</p>
-<p>The most generic algorithms in Pyxu are <code class="docutils literal notranslate"><span class="pre">PD3O</span></code> and <code class="docutils literal notranslate"><span class="pre">CondatVu</span></code>, but they are also the least efficient, so use them only when simpler methods like <code class="docutils literal notranslate"><span class="pre">ADMM</span></code>, <code class="docutils literal notranslate"><span class="pre">APGD</span></code> or <code class="docutils literal notranslate"><span class="pre">CG</span></code> cannot be used. Note that <code class="docutils literal notranslate"><span class="pre">ADAM</span></code> can also be useful when step sizes are too complex to compute.</p>
+<p>The golden rule is to <strong>choose the most specific algorithm</strong> —i.e., the one that makes the most assumptions consistent with your problem. This often results in faster convergence. For example, if your objective functional has a gradient, a gradient-based method like <code class="docutils literal notranslate"><span class="pre">APGD</span></code> will generally be more efficient than a generic proximal-based method like <code class="docutils literal notranslate"><span class="pre">DouglasRachford</span></code> <a class="reference external" href="../api/opt.solver.html#pyxu.opt.solver.DouglasRachford">🔗</a>.</p>
+<p>The most generic algorithms in Pyxu are <code class="docutils literal notranslate"><span class="pre">PD3O</span></code> and <code class="docutils literal notranslate"><span class="pre">CondatVu</span></code>, but they are also the least efficient, so use them only when simpler methods like <code class="docutils literal notranslate"><span class="pre">ADMM</span></code>, <code class="docutils literal notranslate"><span class="pre">APGD</span></code> or <code class="docutils literal notranslate"><span class="pre">CG</span></code> cannot be used. Note that <code class="docutils literal notranslate"><span class="pre">ADAM</span></code> <a class="reference external" href="../api/opt.solver.html#pyxu.opt.solver.Adam">🔗</a> can also be useful when step sizes are too complex to compute.</p>
 </section>
 <section id="Hyperparameter-Tuning">
 <h2>Hyperparameter Tuning<a class="headerlink" href="#Hyperparameter-Tuning" title="Link to this heading">#</a></h2>
@@ -347,7 +348,7 @@ <h2>Example Usage<a class="headerlink" href="#Example-Usage" title="Link to this
 </section>
 <section id="Advanced-Usage:-Guru-Interface">
 <h2>Advanced Usage: Guru Interface<a class="headerlink" href="#Advanced-Usage:-Guru-Interface" title="Link to this heading">#</a></h2>
-<p>For those who want even more control, we provide a guru interface allowing you to overload default settings, including the stopping criteria (see module <code class="docutils literal notranslate"><span class="pre">pyxu.opt.stop</span></code> for available stopping criteria).</p>
+<p>For those who want even more control, we provide a guru interface allowing you to overload default settings, including the stopping criteria (see module <code class="docutils literal notranslate"><span class="pre">pyxu.opt.stop</span></code><a class="reference external" href="../api/opt.stop.html">🔗</a> for available stopping criteria).</p>
 <p>For example, overloading the default stopping criterion of the <code class="docutils literal notranslate"><span class="pre">CondatVu</span></code> solver initialized above can be achieved as follows:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Custom stopping criterion (optional)</span>
 <span class="n">custom_stop_crit</span> <span class="o">=</span> <span class="p">(</span><span class="n">RelError</span><span class="p">(</span><span class="n">eps</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span> <span class="n">var</span><span class="o">=</span><span class="s2">"x"</span><span class="p">,</span> <span class="n">f</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">norm</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">satisfy_all</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="o">&amp;</span>
@@ -361,10 +362,10 @@ <h2>Advanced Usage: Guru Interface<a class="headerlink" href="#Advanced-Usage:-G
 </section>
 <section id="Implementing-New-Algorithms">
 <h2>Implementing New Algorithms<a class="headerlink" href="#Implementing-New-Algorithms" title="Link to this heading">#</a></h2>
-<p>To implement a new iterative solver, users need to sub-class <code class="docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver</span></code> and overwrite some of its core methods, such as <code class="docutils literal notranslate"><span class="pre">m_init()</span></code>, and <code class="docutils literal notranslate"><span class="pre">m_step()</span></code>, which describe the initalization and update step of iterative algorithms (see the API Reference for more details).</p>
+<p>To implement a new iterative solver, users need to sub-class <code class="docutils literal notranslate"><span class="pre">pyxu.abc.solver.Solver</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Solver">🔗</a> and overwrite some of its core methods, such as <code class="docutils literal notranslate"><span class="pre">m_init()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Solver.m_init">🔗</a>, and <code class="docutils literal notranslate"><span class="pre">m_step()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Solver.m_step">🔗</a>, which describe the initalization and update step of iterative algorithms (see the API Reference for more details).</p>
 <p>Sub-classes of <code class="docutils literal notranslate"><span class="pre">Solver</span></code> inherit automatically from its very versatile API for solving optimisation problems, with the following notable features:</p>
 <ul class="simple">
-<li><p>manual/automatic/background execution of solver iterations via parameters provided to <code class="docutils literal notranslate"><span class="pre">fit()</span></code>.</p></li>
+<li><p>manual/automatic/background execution of solver iterations via parameters provided to <code class="docutils literal notranslate"><span class="pre">fit()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Solver.fit">🔗</a>.</p></li>
 <li><p>automatic checkpointing of solver progress, providing a safe restore point in case of faulty numerical code. Each solver instance backs its state and final output to a folder on disk for post-analysis. In particular <code class="docutils literal notranslate"><span class="pre">fit()</span></code> will never crash: detailed exception information will always be available in a logfile for post-analysis.</p></li>
 <li><p>solve for multiple initial points in parallel.</p></li>
 </ul>
@@ -402,8 +403,8 @@ <h2>Implementing New Algorithms<a class="headerlink" href="#Implementing-New-Alg
 <nav class="bd-toc-nav page-toc">
 <ul class="visible nav section-nav flex-column">
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Algorithms-Overview">Algorithms Overview</a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Conjugate-Gradient-(CG)">Conjugate Gradient (CG)</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Accelerated-Proximal-Gradient-Descent-(APGD)">Accelerated Proximal Gradient Descent (APGD)</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Conjugate-Gradient-(CG)-🔗">Conjugate Gradient (CG) 🔗</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Accelerated-Proximal-Gradient-Descent-(APGD)-🔗">Accelerated Proximal Gradient Descent (APGD) 🔗</a></li>
 <li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Primal-Dual-Splitting-(PDS)-Methods">Primal-Dual Splitting (PDS) Methods</a></li>
 </ul>
 </li>
diff --git a/guide/algorithms.ipynb b/guide/algorithms.ipynb
index 3f937752..b6de671f 100644
--- a/guide/algorithms.ipynb
+++ b/guide/algorithms.ipynb
@@ -11,7 +11,7 @@
     "\n",
     "## Algorithms Overview\n",
     "\n",
-    "### Conjugate Gradient (CG)\n",
+    "### Conjugate Gradient (CG) [🔗](../api/opt.solver.html#pyxu.opt.solver.CG)\n",
     "👉 **Use case:** Quadratic problems, particularly when you have a well-conditioned matrix $A$.\n",
     "\n",
     "**Mathematical Form:**\n",
@@ -19,7 +19,7 @@
     "\\min_{x\\in\\mathbb{R}^{N}} \\frac{1}{2} \\mathbf{x}^{T} \\mathbf{A} \\mathbf{x} - \\mathbf{x}^{T} \\mathbf{b}\n",
     "$$\n",
     "\n",
-    "### Accelerated Proximal Gradient Descent (APGD)\n",
+    "### Accelerated Proximal Gradient Descent (APGD)  [🔗](../api/opt.solver.html#pyxu.opt.solver.PGD)\n",
     "👉 **Use case:** Problems that separate into smooth and non-smooth components. \n",
     "\n",
     "**Mathematical Form:**\n",
@@ -31,7 +31,7 @@
     "> **Note:** With acceleration, `APGD` can be shown to be an *optimal* first-order method, with the fastest possible convergence rate!\n",
     "\n",
     "\n",
-    "### Primal-Dual Splitting (PDS) Methods\n",
+    "### Primal-Dual Splitting (PDS) Methods \n",
     "👉 **Use case:** Multi-term problems, with smooth and non-smooth terms, possibly composed with a linear operator $K$.\n",
     "\n",
     "**Mathematical Form:**\n",
@@ -40,7 +40,7 @@
     "$$\n",
     "where $\\mathcal{F}$ is differentiable, $\\mathcal{G}$ and $\\mathcal{H}$ are proximable, and $K$ is a linear operator.\n",
     "\n",
-    "Methods under this category include `CondatVu`, `PD3O`, `ADMM`, `ChambollePock`, and more.\n",
+    "Methods under this category include `CondatVu` [🔗](../api/opt.solver.html#pyxu.opt.solver.CondatVu), `PD3O` [🔗](../api/opt.solver.html#pyxu.opt.solver.PD3O), `ADMM` [🔗](../api/opt.solver.html#pyxu.opt.solver.ADMM), `ChambollePock` [🔗](../api/opt.solver.html#pyxu.opt.solver.ChambollePock), and more.\n",
     "\n",
     "Note that, although implemented for three-term objective functionals, PDS methods can easilybe generalized to objective functionals of the form:\n",
     "$${\\min_{\\mathbf{x}\\in\\mathbb{R}^N} \\;\\mathcal{F}(\\mathbf{x})\\;\\;+\\;\\;\\mathcal{G}(\\mathbf{x})\\;\\;+\\;\\;\\sum_{i=1}^J\\mathcal{H}_i(K_i\\mathbf{x})}$$\n",
@@ -53,9 +53,9 @@
     "\n",
     "## Choosing the Right Algorithm\n",
     "\n",
-    "The golden rule is to **choose the most specific algorithm** —i.e., the one that makes the most assumptions consistent with your problem. This often results in faster convergence. For example, if your objective functional has a gradient, a gradient-based method like `APGD` will generally be more efficient than a generic proximal-based method like `DouglasRachford`.\n",
+    "The golden rule is to **choose the most specific algorithm** —i.e., the one that makes the most assumptions consistent with your problem. This often results in faster convergence. For example, if your objective functional has a gradient, a gradient-based method like `APGD` will generally be more efficient than a generic proximal-based method like `DouglasRachford` [🔗](../api/opt.solver.html#pyxu.opt.solver.DouglasRachford).\n",
     "\n",
-    "The most generic algorithms in Pyxu are `PD3O` and `CondatVu`, but they are also the least efficient, so use them only when simpler methods like `ADMM`, `APGD` or `CG` cannot be used. Note that `ADAM` can also be useful when step sizes are too complex to compute. \n",
+    "The most generic algorithms in Pyxu are `PD3O` and `CondatVu`, but they are also the least efficient, so use them only when simpler methods like `ADMM`, `APGD` or `CG` cannot be used. Note that `ADAM` [🔗](../api/opt.solver.html#pyxu.opt.solver.Adam) can also be useful when step sizes are too complex to compute. \n",
     "\n",
     "## Hyperparameter Tuning\n",
     "\n",
@@ -105,7 +105,7 @@
     "\n",
     "## Advanced Usage: Guru Interface \n",
     "\n",
-    "For those who want even more control, we provide a guru interface allowing you to overload default settings, including the stopping criteria (see module `pyxu.opt.stop` for available stopping criteria).\n",
+    "For those who want even more control, we provide a guru interface allowing you to overload default settings, including the stopping criteria (see module `pyxu.opt.stop`[🔗](../api/opt.stop.html) for available stopping criteria).\n",
     "\n",
     "For example, overloading the default stopping criterion of the `CondatVu` solver initialized above can be achieved as follows:\n",
     "\n",
@@ -121,12 +121,12 @@
     "\n",
     "## Implementing New Algorithms \n",
     "\n",
-    "To implement a new iterative solver, users need to sub-class `pyxu.abc.solver.Solver` and overwrite some of its core methods, such as `m_init()`,  and `m_step()`, which describe the initalization and update step of iterative algorithms (see the API Reference for more details). \n",
+    "To implement a new iterative solver, users need to sub-class `pyxu.abc.solver.Solver`[🔗](../api/abc.html#pyxu.abc.Solver) and overwrite some of its core methods, such as `m_init()`[🔗](../api/abc.html#pyxu.abc.Solver.m_init),  and `m_step()`[🔗](../api/abc.html#pyxu.abc.Solver.m_step), which describe the initalization and update step of iterative algorithms (see the API Reference for more details). \n",
     "\n",
     "\n",
     "Sub-classes of `Solver` inherit automatically from its very versatile API for solving optimisation problems, with the following notable features:\n",
     "\n",
-    " * manual/automatic/background execution of solver iterations via parameters provided to `fit()`. \n",
+    " * manual/automatic/background execution of solver iterations via parameters provided to `fit()`[🔗](../api/abc.html#pyxu.abc.Solver.fit). \n",
     " * automatic checkpointing of solver progress, providing a safe restore point in case of faulty numerical code. Each solver instance backs its state and final output to a folder on disk for post-analysis. In particular `fit()` will never crash: detailed exception information will always be available in a logfile for post-analysis.\n",
     " * solve for multiple initial points in parallel.\n",
     "\n",
diff --git a/examples/DifferentialOperators.html b/guide/diff_ops.html
similarity index 91%
rename from examples/DifferentialOperators.html
rename to guide/diff_ops.html
index ba4db9be..a1422bc9 100644
--- a/examples/DifferentialOperators.html
+++ b/guide/diff_ops.html
@@ -5,7 +5,7 @@
 <head>
 <meta charset="utf-8"/>
 <meta content="width=device-width, initial-scale=1.0" name="viewport"/><meta content="width=device-width, initial-scale=1" name="viewport"/>
-<title>Differential operators in Pyxu — Pyxu Documentation</title>
+<title>Differential Operators in Pyxu — Pyxu Documentation</title>
 <script data-cfasync="false">
     document.documentElement.dataset.mode = localStorage.getItem("mode") || "light";
     document.documentElement.dataset.theme = localStorage.getItem("theme") || "light";
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+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
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-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
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 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
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-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
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@@ -48,12 +48,12 @@
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-<script>DOCUMENTATION_OPTIONS.pagename = 'examples/DifferentialOperators';</script>
+<script>DOCUMENTATION_OPTIONS.pagename = 'guide/diff_ops';</script>
 <link href="../_static/favicon.png" rel="icon"/>
 <link href="../genindex.html" rel="index" title="Index"/>
 <link href="../search.html" rel="search" title="Search"/>
-<link href="../api/index.html" rel="next" title="API Reference"/>
-<link href="Stencils.html" rel="prev" title="Convolution with Pyxu"/>
+<link href="../examples/index.html" rel="next" title="Example Gallery"/>
+<link href="hpc.html" rel="prev" title="High Performance Computing Features"/>
 <meta content="width=device-width, initial-scale=1" name="viewport"/>
 <meta content="en" name="docsearch:language"/>
 </head>
@@ -96,13 +96,13 @@
                         Getting Started
                       </a>
 </li>
-<li class="nav-item">
-<a class="nav-link nav-internal" href="../guide/index.html">
+<li class="nav-item current active">
+<a class="nav-link nav-internal" href="index.html">
                         User Guide
                       </a>
 </li>
-<li class="nav-item current active">
-<a class="nav-link nav-internal" href="index.html">
+<li class="nav-item">
+<a class="nav-link nav-internal" href="../examples/index.html">
                         Example Gallery
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@@ -178,13 +178,13 @@
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-<li class="nav-item">
-<a class="nav-link nav-internal" href="../guide/index.html">
+<li class="nav-item current active">
+<a class="nav-link nav-internal" href="index.html">
                         User Guide
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 </li>
-<li class="nav-item current active">
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+<li class="nav-item">
+<a class="nav-link nav-internal" href="../examples/index.html">
                         Example Gallery
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@@ -226,8 +226,13 @@
 <div class="sidebar-primary-item"><nav aria-label="Section Navigation" class="bd-docs-nav bd-links">
 <p aria-level="1" class="bd-links__title" role="heading">Section Navigation</p>
 <div class="bd-toc-item navbar-nav"><ul class="current nav bd-sidenav">
-<li class="toctree-l1"><a class="reference internal" href="Stencils.html">Convolution with Pyxu</a></li>
-<li class="toctree-l1 current active"><a class="current reference internal" href="#">Differential operators in Pyxu</a></li>
+<li class="toctree-l1"><a class="reference internal" href="fwdops.html">Forward Operators</a></li>
+<li class="toctree-l1"><a class="reference internal" href="funcs.html">Loss &amp; Regularization Functionals</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algebra.html">Operator Algebra Logic</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithms.html">Optimization Algorithms</a></li>
+<li class="toctree-l1"><a class="reference internal" href="lipschitz.html">Lipschitz Constants and Automatic Step Size Tuning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="hpc.html">High Performance Computing Features</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Differential Operators in Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
@@ -250,8 +255,8 @@
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-<li class="breadcrumb-item"><a class="nav-link" href="index.html">Example Gallery</a></li>
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+<li class="breadcrumb-item"><a class="nav-link" href="index.html">User Guide</a></li>
+<li aria-current="page" class="breadcrumb-item active">Differential Operators in Pyxu</li>
 </ul>
 </nav>
 </div>
@@ -260,26 +265,23 @@
 </div>
 <div id="searchbox"></div>
 <article class="bd-article" role="main">
-<section id="Differential-operators-in-Pyxu">
-<h1>Differential operators in Pyxu<a class="headerlink" href="#Differential-operators-in-Pyxu" title="Link to this heading">#</a></h1>
-<p>The <code class="docutils literal notranslate"><span class="pre">pyxu.operator.linop.diff</span></code> module defines a set of classes and functions related to derivative operators.</p>
-<p>In the context of inverse problems, derivative operators come handy when the spatial structure of the object or image be reconstructed can be leveraged. For example, common uses of derivatives are when the image is expected to be smooth in one or more directions, or in contrast, when it is expected to have sharp edges and flat regions. In those cases, the derivative operators are used as part of regularization terms, adding prior knowledge to our solution (see example TODO).</p>
-<section id="1.-Partial-derivatives">
-<h2>1. Partial derivatives<a class="headerlink" href="#1.-Partial-derivatives" title="Link to this heading">#</a></h2>
-<p>The most basic differential operator is the <strong>partial derivative</strong>:</p>
-<p><span class="math">\begin{align}
-\frac{\partial^{n}}{\partial x_0^{n_0} \cdots \partial x_{D-1}^{n_{D-1}}}
-\end{align}</span></p>
+<section id="Differential-Operators-in-Pyxu">
+<h1>Differential Operators in Pyxu<a class="headerlink" href="#Differential-Operators-in-Pyxu" title="Link to this heading">#</a></h1>
+<p>The <code class="docutils literal notranslate"><span class="pre">pyxu.operator.linop.diff</span></code><a class="reference external" href="../api/operator/linop.html#derivatives">🔗</a> module defines a set of classes and functions related to derivative operators.</p>
+<p>In the context of inverse problems, derivative operators come handy when the spatial structure of the object or image be reconstructed can be leveraged. For example, common uses of derivatives are when the image is expected to be smooth in one or more directions, or in contrast, when it is expected to have sharp edges and flat regions. In those cases, the derivative operators are used as part of regularization terms, adding prior knowledge to our solution.</p>
+<section id="Partial-Derivatives">
+<h2>Partial Derivatives<a class="headerlink" href="#Partial-Derivatives" title="Link to this heading">#</a></h2>
+<p>The most basic differential operator is the <code class="docutils literal notranslate"><span class="pre">PartialDerivative</span></code><a class="reference external" href="../api/operator/linop.html#pyxu.operator.PartialDerivative">🔗</a>:</p>
+<div class="math notranslate nohighlight">
+\[\frac{\partial^{n}}{\partial x_0^{n_0} \cdots \partial x_{D-1}^{n_{D-1}}}\]</div>
 <p>Which when applied to an given signal <span class="math notranslate nohighlight">\(\mathbf{f}\)</span>, yields:</p>
-<p><span class="math">\begin{align}
-\frac{\partial^{n}}{\partial x_0^{n_0} \cdots \partial x_{D-1}^{n_{D-1}}}\mathbf{f} =\mathbf{D}\mathbf{f}\in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}}
-\end{align}</span></p>
+<div class="math notranslate nohighlight">
+\[\frac{\partial^{n}}{\partial x_0^{n_0} \cdots \partial x_{D-1}^{n_{D-1}}}\mathbf{f} =\mathbf{D}\mathbf{f}\in \mathbb{R}^{N_0 \times \cdots \times N_{D-1}}\]</div>
 <p>Partial derivatives in <code class="docutils literal notranslate"><span class="pre">Pyxu</span></code> are computed via efficient <strong>matrix-free</strong> implementation, which is based on <a class="reference external" href="https://numba.pydata.org/numba-doc/latest/user/stencil.html">JIT compiled stencils</a>. For illustrative purposes, consider the following approximation to the partial derivatives:</p>
-<p><span class="math">\begin{align}
-\mathbf{D} f [n] = f[n+1] - f[n]
-\end{align}</span></p>
+<div class="math notranslate nohighlight">
+\[\mathbf{D} f [n] = f[n+1] - f[n]\]</div>
 <p>As we will see below, this is the forward finite difference approximation. This could be implemented in <strong>matrix-form</strong>, in which case it would look like this:</p>
-<center><p><img alt="2b333634e40c47ee90063433ab0d14b1" class="no-scaled-link" src="../_images/matrix-form.png" style="width: 400px;"/></p>
+<center><p><img alt="f47d1e97cb64448cb4924f847d09ac30" class="no-scaled-link" src="../_images/matrix-form.png" style="width: 400px;"/></p>
 </center><p>Or, it could be instead implemented via a for loop, in which the case of large input signals, would not require storing a large matrix:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">D</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">"""</span>
@@ -302,14 +304,13 @@ <h2>1. Partial derivatives<a class="headerlink" href="#1.-Partial-derivatives" t
     <span class="k">return</span> <span class="n">y</span>
 </pre></div>
 </div>
-<p>Despite Python being very slow when it comes to for loops, there are some ways to make them really efficient (see <a class="reference external" href="TODO">HPC example</a>).</p>
+<p>Despite Python being very slow when it comes to for-loops, Pyxu leverages existing tools to run them efficiently (see <a class="reference internal" href="hpc.html"><span class="doc">HPC Features</span></a>).</p>
 <!---
- finite_difference = PartialDerivative.finite_difference(
+finite_difference = PartialDerivative.finite_difference(
             arg_shape=(10,),
             order=(1, ),
             scheme="forward",
             accuracy=1,)
-
 fig, ax = plt.subplots(figsize=(5,5))
 im = ax.imshow(finite_difference.asarray(), cmap="RdYlBu")
 ax.set_xticks(np.arange(cut - 1) + 0.5, [])
@@ -319,8 +320,8 @@ <h2>1. Partial derivatives<a class="headerlink" href="#1.-Partial-derivatives" t
 plt.colorbar(im, ax=ax)
 fig.tight_layout()
 fig.savefig("data/images/matrix-form.png", dpi=200)
----><section id="1.1.-Parameters">
-<h3>1.1. Parameters<a class="headerlink" href="#1.1.-Parameters" title="Link to this heading">#</a></h3>
+---><section id="Partial-Derivative-Parametrization">
+<h3>Partial Derivative Parametrization<a class="headerlink" href="#Partial-Derivative-Parametrization" title="Link to this heading">#</a></h3>
 <p>The <code class="docutils literal notranslate"><span class="pre">PartialDerivative</span></code> class implements two main approximations to the partial derivatives as methods:<code class="docutils literal notranslate"><span class="pre">finite_difference</span></code> and <code class="docutils literal notranslate"><span class="pre">gaussian_derivative</span></code>:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">finite_difference</span><span class="p">(</span>
         <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pyct</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
@@ -331,7 +332,7 @@ <h3>1.1. Parameters<a class="headerlink" href="#1.1.-Parameters" title="Link to
         <span class="n">gpu</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
         <span class="n">dtype</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Optional</span><span class="p">[</span><span class="n">pyct</span><span class="o">.</span><span class="n">DType</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
         <span class="n">sampling</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Union</span><span class="p">[</span><span class="n">pyct</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pyct</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="o">...</span><span class="p">]]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
-    <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pyct</span><span class="o">.</span><span class="n">OpT</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pyct</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 </pre></div>
 </div>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">gaussian_derivative</span><span class="p">(</span>
@@ -343,26 +344,20 @@ <h3>1.1. Parameters<a class="headerlink" href="#1.1.-Parameters" title="Link to
         <span class="n">gpu</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
         <span class="n">dtype</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Optional</span><span class="p">[</span><span class="n">pyct</span><span class="o">.</span><span class="n">DType</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
         <span class="n">sampling</span><span class="p">:</span> <span class="n">typ</span><span class="o">.</span><span class="n">Union</span><span class="p">[</span><span class="n">pyct</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="n">cabc</span><span class="o">.</span><span class="n">Sequence</span><span class="p">[</span><span class="n">pyct</span><span class="o">.</span><span class="n">Real</span><span class="p">,</span> <span class="o">...</span><span class="p">]]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
-    <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pyct</span><span class="o">.</span><span class="n">OpT</span>
+    <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">pyct</span><span class="o">.</span><span class="n">OpT</span><span class="p">:</span>
 </pre></div>
 </div>
 <p>The common arguments are:</p>
-<ul>
+<ul class="simple">
 <li><p><code class="docutils literal notranslate"><span class="pre">arg_shape</span></code>: Shape of the input image. This is information is necessary in case batch processing is intended.</p></li>
 <li><p><code class="docutils literal notranslate"><span class="pre">order</span></code>: Derivative order in each axis. For example, for a 2D image input:</p>
 <ul>
-<li><p><code class="docutils literal notranslate"><span class="pre">order=(1,</span> <span class="pre">2)</span></code> would yield:</p>
-<div class="math notranslate nohighlight">
-\[\frac{\partial^{3} \mathbf{f}}{\partial x \partial y^{2}}\]</div>
-</li>
-<li><p><code class="docutils literal notranslate"><span class="pre">order=(2,</span> <span class="pre">0)</span></code> would yield:</p>
-<div class="math notranslate nohighlight">
-\[\frac{\partial^{2} \mathbf{f}}{\partial x^{2}}\]</div>
-</li>
+<li><p><code class="docutils literal notranslate"><span class="pre">order=(1,</span> <span class="pre">2)</span></code> would yield: <span class="math notranslate nohighlight">\(\frac{\partial^{3} \mathbf{f}}{\partial x \partial y^{2}}\)</span></p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">order=(2,</span> <span class="pre">0)</span></code> would yield: <span class="math notranslate nohighlight">\(\frac{\partial^{2} \mathbf{f}}{\partial x^{2}}\)</span></p></li>
 </ul>
 </li>
 <li><p><code class="docutils literal notranslate"><span class="pre">mode</span></code>: Padding mode to define boundary conditions. Pre-padding and post-trimming are computed to yield an output array of the same shape as the input. It can be defined in general (with a <code class="docutils literal notranslate"><span class="pre">string</span></code>) or per axis (with a <code class="docutils literal notranslate"><span class="pre">tuple</span></code>). The available modes are:</p>
-<ul class="simple">
+<ul>
 <li><p>‘constant’</p></li>
 <li><p>‘wrap’</p></li>
 <li><p>‘reflect’</p></li>
@@ -377,8 +372,8 @@ <h3>1.1. Parameters<a class="headerlink" href="#1.1.-Parameters" title="Link to
 <p>The sections below it is explained the differences between these two methods and their specific arguments.</p>
 <div class="alert alert-block alert-warning"><p>Important: Differential operators are not backend nor dtype agnostic! The arguments <code class="docutils literal notranslate"><span class="pre">gpu</span></code> and <code class="docutils literal notranslate"><span class="pre">dtype</span></code> must be chosen adequately.</p>
 </div></section>
-<section id="1.2.-Finite-differences">
-<h3>1.2. Finite differences<a class="headerlink" href="#1.2.-Finite-differences" title="Link to this heading">#</a></h3>
+<section id="Finite-Differences-Approximation-to-the-Partial-Derivative">
+<h3>Finite Differences Approximation to the Partial Derivative<a class="headerlink" href="#Finite-Differences-Approximation-to-the-Partial-Derivative" title="Link to this heading">#</a></h3>
 <p>Finite differences approximate the derivatives by computing the difference between pixel values in the image. There are different variations of finite differences, such as forward differences, backward differences, and central differences.</p>
 <ul class="simple">
 <li><p><em>Forward Differences</em>: <span class="math notranslate nohighlight">\(\mathbf{D}_{F} f [n] = \frac{f[n+1] - f[n]}{h}\)</span></p></li>
@@ -499,13 +494,13 @@ <h3>1.2. Finite differences<a class="headerlink" href="#1.2.-Finite-differences"
 <div class="prompt empty docutils container">
 </div>
 <div class="output_area docutils container">
-<img alt="../_images/examples_DifferentialOperators_13_1.png" src="../_images/examples_DifferentialOperators_13_1.png"/>
+<img alt="../_images/guide_diff_ops_3_1.png" src="../_images/guide_diff_ops_3_1.png"/>
 </div>
 </div>
 <p>These results indicate that finite differences work fine for non-noisy data, but they can be quite <strong>sensitive to noise</strong> in the image and may introduce inaccuracies, especially when the image has high-frequency content. For more detailed information on this topic, check <a class="reference external" href="https://www.crisluengo.net/archives/22/">this great post on Gaussian derivative</a>.</p>
 </section>
-<section id="1.3.Gaussian-derivative">
-<h3>1.3.Gaussian derivative<a class="headerlink" href="#1.3.Gaussian-derivative" title="Link to this heading">#</a></h3>
+<section id="Gaussian-Derivative-Approximation-to-the-Partial-Derivative">
+<h3>Gaussian Derivative Approximation to the Partial Derivative<a class="headerlink" href="#Gaussian-Derivative-Approximation-to-the-Partial-Derivative" title="Link to this heading">#</a></h3>
 <p>The Gaussian derivative is an alternative method for estimating partial derivatives. It is derived by <strong>convolving a signal with a Gaussian kernel and then computing the derivatives</strong> of the resulting smoothed signal.</p>
 <div class="nbinput docutils container">
 <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[4]:
@@ -564,7 +559,7 @@ <h3>1.3.Gaussian derivative<a class="headerlink" href="#1.3.Gaussian-derivative"
 <div class="prompt empty docutils container">
 </div>
 <div class="output_area docutils container">
-<img alt="../_images/examples_DifferentialOperators_19_0.png" src="../_images/examples_DifferentialOperators_19_0.png"/>
+<img alt="../_images/guide_diff_ops_9_0.png" src="../_images/guide_diff_ops_9_0.png"/>
 </div>
 </div>
 <div class="nbinput docutils container">
@@ -606,50 +601,45 @@ <h3>1.3.Gaussian derivative<a class="headerlink" href="#1.3.Gaussian-derivative"
 <div class="prompt empty docutils container">
 </div>
 <div class="output_area docutils container">
-<img alt="../_images/examples_DifferentialOperators_20_0.png" src="../_images/examples_DifferentialOperators_20_0.png"/>
+<img alt="../_images/guide_diff_ops_10_0.png" src="../_images/guide_diff_ops_10_0.png"/>
 </div>
 </div>
 <p>Gaussian derivatives can be computed for different orders of derivatives (e.g., first-order, second-order) and at different scales (by varying the standard deviation of the Gaussian kernel). Higher-order derivatives capture more detailed information about the image’s structure, while larger scales provide a more global representation.</p>
 </section>
-<section id="1.4.-How-to-choose?">
-<h3>1.4. How to choose?<a class="headerlink" href="#1.4.-How-to-choose?" title="Link to this heading">#</a></h3>
-<p>The choice between <em>finite difference</em> and <em>Gaussian derivative</em> can be seen as a <strong>trade-off between bias and variance</strong>: - When estimating partial derivatives, the Gaussian derivative robustly captures the true behavior of the derivative of the smoothed signal, thus introducing bias in the estimation. - On the other hand, finite differences, especially when using a small accuracy value, can be highly sensitive to noise and can produce unstable estimates of the derivative (variance). Gaussian
-derivatives, on the other hand, tend to be smoother and less affected by noise.</p>
+<section id="How-to-choose-between-Finite-Differences-and-Gaussian-Derivative?">
+<h3>How to choose between Finite Differences and Gaussian Derivative?<a class="headerlink" href="#How-to-choose-between-Finite-Differences-and-Gaussian-Derivative?" title="Link to this heading">#</a></h3>
+<p>The choice between <em>finite difference</em> and <em>Gaussian derivative</em> can be seen as a <strong>trade-off between bias and variance</strong>:</p>
+<ul class="simple">
+<li><p>When estimating partial derivatives, the Gaussian derivative robustly captures the true behavior of the derivative of the smoothed signal, thus introducing bias in the estimation.</p></li>
+<li><p>On the other hand, finite differences, especially when using a small accuracy value, can be highly sensitive to noise and can produce unstable estimates of the derivative (variance). Gaussian derivatives, on the other hand, tend to be smoother and less affected by noise.</p></li>
+</ul>
 <p>As a rule of thumb, it is recommended to try both approaches and to use the Gaussian derivative for very noisy signals.</p>
 </section>
 </section>
-<section id="2.-Stacks-of-partial-derivatives">
-<h2>2. Stacks of partial derivatives<a class="headerlink" href="#2.-Stacks-of-partial-derivatives" title="Link to this heading">#</a></h2>
+<section id="Stacks-of-Partial-Derivatives">
+<h2>Stacks of Partial Derivatives<a class="headerlink" href="#Stacks-of-Partial-Derivatives" title="Link to this heading">#</a></h2>
 <p>There are two main classes of stacks of partial derivative:</p>
 <ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">Gradient</span></code>: stack of all first order derivatives (one per axis),</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">Gradient</span></code><a class="reference external" href="../api/operator/linop.html#pyxu.operator.Gradient">🔗</a>: stack of all first order derivatives (one per axis),</p></li>
 </ul>
-<p>:nbsphinx-math:<a href="#id1"><span class="problematic" id="id2">`</span></a>begin{align}
-mathbf{f} = begin{bmatrix}</p>
-<blockquote>
-<div><p>frac{partial mathbf{f}}{partial x_0} \
-vdots \
-frac{partial mathbf{f}}{partial x_{D-1}}
-end{bmatrix} in mathbb{R}^{D times N_{0} times cdots times N_{D-1}}</p>
-</div></blockquote>
-<p>end{align}`</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathbf{f} = \begin{bmatrix}
+   \frac{\partial \mathbf{f}}{\partial x_0} \\
+   \vdots \\
+   \frac{\partial \mathbf{f}}{\partial x_{D-1}}
+   \end{bmatrix} \in \mathbb{R}^{D \times N_{0} \times \cdots \times N_{D-1}}\end{split}\]</div>
 <ul class="simple">
-<li><p><code class="docutils literal notranslate"><span class="pre">Hessian</span></code>: stack of all second order derivatives,</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">Hessian</span></code><a class="reference external" href="../api/operator/linop.html#pyxu.operator.Hessian">🔗</a>: stack of all second order derivatives,</p></li>
 </ul>
-<dl class="simple">
-<dt>:nbsphinx-math:<a href="#id3"><span class="problematic" id="id4">`</span></a>begin{align}</dt><dd><dl class="simple">
-<dt>mathbf{H} mathbf{f} = begin{bmatrix}</dt><dd><p>dfrac{ partial^{2}mathbf{f} }{ partial x_{0}^{2} } &amp;  dfrac{ partial^{2}mathbf{f} }{ partial x_{0},partial x_{1} } &amp; cdots &amp; dfrac{ partial^{2}mathbf{f} }{ partial x_{0} , partial x_{D-1} } \
-dfrac{ partial^{2}mathbf{f} }{ partial x_{1} , partial x_{0} } &amp; dfrac{ partial^{2}mathbf{f} }{ partial x_{1}^{2} } &amp; cdots &amp; dfrac{ partial^{2}mathbf{f} }{partial x_{1} ,partial x_{D-1}} \
-vdots &amp; vdots &amp; ddots &amp; vdots \
-dfrac{ partial^{2}mathbf{f} }{ partial x_{D-1} , partial x_{0} } &amp; dfrac{ partial^{2}mathbf{f} }{ partial x_{D-1} , partial x_{1} } &amp; cdots &amp; dfrac{ partial^{2}mathbf{f} }{ partial x_{D-1}^{2}}
-end{bmatrix}</p>
-</dd>
-</dl>
-</dd>
-</dl>
-<p>end{align}`</p>
-<section id="2.1.-Parameters">
-<h3>2.1. Parameters<a class="headerlink" href="#2.1.-Parameters" title="Link to this heading">#</a></h3>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathbf{H} \mathbf{f} = \begin{bmatrix}
+   \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{0}^{2} } &amp;  \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{0}\,\partial x_{1} } &amp; \cdots &amp; \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{0} \, \partial x_{D-1} } \\
+   \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{1} \, \partial x_{0} } &amp; \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{1}^{2} } &amp; \cdots &amp; \dfrac{ \partial^{2}\mathbf{f} }{\partial x_{1} \,\partial x_{D-1}} \\
+   \vdots &amp; \vdots &amp; \ddots &amp; \vdots \\
+   \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{D-1} \, \partial x_{0} } &amp; \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{D-1} \, \partial x_{1} } &amp; \cdots &amp; \dfrac{ \partial^{2}\mathbf{f} }{ \partial x_{D-1}^{2}}
+   \end{bmatrix}\end{split}\]</div>
+<section id="Parameters">
+<h3>Parameters<a class="headerlink" href="#Parameters" title="Link to this heading">#</a></h3>
 <p>The <code class="docutils literal notranslate"><span class="pre">Gradient</span></code> and <code class="docutils literal notranslate"><span class="pre">Hessian</span></code> objects are parametrized as:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">Gradient</span><span class="p">(</span>
     <span class="n">arg_shape</span><span class="p">:</span> <span class="n">pyct</span><span class="o">.</span><span class="n">NDArrayShape</span><span class="p">,</span>
@@ -688,18 +678,15 @@ <h3>2.1. Parameters<a class="headerlink" href="#2.1.-Parameters" title="Link to
 <p>The sections below it is explained the differences between these two methods and their specific arguments.</p>
 <div class="alert alert-block alert-warning"><p>Important: Be aware that the <code class="docutils literal notranslate"><span class="pre">directions</span></code> argument has different behavior between <code class="docutils literal notranslate"><span class="pre">Gradient</span></code> and <code class="docutils literal notranslate"><span class="pre">Hessian</span></code>. Keep reading for further details.</p>
 </div></section>
-<section id="2.2.-Gradient">
-<h3>2.2. Gradient<a class="headerlink" href="#2.2.-Gradient" title="Link to this heading">#</a></h3>
+<section id="Gradient">
+<h3>Gradient<a class="headerlink" href="#Gradient" title="Link to this heading">#</a></h3>
 <p>The gradient operator applies the first-order derivatives on all dimensions if the signal and concatenates them.</p>
 <p>For example, in the case of a 2-dimensional image, the gradient operator implements:</p>
-<p>:nbsphinx-math:<a href="#id6"><span class="problematic" id="id7">`</span></a>begin{align}
-boldsymbol{nabla} mathbf{f} = begin{bmatrix}</p>
-<blockquote>
-<div><p>frac{partial mathbf{f}}{partial x} \
-frac{partial mathbf{f}}{partial y}
-end{bmatrix} in mathbb{R}^{2 times N_{x} times N_{y}}</p>
-</div></blockquote>
-<p>end{align}`</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\boldsymbol{\nabla} \mathbf{f} = \begin{bmatrix}
+    \frac{\partial \mathbf{f}}{\partial x} \\
+    \frac{\partial \mathbf{f}}{\partial y}
+    \end{bmatrix} \in \mathbb{R}^{2 \times N_{x} \times N_{y}}\end{split}\]</div>
 <div class="nbinput docutils container">
 <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[8]:
 </pre></div>
@@ -753,7 +740,7 @@ <h3>2.2. Gradient<a class="headerlink" href="#2.2.-Gradient" title="Link to this
 <div class="prompt empty docutils container">
 </div>
 <div class="output_area docutils container">
-<img alt="../_images/examples_DifferentialOperators_31_0.png" src="../_images/examples_DifferentialOperators_31_0.png"/>
+<img alt="../_images/guide_diff_ops_21_0.png" src="../_images/guide_diff_ops_21_0.png"/>
 </div>
 </div>
 <div class="highlight-none notranslate"><div class="highlight"><pre><span></span>                                                        ┌───&gt;  Jacobian
@@ -763,8 +750,8 @@ <h3>2.2. Gradient<a class="headerlink" href="#2.2.-Gradient" title="Link to this
 </pre></div>
 </div>
 </section>
-<section id="2.3.-Hessian">
-<h3>2.3. Hessian<a class="headerlink" href="#2.3.-Hessian" title="Link to this heading">#</a></h3>
+<section id="Hessian">
+<h3>Hessian<a class="headerlink" href="#Hessian" title="Link to this heading">#</a></h3>
 <div class="nbinput docutils container">
 <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[9]:
 </pre></div>
@@ -825,7 +812,7 @@ <h3>2.3. Hessian<a class="headerlink" href="#2.3.-Hessian" title="Link to this h
 <div class="prompt empty docutils container">
 </div>
 <div class="output_area docutils container">
-<img alt="../_images/examples_DifferentialOperators_34_0.png" src="../_images/examples_DifferentialOperators_34_0.png"/>
+<img alt="../_images/guide_diff_ops_24_0.png" src="../_images/guide_diff_ops_24_0.png"/>
 </div>
 </div>
 </section>
@@ -836,17 +823,17 @@ <h3>2.3. Hessian<a class="headerlink" href="#2.3.-Hessian" title="Link to this h
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+<p class="prev-next-title">High Performance Computing Features</p>
 </div>
 </a>
-<a class="right-next" href="../api/index.html" title="next page">
+<a class="right-next" href="../examples/index.html" title="next page">
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@@ -861,17 +848,17 @@ <h3>2.3. Hessian<a class="headerlink" href="#2.3.-Hessian" title="Link to this h
   </div>
 <nav class="bd-toc-nav page-toc">
 <ul class="visible nav section-nav flex-column">
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#1.-Partial-derivatives">1. Partial derivatives</a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#1.1.-Parameters">1.1. Parameters</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#1.2.-Finite-differences">1.2. Finite differences</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#1.3.Gaussian-derivative">1.3.Gaussian derivative</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#1.4.-How-to-choose?">1.4. How to choose?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Partial-Derivatives">Partial Derivatives</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Partial-Derivative-Parametrization">Partial Derivative Parametrization</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Finite-Differences-Approximation-to-the-Partial-Derivative">Finite Differences Approximation to the Partial Derivative</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Gaussian-Derivative-Approximation-to-the-Partial-Derivative">Gaussian Derivative Approximation to the Partial Derivative</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#How-to-choose-between-Finite-Differences-and-Gaussian-Derivative?">How to choose between Finite Differences and Gaussian Derivative?</a></li>
 </ul>
 </li>
-<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#2.-Stacks-of-partial-derivatives">2. Stacks of partial derivatives</a><ul class="visible nav section-nav flex-column">
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#2.1.-Parameters">2.1. Parameters</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#2.2.-Gradient">2.2. Gradient</a></li>
-<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#2.3.-Hessian">2.3. Hessian</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Stacks-of-Partial-Derivatives">Stacks of Partial Derivatives</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Parameters">Parameters</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Gradient">Gradient</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#Hessian">Hessian</a></li>
 </ul>
 </li>
 </ul>
@@ -880,7 +867,7 @@ <h3>2.3. Hessian<a class="headerlink" href="#2.3.-Hessian" title="Link to this h
 <div id="searchbox"></div></div>
 <div class="sidebar-secondary-item">
 <div class="tocsection editthispage">
-<a href="https://github.com/matthieumeo/pyxu/edit/main/doc/examples/DifferentialOperators.ipynb">
+<a href="https://github.com/matthieumeo/pyxu/edit/main/doc/guide/diff_ops.ipynb">
 <i class="fa-solid fa-pencil"></i>
       
       
@@ -893,7 +880,7 @@ <h3>2.3. Hessian<a class="headerlink" href="#2.3.-Hessian" title="Link to this h
 </div>
 <div class="sidebar-secondary-item">
 <div class="tocsection sourcelink">
-<a href="../_sources/examples/DifferentialOperators.ipynb">
+<a href="../_sources/guide/diff_ops.ipynb">
 <i class="fa-solid fa-file-lines"></i> Show Source
     </a>
 </div>
diff --git a/examples/DifferentialOperators.ipynb b/guide/diff_ops.ipynb
similarity index 99%
rename from examples/DifferentialOperators.ipynb
rename to guide/diff_ops.ipynb
index 33cd69fa..8031747e 100644
--- a/examples/DifferentialOperators.ipynb
+++ b/guide/diff_ops.ipynb
@@ -1,62 +1,32 @@
 {
  "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "177a858e",
-   "metadata": {},
-   "source": [
-    "# Differential operators in Pyxu"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "ab2b2317",
    "metadata": {},
    "source": [
-    "The `pyxu.operator.linop.diff` module defines a set of classes and functions related to derivative operators. \n",
+    "# Differential Operators in Pyxu\n",
     "\n",
-    "In the context of inverse problems, derivative operators come handy when the spatial structure of the object or image be reconstructed can be leveraged. For example, common uses of derivatives are when the image is expected to be smooth in one or more directions, or in contrast, when it is  expected to have sharp edges and flat regions. In those cases, the derivative operators are used as part of regularization terms, adding prior knowledge to our solution (see example TODO).\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "6e2d5017",
-   "metadata": {},
-   "source": [
-    "## 1. Partial derivatives"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7e401893",
-   "metadata": {},
-   "source": [
+    "The `pyxu.operator.linop.diff`[🔗](../api/operator/linop.html#derivatives)  module defines a set of classes and functions related to derivative operators. \n",
+    "\n",
+    "In the context of inverse problems, derivative operators come handy when the spatial structure of the object or image be reconstructed can be leveraged. For example, common uses of derivatives are when the image is expected to be smooth in one or more directions, or in contrast, when it is  expected to have sharp edges and flat regions. In those cases, the derivative operators are used as part of regularization terms, adding prior knowledge to our solution.\n",
+    "\n",
+    "## Partial Derivatives\n",
     "\n",
-    "The most basic differential operator is the **partial derivative**:\n",
     "\n",
+    "The most basic differential operator is the `PartialDerivative`[🔗](../api/operator/linop.html#pyxu.operator.PartialDerivative):\n",
     "\n",
-    "\\begin{align}\n",
-    "\\frac{\\partial^{n}}{\\partial x_0^{n_0} \\cdots \\partial x_{D-1}^{n_{D-1}}} \n",
-    "\\end{align}\n",
+    "$$\\frac{\\partial^{n}}{\\partial x_0^{n_0} \\cdots \\partial x_{D-1}^{n_{D-1}}}$$\n",
     "\n",
     "Which when applied to an given signal $\\mathbf{f}$, yields:\n",
     "\n",
-    "\\begin{align}\n",
-    "\\frac{\\partial^{n}}{\\partial x_0^{n_0} \\cdots \\partial x_{D-1}^{n_{D-1}}}\\mathbf{f} =\\mathbf{D}\\mathbf{f}\\in \\mathbb{R}^{N_0 \\times \\cdots \\times N_{D-1}}\n",
-    "\\end{align}\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "e8617455",
-   "metadata": {},
-   "source": [
+    "$$\\frac{\\partial^{n}}{\\partial x_0^{n_0} \\cdots \\partial x_{D-1}^{n_{D-1}}}\\mathbf{f} =\\mathbf{D}\\mathbf{f}\\in \\mathbb{R}^{N_0 \\times \\cdots \\times N_{D-1}}$$\n",
+    "\n",
+    "\n",
     "Partial derivatives in `Pyxu` are computed via efficient **matrix-free** implementation, which is based on [JIT compiled stencils](https://numba.pydata.org/numba-doc/latest/user/stencil.html). For illustrative purposes, consider the following approximation to the partial derivatives:\n",
     "\n",
     "\n",
-    "\\begin{align}\n",
-    "\\mathbf{D} f [n] = f[n+1] - f[n]\n",
-    "\\end{align}\n",
+    "$$\\mathbf{D} f [n] = f[n+1] - f[n]$$\n",
     "\n",
     "\n",
     "As we will see below, this is the forward finite difference approximation. This could be implemented in **matrix-form**, in which case it would look like this:\n",
@@ -91,15 +61,14 @@
     "```\n",
     "\n",
     "\n",
-    "Despite Python being very slow when it comes to for loops, there are some ways to make them really efficient (see [HPC example](TODO)).\n",
+    "Despite Python being very slow when it comes to for-loops, Pyxu leverages existing tools to run them efficiently (see [HPC Features](./hpc.ipynb)).\n",
     "\n",
     "<!---\n",
-    " finite_difference = PartialDerivative.finite_difference(\n",
+    "finite_difference = PartialDerivative.finite_difference(\n",
     "            arg_shape=(10,), \n",
     "            order=(1, ),\n",
     "            scheme=\"forward\", \n",
     "            accuracy=1,)\n",
-    "\n",
     "fig, ax = plt.subplots(figsize=(5,5))\n",
     "im = ax.imshow(finite_difference.asarray(), cmap=\"RdYlBu\")\n",
     "ax.set_xticks(np.arange(cut - 1) + 0.5, [])\n",
@@ -109,22 +78,10 @@
     "plt.colorbar(im, ax=ax)\n",
     "fig.tight_layout()\n",
     "fig.savefig(\"data/images/matrix-form.png\", dpi=200)\n",
-    "--->"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "0bdfbd20",
-   "metadata": {},
-   "source": [
-    "### 1.1. Parameters"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b795b197",
-   "metadata": {},
-   "source": [
+    "--->\n",
+    "\n",
+    "### Partial Derivative Parametrization\n",
+    "\n",
     "The `PartialDerivative` class implements two main approximations to the partial derivatives as methods:`finite_difference` and `gaussian_derivative`:\n",
     "\n",
     "```python\n",
@@ -138,8 +95,7 @@
     "        gpu: bool = False,\n",
     "        dtype: typ.Optional[pyct.DType] = None,\n",
     "        sampling: typ.Union[pyct.Real, cabc.Sequence[pyct.Real, ...]] = 1,\n",
-    "    ) -> pyct.OpT\n",
-    "    \n",
+    "    ) -> pyct.OpT:\n",
     "``` \n",
     "\n",
     "```python\n",
@@ -153,16 +109,15 @@
     "        gpu: bool = False,\n",
     "        dtype: typ.Optional[pyct.DType] = None,\n",
     "        sampling: typ.Union[pyct.Real, cabc.Sequence[pyct.Real, ...]] = 1,\n",
-    "    ) -> pyct.OpT\n",
-    "    \n",
+    "    ) -> pyct.OpT:\n",
     "```\n",
     "\n",
     "The common arguments are: \n",
     "        \n",
     "- `arg_shape`: Shape of the input image. This is information is necessary in case batch processing is intended.\n",
     "- `order`: Derivative order in each axis. For example, for a 2D image input: \n",
-    "    - `order=(1, 2)` would yield: $$\\frac{\\partial^{3} \\mathbf{f}}{\\partial x \\partial y^{2}}$$\n",
-    "    - `order=(2, 0)` would yield: $$\\frac{\\partial^{2} \\mathbf{f}}{\\partial x^{2}}$$\n",
+    "    - `order=(1, 2)` would yield: $\\frac{\\partial^{3} \\mathbf{f}}{\\partial x \\partial y^{2}}$\n",
+    "    - `order=(2, 0)` would yield: $\\frac{\\partial^{2} \\mathbf{f}}{\\partial x^{2}}$\n",
     "\n",
     "- `mode`: Padding mode to define boundary conditions. Pre-padding and post-trimming are computed to yield an output array of the same shape as the input. It can be defined in general (with a `string`) or per axis (with a `tuple`). The available modes are: \n",
     "    - 'constant'\n",
@@ -176,44 +131,21 @@
     "- `sampling`: Spacing between pixels. It can be defined in general (with a `float/int`) or per axis (with a `tuple`)\n",
     "        \n",
     "        \n",
-    "The sections below it is explained the differences between these two methods and their specific arguments."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "80b3cc9c",
-   "metadata": {},
-   "source": [
+    "The sections below it is explained the differences between these two methods and their specific arguments.\n",
+    "\n",
     "<div class=\"alert alert-block alert-warning\">  \n",
     "<b>Important:</b> Differential operators are not backend nor dtype agnostic! The arguments `gpu` and `dtype` must be chosen adequately.\n",
-    "</div>\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "fe4582cd",
-   "metadata": {},
-   "source": [
-    "### 1.2. Finite differences"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "b3dc5538",
-   "metadata": {},
-   "source": [
+    "</div>\n",
+    "\n",
+    "\n",
+    "### Finite Differences Approximation to the Partial Derivative\n",
+    "\n",
     "Finite differences approximate the derivatives by computing the difference between pixel values in the image. There are different variations of finite differences, such as forward differences, backward differences, and central differences.\n",
     "\n",
     "* *Forward Differences*: $\\mathbf{D}_{F} f [n] = \\frac{f[n+1] - f[n]}{h}$\n",
     "* *Backward Differences*: $\\mathbf{D}_{B} f [n] = \\frac{f[n] - f[n-1]}{h}$\n",
-    "* *Central Differences*: $\\mathbf{D}_{C} f [n] = \\frac{f[n+1] - f[n-1]}{2h}$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8198e968",
-   "metadata": {},
-   "source": [
+    "* *Central Differences*: $\\mathbf{D}_{C} f [n] = \\frac{f[n+1] - f[n-1]}{2h}$\n",
+    "\n",
     "Another important parameter for finite difference is the accuracy, which defines the number of digits used for the approximation. \n",
     "\n",
     "These are some kernels generated by different parameterizations: the (parenthesis) indicates the central element.\n",
@@ -355,7 +287,7 @@
    "id": "1dd0f18f",
    "metadata": {},
    "source": [
-    "### 1.3.Gaussian derivative"
+    "### Gaussian Derivative Approximation to the Partial Derivative"
    ]
   },
   {
@@ -522,7 +454,7 @@
    "id": "52dcd0e8",
    "metadata": {},
    "source": [
-    "### 1.4. How to choose?"
+    "### How to choose between Finite Differences and Gaussian Derivative?"
    ]
   },
   {
@@ -531,8 +463,9 @@
    "metadata": {},
    "source": [
     "The choice between *finite difference* and *Gaussian derivative* can be seen as a **trade-off between bias and variance**:\n",
-    "- When estimating partial derivatives, the Gaussian derivative robustly captures the true behavior of the derivative of the smoothed signal, thus introducing bias in the estimation. \n",
-    "- On the other hand, finite differences, especially when using a small accuracy value, can be highly sensitive to noise and can produce unstable estimates of the derivative (variance). Gaussian derivatives, on the other hand, tend to be smoother and less affected by noise.\n",
+    "\n",
+    "* When estimating partial derivatives, the Gaussian derivative robustly captures the true behavior of the derivative of the smoothed signal, thus introducing bias in the estimation. \n",
+    "* On the other hand, finite differences, especially when using a small accuracy value, can be highly sensitive to noise and can produce unstable estimates of the derivative (variance). Gaussian derivatives, on the other hand, tend to be smoother and less affected by noise.\n",
     "\n",
     "As a rule of thumb, it is recommended to try both approaches and to use the Gaussian derivative for very noisy signals."
    ]
@@ -542,7 +475,7 @@
    "id": "eb92f038",
    "metadata": {},
    "source": [
-    "## 2. Stacks of partial derivatives"
+    "## Stacks of Partial Derivatives"
    ]
   },
   {
@@ -552,28 +485,24 @@
    "source": [
     "There are two main classes of stacks of partial derivative:\n",
     "\n",
-    "* `Gradient`: stack of all first order derivatives (one per axis), \n",
+    "* `Gradient`[🔗](../api/operator/linop.html#pyxu.operator.Gradient): stack of all first order derivatives (one per axis), \n",
     "\n",
     "\n",
-    "\\begin{align}\n",
-    "\\mathbf{f} = \\begin{bmatrix}\n",
+    "$$\\mathbf{f} = \\begin{bmatrix}\n",
     "   \\frac{\\partial \\mathbf{f}}{\\partial x_0} \\\\\n",
     "   \\vdots \\\\\n",
     "   \\frac{\\partial \\mathbf{f}}{\\partial x_{D-1}}\n",
-    "   \\end{bmatrix} \\in \\mathbb{R}^{D \\times N_{0} \\times \\cdots \\times N_{D-1}}\n",
-    "\\end{align}\n",
+    "   \\end{bmatrix} \\in \\mathbb{R}^{D \\times N_{0} \\times \\cdots \\times N_{D-1}}$$\n",
     "\n",
     "\n",
-    "* `Hessian`: stack of all second order derivatives,\n",
+    "* `Hessian`[🔗](../api/operator/linop.html#pyxu.operator.Hessian): stack of all second order derivatives,\n",
     "\n",
-    "\\begin{align}\n",
-    " \\mathbf{H} \\mathbf{f} = \\begin{bmatrix}\n",
+    "$$\\mathbf{H} \\mathbf{f} = \\begin{bmatrix}\n",
     "   \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{0}^{2} } &  \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{0}\\,\\partial x_{1} } & \\cdots & \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{0} \\, \\partial x_{D-1} } \\\\\n",
     "   \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{1} \\, \\partial x_{0} } & \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{1}^{2} } & \\cdots & \\dfrac{ \\partial^{2}\\mathbf{f} }{\\partial x_{1} \\,\\partial x_{D-1}} \\\\\n",
     "   \\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
     "   \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{D-1} \\, \\partial x_{0} } & \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{D-1} \\, \\partial x_{1} } & \\cdots & \\dfrac{ \\partial^{2}\\mathbf{f} }{ \\partial x_{D-1}^{2}}\n",
-    "   \\end{bmatrix}\n",
-    "\\end{align}"
+    "   \\end{bmatrix}$$"
    ]
   },
   {
@@ -581,7 +510,7 @@
    "id": "1eca7161",
    "metadata": {},
    "source": [
-    "### 2.1. Parameters"
+    "### Parameters"
    ]
   },
   {
@@ -624,9 +553,9 @@
     "\n",
     "There are some common arguments that we didn't see in the previous `PartialDerivative` class:\n",
     "        \n",
-    "- `diff_method`: This will select between `finite_difference` ('fd') or `gaussian_derivative` ('gd') type of partial derivatives.\n",
-    "- `parallel`: If `True`, it will compute the different partial derivatives in parrellalel on different threads.\n",
-    "- `diff_kwargs`: Placeholder to specify arguments that are specific to `finite_difference` and `gaussian_derivative`.\n",
+    "* `diff_method`: This will select between `finite_difference` ('fd') or `gaussian_derivative` ('gd') type of partial derivatives.\n",
+    "* `parallel`: If `True`, it will compute the different partial derivatives in parrellalel on different threads.\n",
+    "* `diff_kwargs`: Placeholder to specify arguments that are specific to `finite_difference` and `gaussian_derivative`.\n",
     "        \n",
     "The sections below it is explained the differences between these two methods and their specific arguments."
    ]
@@ -646,7 +575,7 @@
    "id": "816838de",
    "metadata": {},
    "source": [
-    "### 2.2. Gradient"
+    "### Gradient"
    ]
   },
   {
@@ -658,12 +587,10 @@
     "\n",
     "For example, in the case of a 2-dimensional image, the gradient operator implements:\n",
     "\n",
-    "\\begin{align}\n",
-    "\\boldsymbol{\\nabla} \\mathbf{f} = \\begin{bmatrix}\n",
+    "$$\\boldsymbol{\\nabla} \\mathbf{f} = \\begin{bmatrix}\n",
     "    \\frac{\\partial \\mathbf{f}}{\\partial x} \\\\\n",
     "    \\frac{\\partial \\mathbf{f}}{\\partial y}\n",
-    "    \\end{bmatrix} \\in \\mathbb{R}^{2 \\times N_{x} \\times N_{y}}\n",
-    "\\end{align}\n",
+    "    \\end{bmatrix} \\in \\mathbb{R}^{2 \\times N_{x} \\times N_{y}}$$\n",
     "\n"
    ]
   },
@@ -752,7 +679,7 @@
    "id": "9bdfc5cb",
    "metadata": {},
    "source": [
-    "### 2.3. Hessian"
+    "### Hessian"
    ]
   },
   {
diff --git a/guide/funcs.html b/guide/funcs.html
index 88ef9bb7..efd81a0c 100644
--- a/guide/funcs.html
+++ b/guide/funcs.html
@@ -18,7 +18,7 @@
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" rel="preload" type="font/woff2"/>
-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
 <link href="../_static/sphinx-codeautolink.css?v=125d5c1c" rel="stylesheet" type="text/css"/>
 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -28,11 +28,11 @@
 <link href="../_static/sg_gallery-dataframe.css?v=2082cf3c" rel="stylesheet" type="text/css"/>
 <link href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" rel="stylesheet" type="text/css"/>
 <link href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" rel="stylesheet" type="text/css"/>
-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
 <!-- Pre-loaded scripts that we'll load fully later -->
 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
 <link as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" rel="preload"/>
-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
 <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -231,6 +231,7 @@
 <li class="toctree-l1"><a class="reference internal" href="algorithms.html">Optimization Algorithms</a></li>
 <li class="toctree-l1"><a class="reference internal" href="lipschitz.html">Lipschitz Constants and Automatic Step Size Tuning</a></li>
 <li class="toctree-l1"><a class="reference internal" href="hpc.html">High Performance Computing Features</a></li>
+<li class="toctree-l1"><a class="reference internal" href="diff_ops.html">Differential Operators in Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
@@ -277,18 +278,18 @@ <h2>Functionals Hierarchy in Pyxu<a class="headerlink" href="#Functionals-Hierar
 <div><p><strong>Important Note</strong>: The base classes described below are designed as abstract base classes. This means they serve as templates or “blueprints” for creating specific functionals that suit your project needs. You’re not supposed to instantiate them directly. Instead, you have two main options:</p>
 <ol class="arabic simple">
 <li><p><strong>Subclassing</strong>: Extend these classes to create customized functionals tailored to your problem.</p></li>
-<li><p><strong>Generic Constructor Routine</strong>: Utilize the <code class="docutils literal notranslate"><span class="pre">from_source</span></code> method to define new functionals from their core methods, like <code class="docutils literal notranslate"><span class="pre">apply()</span></code>, <code class="docutils literal notranslate"><span class="pre">grad()</span></code>, or <code class="docutils literal notranslate"><span class="pre">prox()</span></code>.</p></li>
+<li><p><strong>Generic Constructor Routine</strong>: Utilize the <code class="docutils literal notranslate"><span class="pre">from_source</span></code><a class="reference external" href="../api/operator.interop.html#general">🔗</a> method to define new functionals from their core methods, like <code class="docutils literal notranslate"><span class="pre">apply()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Map.apply">🔗</a>, <code class="docutils literal notranslate"><span class="pre">grad()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffFunc.grad">🔗</a>, or <code class="docutils literal notranslate"><span class="pre">prox()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.ProxFunc.prox">🔗</a>.</p></li>
 </ol>
 <p>Additionally, don’t forget to explore our comprehensive Reference API. It features pre-implemented versions of many commonly used functionals, serving as both a shortcut for common tasks and a useful learning resource.</p>
 </div></blockquote>
 <section id="Func:-The-Foundation-Stone-🧱">
 <h3><code class="docutils literal notranslate"><span class="pre">Func</span></code>: The Foundation Stone 🧱<a class="headerlink" href="#Func:-The-Foundation-Stone-🧱" title="Link to this heading">#</a></h3>
-<p>The <code class="docutils literal notranslate"><span class="pre">Func</span></code> class is the base class in the functional hierarchy. Its core method is <code class="docutils literal notranslate"><span class="pre">apply()</span></code>, which computes the value of the functional at a given input.</p>
+<p>The <code class="docutils literal notranslate"><span class="pre">Func</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Func">🔗</a> class is the base class in the functional hierarchy. Its core method is <code class="docutils literal notranslate"><span class="pre">apply()</span></code>, which computes the value of the functional at a given input.</p>
 <p>Here’s a simplified example, implementing the squared <span class="math notranslate nohighlight">\(L_2\)</span> norm:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
-<span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.Func" title="pyxu.abc.operator.Func"><span class="n">Func</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.Func" title="pyxu.abc.operator.Func"><span class="n">Func</span></a>
 
-<span class="k">class</span> <span class="nc">SquaredL2</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.Func" title="pyxu.abc.operator.Func"><span class="n">Func</span></a><span class="p">):</span>
+<span class="k">class</span> <span class="nc">SquaredL2</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.Func" title="pyxu.abc.operator.Func"><span class="n">Func</span></a><span class="p">):</span>
     <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
         <span class="k">return</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html#numpy.linalg.norm" title="numpy.linalg.norm"><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
 </pre></div>
@@ -305,10 +306,10 @@ <h3><code class="docutils literal notranslate"><span class="pre">Func</span></co
 </section>
 <section id="DiffFunc:-Differentiable-Functionals-🎯">
 <h3><code class="docutils literal notranslate"><span class="pre">DiffFunc</span></code>: Differentiable Functionals 🎯<a class="headerlink" href="#DiffFunc:-Differentiable-Functionals-🎯" title="Link to this heading">#</a></h3>
-<p>The <code class="docutils literal notranslate"><span class="pre">DiffFunc</span></code> class extends <code class="docutils literal notranslate"><span class="pre">Func</span></code> for functionals that have a well-defined gradient. It introduces an additional method, <code class="docutils literal notranslate"><span class="pre">grad()</span></code>, for gradient computation.</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><span class="n">DiffFunc</span></a>
+<p>The <code class="docutils literal notranslate"><span class="pre">DiffFunc</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffFunc">🔗</a> class extends <code class="docutils literal notranslate"><span class="pre">Func</span></code> for functionals that have a well-defined gradient. It introduces an additional method, <code class="docutils literal notranslate"><span class="pre">grad()</span></code>, for gradient computation.</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><span class="n">DiffFunc</span></a>
 
-<span class="k">class</span> <span class="nc">SquaredL2</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><span class="n">DiffFunc</span></a><span class="p">):</span>
+<span class="k">class</span> <span class="nc">SquaredL2</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.DiffFunc" title="pyxu.abc.operator.DiffFunc"><span class="n">DiffFunc</span></a><span class="p">):</span>
     <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
         <span class="k">return</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html#numpy.linalg.norm" title="numpy.linalg.norm"><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span></a><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span>
 
@@ -317,15 +318,15 @@ <h3><code class="docutils literal notranslate"><span class="pre">DiffFunc</span>
 </pre></div>
 </div>
 <blockquote>
-<div><p>🌈Tip: With Pyxu, you can use <code class="docutils literal notranslate"><span class="pre">from_torch</span></code> or <code class="docutils literal notranslate"><span class="pre">from_jax</span></code> to automatically compute the gradient if you have a PyTorch or JAX implementation of your functional.</p>
+<div><p>🌈Tip: With Pyxu, you can use <code class="docutils literal notranslate"><span class="pre">from_torch</span></code><a class="reference external" href="../api/operator.interop.html#pyxu.operator.interop.from_torch">🔗</a> or <code class="docutils literal notranslate"><span class="pre">from_jax</span></code><a class="reference external" href="../api/operator.interop.html#pyxu.operator.interop.from_jax">🔗</a> to automatically compute the gradient if you have a PyTorch or JAX implementation of your functional.</p>
 </div></blockquote>
 </section>
 <section id="ProxFunc:-Proximable-Functionals-🛡️">
 <h3><code class="docutils literal notranslate"><span class="pre">ProxFunc</span></code>: Proximable Functionals 🛡️<a class="headerlink" href="#ProxFunc:-Proximable-Functionals-🛡️" title="Link to this heading">#</a></h3>
-<p>For functionals with a simple proximal operator, you’ll find <code class="docutils literal notranslate"><span class="pre">ProxFunc</span></code> extremely useful. It offers the <code class="docutils literal notranslate"><span class="pre">prox()</span></code> method, which evaluates the proximal operator of the functional. Here’s an example using the <span class="math notranslate nohighlight">\(L_1\)</span> norm:</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a>
+<p>For functionals with a simple proximal operator, you’ll find <code class="docutils literal notranslate"><span class="pre">ProxFunc</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.ProxFunc">🔗</a> extremely useful. It offers the <code class="docutils literal notranslate"><span class="pre">prox()</span></code> method, which evaluates the proximal operator of the functional. Here’s an example using the <span class="math notranslate nohighlight">\(L_1\)</span> norm:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a>
 
-<span class="k">class</span> <span class="nc">L1Norm</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a><span class="p">):</span>
+<span class="k">class</span> <span class="nc">L1Norm</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a><span class="p">):</span>
     <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
         <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
 
@@ -335,7 +336,7 @@ <h3><code class="docutils literal notranslate"><span class="pre">ProxFunc</span>
 </div>
 <section id="Moreau-Envelope-for-Smoothing">
 <h4>Moreau Envelope for Smoothing<a class="headerlink" href="#Moreau-Envelope-for-Smoothing" title="Link to this heading">#</a></h4>
-<p>You can also smooth out a proximable functional using the <code class="docutils literal notranslate"><span class="pre">moreau_envelope()</span></code> method. For example, you can smooth the L1 norm to create the <a class="reference external" href="https://www.wikiwand.com/en/Huber_loss">Huber loss function</a> as follows:</p>
+<p>You can also smooth out a proximable functional using the <code class="docutils literal notranslate"><span class="pre">moreau_envelope()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.ProxFunc.moreau_envelope">🔗</a> method. For example, you can smooth the L1 norm to create the <a class="reference external" href="https://www.wikiwand.com/en/Huber_loss">Huber loss function</a> as follows:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">huber</span> <span class="o">=</span> <span class="n">L1Norm</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span><span class="o">.</span><span class="n">moreau_envelope</span><span class="p">(</span><span class="n">mu</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
 </pre></div>
 </div>
@@ -353,7 +354,7 @@ <h4>Demystifying the Proximal Operator 🎭<a class="headerlink" href="#Demystif
 </section>
 <section id="Specialized-Classes:-ProxDiffFunc,-LinFunc,-QuadraticFunc-🎨">
 <h3>Specialized Classes: <code class="docutils literal notranslate"><span class="pre">ProxDiffFunc</span></code>, <code class="docutils literal notranslate"><span class="pre">LinFunc</span></code>, <code class="docutils literal notranslate"><span class="pre">QuadraticFunc</span></code> 🎨<a class="headerlink" href="#Specialized-Classes:-ProxDiffFunc,-LinFunc,-QuadraticFunc-🎨" title="Link to this heading">#</a></h3>
-<p>These classes are for functionals that offer even more, like being both proximable and differentiable (<code class="docutils literal notranslate"><span class="pre">ProxDiffFunc</span></code>), or being linear (<code class="docutils literal notranslate"><span class="pre">LinFunc</span></code>) or quadratic (<code class="docutils literal notranslate"><span class="pre">QuadraticFunc</span></code>). Quadratic functionals are especially important in primal-dual methods for faster convergence, so do use them when you can!</p>
+<p>These classes are for functionals that offer even more, like being both proximable and differentiable (<code class="docutils literal notranslate"><span class="pre">ProxDiffFunc</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.ProxDiffFunc">🔗</a>), or being linear (<code class="docutils literal notranslate"><span class="pre">LinFunc</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinFunc">🔗</a>) or quadratic (<code class="docutils literal notranslate"><span class="pre">QuadraticFunc</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.QuadraticFunc">🔗</a>). Quadratic functionals are especially important in primal-dual methods for faster convergence, so do use them when you can!</p>
 <blockquote>
 <div><p>Note: when dealing with <code class="docutils literal notranslate"><span class="pre">ProxDiffFunc</span></code> instances, it can be hard to decide whether the gradient or proximal operator should be used for optimization purposes. The general rule-of-thumb is to use the gradient as much as possible, as the latter requires more regularity on the objective functional, which can be leveraged by solvers for fatser convergence.</p>
 </div></blockquote>
@@ -361,10 +362,10 @@ <h3>Specialized Classes: <code class="docutils literal notranslate"><span class=
 <section id="Implicit-Functionals:-The-Undercover-Agents-🕵️‍♀️">
 <h3>Implicit Functionals: The Undercover Agents 🕵️‍♀️<a class="headerlink" href="#Implicit-Functionals:-The-Undercover-Agents-🕵️‍♀️" title="Link to this heading">#</a></h3>
 <p>In some cases, you may not know the functional itself but you might know its proximal operator or gradient (e.g. for plug-and-play or score-based priors). Pyxu lets you define such “implicit functionals” as follows:</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a>
 <span class="kn">from</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/ndimage.html#module-scipy.ndimage" title="scipy.ndimage"><span class="nn">scipy.ndimage</span></a> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.median_filter.html#scipy.ndimage.median_filter" title="scipy.ndimage.median_filter"><span class="n">median_filter</span></a>
 
-<span class="k">class</span> <span class="nc">MedianFilterPrior</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a><span class="p">):</span>
+<span class="k">class</span> <span class="nc">MedianFilterPrior</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.ProxFunc" title="pyxu.abc.operator.ProxFunc"><span class="n">ProxFunc</span></a><span class="p">):</span>
     <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
         <span class="k">return</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/constants.html#NotImplemented" title="NotImplemented"><span class="bp">NotImplemented</span></a> <span class="c1"># apply method not provided</span>
 
diff --git a/guide/funcs.ipynb b/guide/funcs.ipynb
index c6dc7dab..b22ac70f 100644
--- a/guide/funcs.ipynb
+++ b/guide/funcs.ipynb
@@ -21,13 +21,12 @@
     "> \n",
     "> 1. **Subclassing**: Extend these classes to create customized functionals tailored to your problem. \n",
     "> \n",
-    "> 2. **Generic Constructor Routine**: Utilize the `from_source` method to define new functionals from their core methods, like `apply()`, `grad()`, or `prox()`.\n",
+    "> 2. **Generic Constructor Routine**: Utilize the `from_source`[🔗](../api/operator.interop.html#general) method to define new functionals from their core methods, like `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply), `grad()`[🔗](../api/abc.html#pyxu.abc.DiffFunc.grad), or `prox()`[🔗](../api/abc.html#pyxu.abc.ProxFunc.prox).\n",
     ">\n",
     "> Additionally, don't forget to explore our comprehensive Reference API. It features pre-implemented versions of many commonly used functionals, serving as both a shortcut for common tasks and a useful learning resource.\n",
     "\n",
     "### `Func`: The Foundation Stone 🧱\n",
-    "\n",
-    "The `Func` class is the base class in the functional hierarchy. Its core method is `apply()`, which computes the value of the functional at a given input.\n",
+    "The `Func`[🔗](../api/abc.html#pyxu.abc.Func) class is the base class in the functional hierarchy. Its core method is `apply()`, which computes the value of the functional at a given input.\n",
     "\n",
     "Here's a simplified example, implementing the squared $L_2$ norm:\n",
     "\n",
@@ -54,7 +53,7 @@
     "\n",
     "### `DiffFunc`: Differentiable Functionals 🎯\n",
     "\n",
-    "The `DiffFunc` class extends `Func` for functionals that have a well-defined gradient. It introduces an additional method, `grad()`, for gradient computation.\n",
+    "The `DiffFunc`[🔗](../api/abc.html#pyxu.abc.DiffFunc) class extends `Func` for functionals that have a well-defined gradient. It introduces an additional method, `grad()`, for gradient computation.\n",
     "\n",
     "```python\n",
     "from pyxu.abc import DiffFunc\n",
@@ -67,11 +66,11 @@
     "        return 2 * x\n",
     "```\n",
     "\n",
-    ">🌈Tip: With Pyxu, you can use `from_torch` or `from_jax` to automatically compute the gradient if you have a PyTorch or JAX implementation of your functional.\n",
+    ">🌈Tip: With Pyxu, you can use `from_torch`[🔗](../api/operator.interop.html#pyxu.operator.interop.from_torch) or `from_jax`[🔗](../api/operator.interop.html#pyxu.operator.interop.from_jax) to automatically compute the gradient if you have a PyTorch or JAX implementation of your functional.\n",
     "\n",
     "### `ProxFunc`: Proximable Functionals 🛡️\n",
     "\n",
-    "For functionals with a simple proximal operator, you'll find `ProxFunc` extremely useful. It offers the `prox()` method, which evaluates the proximal operator of the functional. Here's an example using the $L_1$ norm:\n",
+    "For functionals with a simple proximal operator, you'll find `ProxFunc`[🔗](../api/abc.html#pyxu.abc.ProxFunc) extremely useful. It offers the `prox()` method, which evaluates the proximal operator of the functional. Here's an example using the $L_1$ norm:\n",
     "\n",
     "```python\n",
     "from pyxu.abc import ProxFunc\n",
@@ -86,7 +85,7 @@
     "\n",
     "#### Moreau Envelope for Smoothing\n",
     "\n",
-    "You can also smooth out a proximable functional using the `moreau_envelope()` method. For example, you can smooth the L1 norm to create the [Huber loss function](https://www.wikiwand.com/en/Huber_loss) as follows:\n",
+    "You can also smooth out a proximable functional using the `moreau_envelope()`[🔗](../api/abc.html#pyxu.abc.ProxFunc.moreau_envelope) method. For example, you can smooth the L1 norm to create the [Huber loss function](https://www.wikiwand.com/en/Huber_loss) as follows:\n",
     "\n",
     "```python\n",
     "huber = L1Norm(dim).moreau_envelope(mu=0.1)\n",
@@ -110,7 +109,7 @@
     "\n",
     "### Specialized Classes: `ProxDiffFunc`, `LinFunc`, `QuadraticFunc` 🎨\n",
     "\n",
-    "These classes are for functionals that offer even more, like being both proximable and differentiable (`ProxDiffFunc`), or being linear (`LinFunc`) or quadratic (`QuadraticFunc`). Quadratic functionals are especially important in primal-dual methods for faster convergence, so do use them when you can! \n",
+    "These classes are for functionals that offer even more, like being both proximable and differentiable (`ProxDiffFunc`[🔗](../api/abc.html#pyxu.abc.ProxDiffFunc)), or being linear (`LinFunc`[🔗](../api/abc.html#pyxu.abc.LinFunc)) or quadratic (`QuadraticFunc`[🔗](../api/abc.html#pyxu.abc.QuadraticFunc)). Quadratic functionals are especially important in primal-dual methods for faster convergence, so do use them when you can! \n",
     "\n",
     "> Note: when dealing with `ProxDiffFunc` instances, it can be hard to decide whether the gradient or proximal operator should be used for optimization purposes. The general rule-of-thumb is to use the gradient as much as possible, as the latter requires more regularity on the objective functional, which can be leveraged by solvers for fatser convergence. \n",
     "\n",
diff --git a/guide/fwdops.html b/guide/fwdops.html
index b25d75fa..465b541e 100644
--- a/guide/fwdops.html
+++ b/guide/fwdops.html
@@ -18,7 +18,7 @@
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-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
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+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
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@@ -231,6 +231,7 @@
 <li class="toctree-l1"><a class="reference internal" href="algorithms.html">Optimization Algorithms</a></li>
 <li class="toctree-l1"><a class="reference internal" href="lipschitz.html">Lipschitz Constants and Automatic Step Size Tuning</a></li>
 <li class="toctree-l1"><a class="reference internal" href="hpc.html">High Performance Computing Features</a></li>
+<li class="toctree-l1"><a class="reference internal" href="diff_ops.html">Differential Operators in Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
@@ -265,14 +266,14 @@
 <article class="bd-article" role="main">
 <section id="Forward-Operators">
 <h1>Forward Operators<a class="headerlink" href="#Forward-Operators" title="Link to this heading">#</a></h1>
-<p>In computational imaging, the ability to accurately model the acquisition system is cornerstone to solving inverse problems. The <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code> class in Pyxu serves as a foundational abstraction for defining linear forward operators, essentially mapping the original signal or image to the data we observe. This guide distills the knowledge needed to implement custom forward operators using the <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code> class, as well as related classes in the Pyxu library.</p>
+<p>In computational imaging, the ability to accurately model the acquisition system is cornerstone to solving inverse problems. The <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp">🔗</a> class in Pyxu serves as a foundational abstraction for defining linear forward operators, essentially mapping the original signal or image to the data we observe. This guide distills the knowledge needed to implement custom forward operators using the <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code> class, as well as related classes in the Pyxu library.</p>
 <blockquote>
 <div><p><strong>Important Note</strong>: The <code class="docutils literal notranslate"><span class="pre">LinOp</span></code> class and its derivatives are designed as abstract base classes. This means they serve as templates or “blueprints” for creating specific operators that suit your project needs. You’re not supposed to instantiate them directly. Instead, you have two main options:</p>
 <ol class="arabic simple">
 <li><p><strong>Subclassing</strong>: Extend these classes to create customized operators tailored to your problem.</p></li>
-<li><p><strong>Generic Constructor Routine</strong>: Utilize the <code class="docutils literal notranslate"><span class="pre">from_source</span></code> method to define new operators from their core methods, like <code class="docutils literal notranslate"><span class="pre">apply()</span></code>, <code class="docutils literal notranslate"><span class="pre">adjoint()</span></code>, or <code class="docutils literal notranslate"><span class="pre">jacobian()</span></code>.</p></li>
+<li><p><strong>Generic Constructor Routine</strong>: Utilize the <code class="docutils literal notranslate"><span class="pre">from_source</span></code><a class="reference external" href="../api/operator.interop.html#general">🔗</a> method to define new operators from their core methods, like <code class="docutils literal notranslate"><span class="pre">apply()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Map.apply">🔗</a>, <code class="docutils literal notranslate"><span class="pre">adjoint()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp.adjoint">🔗</a>, or <code class="docutils literal notranslate"><span class="pre">jacobian()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffMap.jacobian">🔗</a>.</p></li>
 </ol>
-<p>Additionally, don’t forget to explore our comprehensive Reference API. It features pre-implemented versions of many commonly used forward operators, serving as both a shortcut for common tasks and a useful learning resource.</p>
+<p>Additionally, don’t forget to explore our comprehensive (Reference API)[../api/index.html]. It features pre-implemented versions of many commonly used forward operators, serving as both a shortcut for common tasks and a useful learning resource.</p>
 </div></blockquote>
 <section id="The-Importance-of-Matrix-Free-Operators">
 <h2>The Importance of Matrix-Free Operators<a class="headerlink" href="#The-Importance-of-Matrix-Free-Operators" title="Link to this heading">#</a></h2>
@@ -293,24 +294,24 @@ <h2>The Importance of Matrix-Free Operators<a class="headerlink" href="#The-Impo
     <span class="k">pass</span>
 </pre></div>
 </div>
-<p>Here, a new class called <code class="docutils literal notranslate"><span class="pre">Sum()</span></code> is defined, inheriting from Pyxu’s <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code> base class, the primary abstraction for designing real-valued linear operators. This inheritance means that <code class="docutils literal notranslate"><span class="pre">Sum()</span></code> is expected to implement certain core methods, namely <code class="docutils literal notranslate"><span class="pre">apply()</span></code> and <code class="docutils literal notranslate"><span class="pre">adjoint()</span></code>.</p>
+<p>Here, a new class called <code class="docutils literal notranslate"><span class="pre">Sum()</span></code> is defined, inheriting from Pyxu’s <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp">🔗</a> base class, the primary abstraction for designing real-valued linear operators. This inheritance means that <code class="docutils literal notranslate"><span class="pre">Sum()</span></code> is expected to implement certain core methods, namely <code class="docutils literal notranslate"><span class="pre">apply()</span></code> and <code class="docutils literal notranslate"><span class="pre">adjoint()</span></code>.</p>
 </li>
-<li><p><strong>The ``apply()`` Method:</strong></p>
+<li><p><strong>The</strong> <code class="docutils literal notranslate"><span class="pre">apply()</span></code> <strong>Method:</strong></p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span>
     <span class="k">return</span> <span class="n">arr</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 </pre></div>
 </div>
-<p>The <code class="docutils literal notranslate"><span class="pre">apply()</span></code> method takes an array <code class="docutils literal notranslate"><span class="pre">arr</span></code> as input and returns the sum of its elements. This is the core functionality of the operator. Instead of representing the sum operation as a matrix and performing matrix-vector multiplication, the method directly computes the sum, making it “matrix-free.”</p>
+<p>The <code class="docutils literal notranslate"><span class="pre">apply()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Map.apply">🔗</a> method takes an array <code class="docutils literal notranslate"><span class="pre">arr</span></code> as input and returns the sum of its elements. This is the core functionality of the operator. Instead of representing the sum operation as a matrix and performing matrix-vector multiplication, the method directly computes the sum, making it “matrix-free.”</p>
 <blockquote>
 <div><p><strong>Note</strong>: <code class="docutils literal notranslate"><span class="pre">keepdims=True</span></code> is required since, as per the <code class="docutils literal notranslate"><span class="pre">LinOp.apply()</span></code> signature, it must return an NDArray, and not a scalar.</p>
 </div></blockquote>
 </li>
-<li><p><strong>The ``adjoint()`` Method:</strong></p>
+<li><p><strong>The</strong> <code class="docutils literal notranslate"><span class="pre">adjoint()</span></code> <strong>Method:</strong></p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">adjoint</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span>
     <span class="k">return</span> <span class="n">arr</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
 </pre></div>
 </div>
-<p>The <code class="docutils literal notranslate"><span class="pre">adjoint()</span></code> method also takes an array <code class="docutils literal notranslate"><span class="pre">arr</span></code> as input. The adjoint operation for this sum operator is effectively a <em>broadcast</em> operation, mapping a scalar to a vector with the same dimension of the original array space.</p>
+<p>The <code class="docutils literal notranslate"><span class="pre">adjoint()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp.adjoint">🔗</a> method also takes an array <code class="docutils literal notranslate"><span class="pre">arr</span></code> as input. The adjoint operation for this sum operator is effectively a <em>broadcast</em> operation, mapping a scalar to a vector with the same dimension of the original array space.</p>
 </li>
 </ul>
 </section>
@@ -335,50 +336,51 @@ <h3>Quality Assurance for Adjoint Operators in Pyxu<a class="headerlink" href="#
 </section>
 <section id="Additional-Features-of-LinOp:-Batteries-Included">
 <h2>Additional Features of LinOp: Batteries Included<a class="headerlink" href="#Additional-Features-of-LinOp:-Batteries-Included" title="Link to this heading">#</a></h2>
-<p>Pyxu’s <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code> is designed to be as versatile and useful as possible for computational imaging. Here are some of the extra capabilities baked right into the class to facilitate both simple and complex tasks:</p>
+<p>Pyxu’s <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp">🔗</a> is designed to be as versatile and useful as possible for computational imaging. Here are some of the extra capabilities baked right into the class to facilitate both simple and complex tasks:</p>
 <ul class="simple">
-<li><p><strong>Lipschitz Constant</strong>: Knowing the Lipschitz constant of an operator is invaluable for optimization routines. If you know it, you can directly store it in the <code class="docutils literal notranslate"><span class="pre">lipschitz</span></code> property. Don’t know it? No problem! The <code class="docutils literal notranslate"><span class="pre">estimate_lipschitz()</span></code> method will compute it for you, offering various methods to balance accuracy and execution time.</p></li>
+<li><p><strong>Lipschitz Constant</strong>: Knowing the Lipschitz constant of an operator is invaluable for optimization routines. If you know it, you can directly store it in the <code class="docutils literal notranslate"><span class="pre">lipschitz</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Map.lipschitz">🔗</a> property. Don’t know it? No problem! The <code class="docutils literal notranslate"><span class="pre">estimate_lipschitz()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Map.estimate_lipschitz">🔗</a> method will compute it for you, offering various methods to balance accuracy and execution time.</p></li>
 </ul>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">my_operator</span><span class="o">.</span><span class="n">lipschitz</span> <span class="o">=</span> <span class="n">my_operator</span><span class="o">.</span><span class="n">estimate_lipschitz</span><span class="p">()</span>
 </pre></div>
 </div>
 <ul class="simple">
-<li><p><strong>Singular Value Decomposition</strong>: Ever needed to compute the singular values of your operator? Use the <code class="docutils literal notranslate"><span class="pre">svdvals()</span></code> method which employs the Arnoldi algorithm to get the job done without breaking the matrix-free paradigm.</p></li>
-<li><p><strong>Trace of Operator</strong>: Sometimes you may need to compute the trace of an operator. The <code class="docutils literal notranslate"><span class="pre">trace()</span></code> method uses a stochastic approximation with the Hutch++ algorithm to efficiently it.</p></li>
-<li><p><strong>Pseudo-Inverse</strong>: If you’re looking to solve an inverse problem, the <code class="docutils literal notranslate"><span class="pre">pinv()</span></code> method helps you evaluate the pseudo-inverse by solving the (dampened) normal equations, making it the most straightforward way to reverse your operations.</p></li>
+<li><p><strong>Singular Value Decomposition</strong>: Ever needed to compute the singular values of your operator? Use the <code class="docutils literal notranslate"><span class="pre">svdvals()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp.svdvals">🔗</a> method which employs the Arnoldi algorithm to get the job done without breaking the matrix-free paradigm.</p></li>
+<li><p><strong>Trace of Operator</strong>: Sometimes you may need to compute the trace of an operator. The <code class="docutils literal notranslate"><span class="pre">trace()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.SquareOp.trace">🔗</a> method uses a stochastic approximation with the Hutch++ algorithm to efficiently it.</p></li>
+<li><p><strong>Pseudo-Inverse</strong>: If you’re looking to solve an inverse problem, the <code class="docutils literal notranslate"><span class="pre">pinv()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp.pinv">🔗</a> method helps you evaluate the pseudo-inverse by solving the (dampened) normal equations, making it the most straightforward way to reverse your operations.</p></li>
 </ul>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">pseudo_inv_result</span> <span class="o">=</span> <span class="n">my_operator</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">my_array</span><span class="p">,</span> <span class="n">damp</span><span class="o">=</span><span class="n">value</span><span class="p">)</span>
 </pre></div>
 </div>
 <ul class="simple">
-<li><p><strong>Support for Explicit Matrices</strong>: Though <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code> is primarily built for matrix-free operations, you are not restricted to them. If you prefer, you can work with explicit matrices using the <code class="docutils literal notranslate"><span class="pre">from_array()</span></code> method, supporting a variety of array formats including <code class="docutils literal notranslate"><span class="pre">numpy</span></code>, <code class="docutils literal notranslate"><span class="pre">cupy</span></code>, <code class="docutils literal notranslate"><span class="pre">sparse</span></code>, and <code class="docutils literal notranslate"><span class="pre">dask</span></code>.</p></li>
+<li><p><strong>Support for Explicit Matrices</strong>: Though <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp">🔗</a> is primarily built for matrix-free operations, you are not restricted to them. If you prefer, you can work with explicit matrices using the <code class="docutils literal notranslate"><span class="pre">from_array()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp.from_array">🔗</a> method, supporting a variety of array formats including <code class="docutils literal notranslate"><span class="pre">numpy</span></code>, <code class="docutils literal notranslate"><span class="pre">cupy</span></code>, <code class="docutils literal notranslate"><span class="pre">sparse</span></code>, and <code class="docutils literal notranslate"><span class="pre">dask</span></code>.</p></li>
 </ul>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">op</span> <span class="o">=</span> <span class="n">LinOp</span><span class="o">.</span><span class="n">from_array</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="n">N</span><span class="p">)))</span>
 </pre></div>
 </div>
-<p>With all these tools and methods at your disposal, <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code> aims to be your go-to solution for implementing linear operators in computational imaging tasks.</p>
+<p>With all these tools and methods at your disposal, <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp">🔗</a> aims to be your go-to solution for implementing linear operators in computational imaging tasks.</p>
 </section>
 <section id="DiffMap-for-Non-linear-Forward-Operators">
 <h2>DiffMap for Non-linear Forward Operators<a class="headerlink" href="#DiffMap-for-Non-linear-Forward-Operators" title="Link to this heading">#</a></h2>
-<p>Linear models are often an idealized representation. In some situations forward operators are inherently non-linear. Take phase retrieval or some forms of tomography as examples: these are scenarios where the relationship between the object and its measurements isn’t just a linear transformation. For such cases, Pyxu provides the <code class="docutils literal notranslate"><span class="pre">DiffMap()</span></code> class to implement these non-linear forward operators.</p>
+<p>Linear models are often an idealized representation. In some situations forward operators are inherently non-linear. Take phase retrieval or some forms of tomography as examples: these are scenarios where the relationship between the object and its measurements isn’t just a linear transformation. For such cases, Pyxu provides the <code class="docutils literal notranslate"><span class="pre">DiffMap()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffMap">🔗</a> class to implement these non-linear forward operators.</p>
 <section id="Core-Methods">
 <h3>Core Methods<a class="headerlink" href="#Core-Methods" title="Link to this heading">#</a></h3>
 <ul class="simple">
-<li><p><strong>``apply()``</strong>: This method is where you’ll implement your forward model. Just like in <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code>, you override this function to define how your specific forward model operates on an input array.</p></li>
-<li><p><strong>``jacobian``</strong>: In calculus, the Jacobian matrix represents the best linear approximation to a function at a given point. For a function <span class="math notranslate nohighlight">\(\mathbf{f}: \mathbb{R}^{M} \to \mathbb{R}^{N}\)</span>, the Jacobian <span class="math notranslate nohighlight">\(\mathbf{J}_{\mathbf{f}}(\mathbf{x})\)</span> at a point <span class="math notranslate nohighlight">\(\mathbf{x}\)</span> is an <span class="math notranslate nohighlight">\(N \times M\)</span> matrix where the entry <span class="math notranslate nohighlight">\((i, j)\)</span> is <span class="math notranslate nohighlight">\(\frac{\partial f_{i}}{\partial x_{j}}\)</span>. When the forward operator is non-linear, knowing the Jacobian is crucial for optimization algorithms.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">apply()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Map.apply">🔗</a>: This method is where you’ll implement your forward model. Just like in <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp">🔗</a>, you override this function to define how your specific forward model operates on an input array.</p></li>
+<li><p><code class="docutils literal notranslate"><span class="pre">jacobian()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffMap.jacobian">🔗</a>: In calculus, the Jacobian matrix represents the best linear approximation to a function at a given point. For a function <span class="math notranslate nohighlight">\(\mathbf{f}: \mathbb{R}^{M} \to \mathbb{R}^{N}\)</span>, the Jacobian <span class="math notranslate nohighlight">\(\mathbf{J}_{\mathbf{f}}(\mathbf{x})\)</span> at a point <span class="math notranslate nohighlight">\(\mathbf{x}\)</span> is an <span class="math notranslate nohighlight">\(N \times M\)</span> matrix where the entry <span class="math notranslate nohighlight">\((i, j)\)</span> is <span class="math notranslate nohighlight">\(\frac{\partial f_{i}}{\partial x_{j}}\)</span>. When the forward operator is non-linear, knowing the
+Jacobian is crucial for optimization algorithms.</p></li>
 </ul>
 <p>The <code class="docutils literal notranslate"><span class="pre">jacobian()</span></code> method allows you to evaluate (implicitly) this matrix, giving you the flexibility to implement the best way to approximate your non-linear operator linearly at a specific point.</p>
 </section>
 <section id="A-Nod-to-Deep-Learning-🚀">
 <h3>A Nod to Deep Learning 🚀<a class="headerlink" href="#A-Nod-to-Deep-Learning-🚀" title="Link to this heading">#</a></h3>
 <p>When the Jacobian is unknown or too complex to derive analytically, techniques from deep learning come in handy. Libraries like JAX or PyTorch offer automatic differentiation techniques (autograd) to compute derivatives, which you can use to obtain the Jacobian efficiently in matrix-free fashion.</p>
-<p>In Pyxu, methods <code class="docutils literal notranslate"><span class="pre">from_torch()</span></code> and <code class="docutils literal notranslate"><span class="pre">from_jax()</span></code> allow you to define operators whose Jacobians are computed via autograd. This means you can utilize the power of these deep learning libraries to implement non-linear operators seamlessly.</p>
-<p>With <code class="docutils literal notranslate"><span class="pre">DiffMap()</span></code>, you’re well-equipped to tackle the challenges posed by non-linear forward operators in computational imaging.</p>
+<p>In Pyxu, methods <code class="docutils literal notranslate"><span class="pre">from_torch</span></code><a class="reference external" href="../api/operator.interop.html#pyxu.operator.interop.from_torch">🔗</a> and <code class="docutils literal notranslate"><span class="pre">from_jax</span></code><a class="reference external" href="../api/operator.interop.html#pyxu.operator.interop.from_jax">🔗</a> allow you to define operators whose Jacobians are computed via autograd. This means you can utilize the power of these deep learning libraries to implement non-linear operators seamlessly.</p>
+<p>With <code class="docutils literal notranslate"><span class="pre">DiffMap()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffMap">🔗</a>, you’re well-equipped to tackle the challenges posed by non-linear forward operators in computational imaging.</p>
 </section>
 </section>
 <section id="Wrapping-Up">
 <h2>Wrapping Up<a class="headerlink" href="#Wrapping-Up" title="Link to this heading">#</a></h2>
-<p>Pyxu offers a robust and scalable framework for computational imaging professionals to deal with both linear and non-linear forward operators. With the abstraction provided by classes like <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code> and <code class="docutils literal notranslate"><span class="pre">DiffMap()</span></code>, you can focus on the problem you’re solving rather than computational limitations. These classes are meant to be subclassed to tailor to your specific problem domain. Happy coding! 🚀</p>
+<p>Pyxu offers a robust and scalable framework for computational imaging professionals to deal with both linear and non-linear forward operators. With the abstraction provided by classes like <code class="docutils literal notranslate"><span class="pre">LinOp()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.LinOp">🔗</a> and <code class="docutils literal notranslate"><span class="pre">DiffMap()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffMap">🔗</a>, you can focus on the problem you’re solving rather than computational limitations. These classes are meant to be subclassed to tailor to your specific problem domain. Happy coding! 🚀</p>
 </section>
 </section>
 </article>
diff --git a/guide/fwdops.ipynb b/guide/fwdops.ipynb
index 9c31a608..03d47405 100644
--- a/guide/fwdops.ipynb
+++ b/guide/fwdops.ipynb
@@ -8,7 +8,7 @@
     "# Forward Operators\n",
     "\n",
     "In computational imaging, the ability to accurately model the acquisition system is cornerstone to solving inverse\n",
-    "problems. The `LinOp()` class in Pyxu serves as a foundational abstraction for defining linear forward operators,\n",
+    "problems. The `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) class in Pyxu serves as a foundational abstraction for defining linear forward operators,\n",
     "essentially mapping the original signal or image to the data we observe. This guide distills the knowledge needed to\n",
     "implement custom forward operators using the `LinOp()` class, as well as related classes in the Pyxu library.\n",
     "\n",
@@ -16,9 +16,9 @@
     "> \n",
     "> 1. **Subclassing**: Extend these classes to create customized operators tailored to your problem. \n",
     "> \n",
-    "> 2. **Generic Constructor Routine**: Utilize the `from_source` method to define new operators from their core methods, like `apply()`, `adjoint()`, or `jacobian()`.\n",
+    "> 2. **Generic Constructor Routine**: Utilize the `from_source`[🔗](../api/operator.interop.html#general) method to define new operators from their core methods, like `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply), `adjoint()`[🔗](../api/abc.html#pyxu.abc.LinOp.adjoint), or `jacobian()`[🔗](../api/abc.html#pyxu.abc.DiffMap.jacobian).\n",
     ">\n",
-    "> Additionally, don't forget to explore our comprehensive Reference API. It features pre-implemented versions of many commonly used forward operators, serving as both a shortcut for common tasks and a useful learning resource.\n",
+    "> Additionally, don't forget to explore our comprehensive (Reference API)[../api/index.html]. It features pre-implemented versions of many commonly used forward operators, serving as both a shortcut for common tasks and a useful learning resource.\n",
     "\n",
     "## The Importance of Matrix-Free Operators\n",
     "\n",
@@ -47,31 +47,31 @@
     "    class Sum(LinOp):\n",
     "        pass\n",
     "    ```\n",
-    "    Here, a new class called `Sum()` is defined, inheriting from Pyxu's `LinOp()` base class, the primary abstraction\n",
+    "    Here, a new class called `Sum()` is defined, inheriting from Pyxu's `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) base class, the primary abstraction\n",
     "    for designing real-valued linear operators. This inheritance means that `Sum()` is expected to implement certain\n",
     "    core methods, namely `apply()` and `adjoint()`. \n",
     "\n",
     "\n",
-    "- **The ``apply()`` Method:**\n",
+    "- **The** ``apply()`` **Method:**\n",
     "  \n",
     "    ```python\n",
     "        def apply(self, arr):\n",
     "            return arr.sum(keepdims=True)\n",
     "    ```\n",
-    "    The `apply()` method takes an array `arr` as input and returns the sum of its elements. This is the core\n",
+    "    The `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply) method takes an array `arr` as input and returns the sum of its elements. This is the core\n",
     "    functionality of the operator. Instead of representing the sum operation as a matrix and performing matrix-vector\n",
     "    multiplication, the method directly computes the sum, making it \"matrix-free.\"\n",
     "\n",
     "    > **Note**: `keepdims=True` is required since, as per the `LinOp.apply()` signature, it must return an NDArray, and\n",
     "    > not a scalar.\n",
     "\n",
-    "- **The ``adjoint()`` Method:**\n",
+    "- **The** ``adjoint()`` **Method:**\n",
     "  \n",
     "    ```python\n",
     "        def adjoint(self, arr):\n",
     "            return arr * np.ones(self.shape[1])\n",
     "    ```\n",
-    "    The `adjoint()` method also takes an array `arr` as input. The adjoint operation for this sum operator is\n",
+    "    The `adjoint()`[🔗](../api/abc.html#pyxu.abc.LinOp.adjoint) method also takes an array `arr` as input. The adjoint operation for this sum operator is\n",
     "    effectively a *broadcast* operation, mapping a scalar to a vector with the same dimension of the original array\n",
     "    space.\n",
     "\n",
@@ -127,24 +127,24 @@
     "\n",
     "## Additional Features of LinOp: Batteries Included \n",
     "\n",
-    "Pyxu's `LinOp()` is designed to be as versatile and useful as possible for computational imaging. Here are some of the\n",
+    "Pyxu's `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) is designed to be as versatile and useful as possible for computational imaging. Here are some of the\n",
     "extra capabilities baked right into the class to facilitate both simple and complex tasks:\n",
     "\n",
     "- **Lipschitz Constant**: Knowing the Lipschitz constant of an operator is invaluable for optimization routines. If you\n",
-    "  know it, you can directly store it in the `lipschitz` property. Don't know it? No problem! The `estimate_lipschitz()`\n",
+    "  know it, you can directly store it in the `lipschitz`[🔗](../api/abc.html#pyxu.abc.Map.lipschitz) property. Don't know it? No problem! The `estimate_lipschitz()`[🔗](../api/abc.html#pyxu.abc.Map.estimate_lipschitz)\n",
     "  method will compute it for you, offering various methods to balance accuracy and execution time.\n",
     "\n",
     "```python\n",
     "my_operator.lipschitz = my_operator.estimate_lipschitz()\n",
     "```\n",
     "\n",
-    "- **Singular Value Decomposition**: Ever needed to compute the singular values of your operator? Use the `svdvals()`\n",
+    "- **Singular Value Decomposition**: Ever needed to compute the singular values of your operator? Use the `svdvals()`[🔗](../api/abc.html#pyxu.abc.LinOp.svdvals)\n",
     "  method which employs the Arnoldi algorithm to get the job done without breaking the matrix-free paradigm.\n",
     "\n",
-    "- **Trace of Operator**: Sometimes you may need to compute the trace of an operator. The `trace()` method uses a\n",
+    "- **Trace of Operator**: Sometimes you may need to compute the trace of an operator. The `trace()`[🔗](../api/abc.html#pyxu.abc.SquareOp.trace) method uses a\n",
     "  stochastic approximation with the Hutch++ algorithm to efficiently it.\n",
     "\n",
-    "- **Pseudo-Inverse**: If you're looking to solve an inverse problem, the `pinv()` method helps you evaluate the\n",
+    "- **Pseudo-Inverse**: If you're looking to solve an inverse problem, the `pinv()`[🔗](../api/abc.html#pyxu.abc.LinOp.pinv) method helps you evaluate the\n",
     "  pseudo-inverse by solving the (dampened) normal equations, making it the most straightforward way to reverse your\n",
     "  operations.\n",
     "\n",
@@ -152,30 +152,30 @@
     "pseudo_inv_result = my_operator.pinv(my_array, damp=value)\n",
     "```\n",
     "\n",
-    "- **Support for Explicit Matrices**: Though `LinOp()` is primarily built for matrix-free operations, you are not\n",
-    "  restricted to them. If you prefer, you can work with explicit matrices using the `from_array()` method, supporting a\n",
+    "- **Support for Explicit Matrices**: Though `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) is primarily built for matrix-free operations, you are not\n",
+    "  restricted to them. If you prefer, you can work with explicit matrices using the `from_array()`[🔗](../api/abc.html#pyxu.abc.LinOp.from_array) method, supporting a\n",
     "  variety of array formats including `numpy`, `cupy`, `sparse`, and `dask`.\n",
     "\n",
     "```python\n",
     "op = LinOp.from_array(np.ones((N, N)))\n",
     "```\n",
     "\n",
-    "With all these tools and methods at your disposal, `LinOp()` aims to be your go-to solution for implementing linear\n",
+    "With all these tools and methods at your disposal, `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) aims to be your go-to solution for implementing linear\n",
     "operators in computational imaging tasks.\n",
     "\n",
     "## DiffMap for Non-linear Forward Operators \n",
     "\n",
     "Linear models are often an idealized representation. In some situations forward operators are inherently non-linear.\n",
     "Take phase retrieval or some forms of tomography as examples: these are scenarios where the relationship between the\n",
-    "object and its measurements isn't just a linear transformation. For such cases, Pyxu provides the `DiffMap()` class to\n",
+    "object and its measurements isn't just a linear transformation. For such cases, Pyxu provides the `DiffMap()`[🔗](../api/abc.html#pyxu.abc.DiffMap) class to\n",
     "implement these non-linear forward operators.\n",
     "\n",
     "### Core Methods\n",
     "\n",
-    "- **`apply()`**: This method is where you'll implement your forward model. Just like in `LinOp()`, you override this\n",
+    "- `apply()`[🔗](../api/abc.html#pyxu.abc.Map.apply): This method is where you'll implement your forward model. Just like in `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp), you override this\n",
     "  function to define how your specific forward model operates on an input array.\n",
     "\n",
-    "- **`jacobian`**: In calculus, the Jacobian matrix represents the best linear approximation to a function at a given\n",
+    "- `jacobian()`[🔗](../api/abc.html#pyxu.abc.DiffMap.jacobian): In calculus, the Jacobian matrix represents the best linear approximation to a function at a given\n",
     "  point. For a function $\\mathbf{f}: \\mathbb{R}^{M} \\to \\mathbb{R}^{N}$, the Jacobian\n",
     "  $\\mathbf{J}_{\\mathbf{f}}(\\mathbf{x})$ at a point $\\mathbf{x}$ is an $N \\times M$ matrix where the entry $(i, j)$ is\n",
     "  $\\frac{\\partial f_{i}}{\\partial x_{j}}$. When the forward operator is non-linear, knowing the Jacobian is crucial for\n",
@@ -190,17 +190,17 @@
     "Libraries like JAX or PyTorch offer automatic differentiation techniques (autograd) to compute derivatives, which you\n",
     "can use to obtain the Jacobian efficiently in matrix-free fashion.\n",
     "\n",
-    "In Pyxu, methods `from_torch()` and `from_jax()` allow you to define operators whose Jacobians are computed via\n",
+    "In Pyxu, methods `from_torch`[🔗](../api/operator.interop.html#pyxu.operator.interop.from_torch) and `from_jax`[🔗](../api/operator.interop.html#pyxu.operator.interop.from_jax) allow you to define operators whose Jacobians are computed via\n",
     "autograd.  This means you can utilize the power of these deep learning libraries to implement non-linear operators\n",
     "seamlessly.\n",
     "\n",
-    "With `DiffMap()`, you're well-equipped to tackle the challenges posed by non-linear forward operators in computational\n",
+    "With `DiffMap()`[🔗](../api/abc.html#pyxu.abc.DiffMap), you're well-equipped to tackle the challenges posed by non-linear forward operators in computational\n",
     "imaging.\n",
     "\n",
     "## Wrapping Up\n",
     "\n",
     "Pyxu offers a robust and scalable framework for computational imaging professionals to deal with both linear and\n",
-    "non-linear forward operators. With the abstraction provided by classes like `LinOp()` and `DiffMap()`, you can focus on\n",
+    "non-linear forward operators. With the abstraction provided by classes like `LinOp()`[🔗](../api/abc.html#pyxu.abc.LinOp) and `DiffMap()`[🔗](../api/abc.html#pyxu.abc.DiffMap), you can focus on\n",
     "the problem you're solving rather than computational limitations. These classes are meant to be subclassed to tailor to\n",
     "your specific problem domain. Happy coding! 🚀\n"
    ]
diff --git a/guide/hpc.html b/guide/hpc.html
index b3a28d02..c1175231 100644
--- a/guide/hpc.html
+++ b/guide/hpc.html
@@ -18,7 +18,7 @@
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" rel="preload" type="font/woff2"/>
-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
 <link href="../_static/sphinx-codeautolink.css?v=125d5c1c" rel="stylesheet" type="text/css"/>
 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -29,11 +29,11 @@
 <link href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" rel="stylesheet" type="text/css"/>
 <link href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" rel="stylesheet" type="text/css"/>
 <link href="../_static/nbsphinx-code-cells.css?v=2aa19091" rel="stylesheet" type="text/css"/>
-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
 <!-- Pre-loaded scripts that we'll load fully later -->
 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
 <link as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" rel="preload"/>
-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
 <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -52,7 +52,7 @@
 <link href="../_static/favicon.png" rel="icon"/>
 <link href="../genindex.html" rel="index" title="Index"/>
 <link href="../search.html" rel="search" title="Search"/>
-<link href="../examples/index.html" rel="next" title="Example Gallery"/>
+<link href="diff_ops.html" rel="next" title="Differential Operators in Pyxu"/>
 <link href="lipschitz.html" rel="prev" title="Lipschitz Constants and Automatic Step Size Tuning"/>
 <meta content="width=device-width, initial-scale=1" name="viewport"/>
 <meta content="en" name="docsearch:language"/>
@@ -232,6 +232,7 @@
 <li class="toctree-l1"><a class="reference internal" href="algorithms.html">Optimization Algorithms</a></li>
 <li class="toctree-l1"><a class="reference internal" href="lipschitz.html">Lipschitz Constants and Automatic Step Size Tuning</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">High Performance Computing Features</a></li>
+<li class="toctree-l1"><a class="reference internal" href="diff_ops.html">Differential Operators in Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
@@ -345,12 +346,12 @@ <h2>Hands-on Example:<a class="headerlink" href="#Hands-on-Example:" title="Link
 <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[1]:
 </pre></div>
 </div>
-<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.Map" title="pyxu.abc.operator.Map"><span class="n">Map</span></a>
-<span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util/array_module.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><span class="n">get_array_module</span></a>
+<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.Map" title="pyxu.abc.operator.Map"><span class="n">Map</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><span class="n">get_array_module</span></a>
 <span class="kn">from</span> <a class="sphinx-codeautolink-a" href="../api/runtime.html#module-pyxu.runtime" title="pyxu.runtime"><span class="nn">pyxu.runtime</span></a> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/runtime.html#pyxu.runtime.enforce_precision" title="pyxu.runtime.enforce_precision"><span class="n">enforce_precision</span></a>
 
 
-<span class="k">class</span> <span class="nc">Median</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.Map" title="pyxu.abc.operator.Map"><span class="n">Map</span></a><span class="p">):</span>
+<span class="k">class</span> <span class="nc">Median</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.Map" title="pyxu.abc.operator.Map"><span class="n">Map</span></a><span class="p">):</span>
     <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">dim</span><span class="p">):</span>
         <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#super" title="super"><span class="nb">super</span></a><span class="p">(</span><span class="n">Median</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">dim</span><span class="p">))</span>
 
@@ -358,7 +359,7 @@ <h2>Hands-on Example:<a class="headerlink" href="#Hands-on-Example:" title="Link
     <a class="sphinx-codeautolink-a" href="../api/runtime.html#pyxu.runtime.enforce_precision" title="pyxu.runtime.enforce_precision"><span class="nd">@enforce_precision</span></a><span class="p">(</span><span class="n">i</span><span class="o">=</span><span class="s2">"arr"</span><span class="p">)</span>
     <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span>
         <span class="c1"># Find the array module.</span>
-        <span class="n">xp</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util/array_module.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><span class="n">get_array_module</span></a><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+        <span class="n">xp</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><span class="n">get_array_module</span></a><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
         <span class="k">return</span> <span class="n">xp</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
         <span class="c1"># Dispatch the median call to the right backend</span>
         <span class="c1"># Allow for batch dimensions.</span>
@@ -371,16 +372,16 @@ <h2>Hands-on Example:<a class="headerlink" href="#Hands-on-Example:" title="Link
 </pre></div>
 </div>
 <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/time.html#module-time" title="time"><span class="nn">time</span></a> <span class="k">as</span> <span class="nn">t</span>
-<span class="kn">from</span> <span class="nn">pyxu.util.deps</span> <span class="kn">import</span> <span class="n">supported_array_modules</span>
-<span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util/misc.html#pyxu.util.compute" title="pyxu.util.compute"><span class="n">compute</span></a>
+<span class="kn">from</span> <a class="sphinx-codeautolink-a" href="../api/info.deps.html#module-pyxu.info.deps" title="pyxu.info.deps"><span class="nn">pyxu.info.deps</span></a> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/info.deps.html#pyxu.info.deps.supported_array_modules" title="pyxu.info.deps.supported_array_modules"><span class="n">supported_array_modules</span></a>
+<span class="kn">from</span> <span class="nn">pyxu.util</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.compute" title="pyxu.util.compute"><span class="n">compute</span></a>
 
 <span class="n">timings</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#dict" title="dict"><span class="nb">dict</span></a><span class="p">()</span>
 <span class="n">m</span> <span class="o">=</span> <span class="n">Median</span><span class="p">()</span>
-<span class="k">for</span> <span class="n">xp</span> <span class="ow">in</span> <span class="n">supported_array_modules</span><span class="p">():</span> <span class="c1"># Loops over supported array backends</span>
+<span class="k">for</span> <span class="n">xp</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="../api/info.deps.html#pyxu.info.deps.supported_array_modules" title="pyxu.info.deps.supported_array_modules"><span class="n">supported_array_modules</span></a><span class="p">():</span> <span class="c1"># Loops over supported array backends</span>
     <span class="c1"># Apply the operator in turn on a various array types.</span>
     <span class="n">t1</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/time.html#time.time" title="time.time"><span class="n">t</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span>
     <span class="n">arr</span> <span class="o">=</span> <span class="n">xp</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">260</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">13</span><span class="p">)</span>
-    <span class="n">out</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util/misc.html#pyxu.util.compute" title="pyxu.util.compute"><span class="n">compute</span></a><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">))</span>
+    <span class="n">out</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.compute" title="pyxu.util.compute"><span class="n">compute</span></a><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">))</span>
     <span class="n">timings</span><span class="p">[</span><span class="n">xp</span><span class="o">.</span><span class="vm">__name__</span><span class="p">]</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/time.html#time.time" title="time.time"><span class="n">t</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t1</span>
 <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#print" title="print"><span class="nb">print</span></a><span class="p">(</span><span class="n">timings</span><span class="p">)</span>
 </pre></div>
@@ -394,7 +395,7 @@ <h2>Hands-on Example:<a class="headerlink" href="#Hands-on-Example:" title="Link
 {'numpy': 0.0005955696105957031, 'cupy': 2.3291730880737305, 'dask.array': 0.0022661685943603516}
 </pre></div></div>
 </div>
-<p>If called from within the context manager <code class="docutils literal notranslate"><span class="pre">Precision</span></code>, the decorated apply method will automatically coerce the input/output to the user-specified precision:</p>
+<p>If called from within the context manager <code class="docutils literal notranslate"><span class="pre">Precision</span></code><a class="reference external" href="../api/runtime.html#pyxu.runtime.Precision">🔗</a>, the decorated apply method will automatically coerce the input/output to the user-specified precision:</p>
 <div class="nbinput docutils container">
 <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[7]:
 </pre></div>
@@ -441,7 +442,7 @@ <h2>Hands-on Example:<a class="headerlink" href="#Hands-on-Example:" title="Link
 <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">HierarchicalMedian</span><span class="p">(</span><span class="n">Median</span><span class="p">):</span>
 
     <span class="k">def</span> <span class="nf">apply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">):</span>
-        <span class="n">xp</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util/array_module.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><span class="n">get_array_module</span></a><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+        <span class="n">xp</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.get_array_module" title="pyxu.util.get_array_module"><span class="n">get_array_module</span></a><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
         <span class="n">out</span> <span class="o">=</span> <span class="p">[]</span>
         <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#zip" title="zip"><span class="nb">zip</span></a><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#range" title="range"><span class="nb">range</span></a><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">arr</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="mi">10</span><span class="p">),</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#range" title="range"><span class="nb">range</span></a><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="n">arr</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="mi">10</span><span class="p">)):</span>
             <span class="n">out</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#super" title="super"><span class="nb">super</span></a><span class="p">()</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span><span class="n">j</span><span class="p">]))</span>
@@ -473,9 +474,9 @@ <h2>Hands-on Example:<a class="headerlink" href="#Hands-on-Example:" title="Link
 </pre></div>
 </div>
 <div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">timings</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/stdtypes.html#dict" title="dict"><span class="nb">dict</span></a><span class="p">()</span>
-<span class="k">for</span> <span class="n">xp</span> <span class="ow">in</span> <span class="n">supported_array_modules</span><span class="p">():</span>
+<span class="k">for</span> <span class="n">xp</span> <span class="ow">in</span> <a class="sphinx-codeautolink-a" href="../api/info.deps.html#pyxu.info.deps.supported_array_modules" title="pyxu.info.deps.supported_array_modules"><span class="n">supported_array_modules</span></a><span class="p">():</span>
     <span class="n">t1</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/time.html#time.time" title="time.time"><span class="n">t</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span>
-    <span class="n">out</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util/misc.html#pyxu.util.compute" title="pyxu.util.compute"><span class="n">compute</span></a><span class="p">(</span><span class="n">hm</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">xp</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">2600</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">130</span><span class="p">)))</span>
+    <span class="n">out</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/util.html#pyxu.util.compute" title="pyxu.util.compute"><span class="n">compute</span></a><span class="p">(</span><span class="n">hm</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="n">xp</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">2600</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">130</span><span class="p">)))</span>
     <span class="n">timings</span><span class="p">[</span><span class="n">xp</span><span class="o">.</span><span class="vm">__name__</span><span class="p">]</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/time.html#time.time" title="time.time"><span class="n">t</span><span class="o">.</span><span class="n">time</span></a><span class="p">()</span><span class="o">-</span><span class="n">t1</span>
 <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#print" title="print"><span class="nb">print</span></a><span class="p">(</span><span class="n">timings</span><span class="p">)</span>
 </pre></div>
@@ -509,10 +510,10 @@ <h2>Final thoughts<a class="headerlink" href="#Final-thoughts" title="Link to th
 <p class="prev-next-title">Lipschitz Constants and Automatic Step Size Tuning</p>
 </div>
 </a>
-<a class="right-next" href="../examples/index.html" title="next page">
+<a class="right-next" href="diff_ops.html" title="next page">
 <div class="prev-next-info">
 <p class="prev-next-subtitle">next</p>
-<p class="prev-next-title">Example Gallery</p>
+<p class="prev-next-title">Differential Operators in Pyxu</p>
 </div>
 <i class="fa-solid fa-angle-right"></i>
 </a>
diff --git a/guide/hpc.ipynb b/guide/hpc.ipynb
index 5438dabd..89add656 100644
--- a/guide/hpc.ipynb
+++ b/guide/hpc.ipynb
@@ -185,7 +185,7 @@
    ],
    "source": [
     "import time as t\n",
-    "from pyxu.util.deps import supported_array_modules\n",
+    "from pyxu.info.deps import supported_array_modules\n",
     "from pyxu.util import compute\n",
     "\n",
     "timings = dict()\n",
@@ -208,7 +208,7 @@
     }
    },
    "source": [
-    "If called from within the context manager ``Precision``, the decorated apply method will automatically coerce the input/output to the user-specified precision:"
+    "If called from within the context manager ``Precision``[🔗](../api/runtime.html#pyxu.runtime.Precision), the decorated apply method will automatically coerce the input/output to the user-specified precision:"
    ]
   },
   {
diff --git a/guide/index.html b/guide/index.html
index 7637e79c..b74ad14c 100644
--- a/guide/index.html
+++ b/guide/index.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -412,6 +412,7 @@
 <li class="toctree-l1"><a class="reference internal" href="algorithms.html">Optimization Algorithms</a></li>
 <li class="toctree-l1"><a class="reference internal" href="lipschitz.html">Lipschitz Constants and Automatic Step Size Tuning</a></li>
 <li class="toctree-l1"><a class="reference internal" href="hpc.html">High Performance Computing Features</a></li>
+<li class="toctree-l1"><a class="reference internal" href="diff_ops.html">Differential Operators in Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
diff --git a/guide/lipschitz.html b/guide/lipschitz.html
index 4509eca4..75994da2 100644
--- a/guide/lipschitz.html
+++ b/guide/lipschitz.html
@@ -18,7 +18,7 @@
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" rel="preload" type="font/woff2"/>
 <link as="font" crossorigin="" href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" rel="preload" type="font/woff2"/>
-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
 <link href="../_static/plot_directive.css?v=7f9a90b1" rel="stylesheet" type="text/css"/>
 <link href="../_static/sphinx-codeautolink.css?v=125d5c1c" rel="stylesheet" type="text/css"/>
 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -29,11 +29,11 @@
 <link href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" rel="stylesheet" type="text/css"/>
 <link href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" rel="stylesheet" type="text/css"/>
 <link href="../_static/nbsphinx-code-cells.css?v=2aa19091" rel="stylesheet" type="text/css"/>
-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
 <!-- Pre-loaded scripts that we'll load fully later -->
 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
 <link as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" rel="preload"/>
-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
 <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -232,6 +232,7 @@
 <li class="toctree-l1"><a class="reference internal" href="algorithms.html">Optimization Algorithms</a></li>
 <li class="toctree-l1 current active"><a class="current reference internal" href="#">Lipschitz Constants and Automatic Step Size Tuning</a></li>
 <li class="toctree-l1"><a class="reference internal" href="hpc.html">High Performance Computing Features</a></li>
+<li class="toctree-l1"><a class="reference internal" href="diff_ops.html">Differential Operators in Pyxu</a></li>
 </ul>
 </div>
 </nav></div>
@@ -277,7 +278,7 @@ <h2>Introduction to Lipschitz Constants<a class="headerlink" href="#Introduction
 </section>
 <section id="Accessing-Lipschitz-Constants">
 <h2>Accessing Lipschitz Constants<a class="headerlink" href="#Accessing-Lipschitz-Constants" title="Link to this heading">#</a></h2>
-<p>Pyxu operators come equipped with attributes <code class="docutils literal notranslate"><span class="pre">lipschitz</span></code> and <code class="docutils literal notranslate"><span class="pre">diff_lipschitz</span></code> for storing the Lipschitz constants of a map and its derivative (if defined), respectively. These constants are leveraged under the hood by Pyxu to auto-tune the step sizes in various optimization algorithms.</p>
+<p>Pyxu operators come equipped with attributes <code class="docutils literal notranslate"><span class="pre">lipschitz</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Map.lipschitz">🔗</a> and <code class="docutils literal notranslate"><span class="pre">diff_lipschitz</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.DiffMap.diff_lipschitz">🔗</a> for storing the Lipschitz constants of a map and its derivative (if defined), respectively. These constants are leveraged under the hood by Pyxu to auto-tune the step sizes in various optimization algorithms.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Access Lipschitz constant of an operator 'op'</span>
 <span class="n">lip_const</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">lipschitz</span>
 </pre></div>
@@ -285,7 +286,7 @@ <h2>Accessing Lipschitz Constants<a class="headerlink" href="#Accessing-Lipschit
 </section>
 <section id="Estimating-Lipschitz-Constants">
 <h2>Estimating Lipschitz Constants<a class="headerlink" href="#Estimating-Lipschitz-Constants" title="Link to this heading">#</a></h2>
-<p>For user-defined or complicated operators where Lipschitz constants are unknown, you can estimate them using Pyxu’s <code class="docutils literal notranslate"><span class="pre">estimate_lipschitz()</span></code> method.</p>
+<p>For user-defined or complicated operators where Lipschitz constants are unknown, you can estimate them using Pyxu’s <code class="docutils literal notranslate"><span class="pre">estimate_lipschitz()</span></code><a class="reference external" href="../api/abc.html#pyxu.abc.Map.estimate_lipschitz">🔗</a> method.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Estimate Lipschitz constant and update the attribute</span>
 <span class="n">op</span><span class="o">.</span><span class="n">lipschitz</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">estimate_lipschitz</span><span class="p">()</span>
 </pre></div>
@@ -294,13 +295,13 @@ <h2>Estimating Lipschitz Constants<a class="headerlink" href="#Estimating-Lipsch
 <h3>Supported Backends 🎛️<a class="headerlink" href="#Supported-Backends-🎛️" title="Link to this heading">#</a></h3>
 <p>Pyxu offers two methods to estimate Lipschitz constants:</p>
 <ol class="arabic">
-<li><p><strong>Trace Method (``trace``)</strong>: This is the default and computationally lighter option. It computes a rough estimate using the Frobenius norm of the operator, making use of the <a class="reference external" href="https://arxiv.org/abs/2010.09649">Hutch++ stochastic algorithm</a>:</p>
+<li><p><strong>Trace Method (</strong><code class="docutils literal notranslate"><span class="pre">trace</span></code><strong>)</strong>: This is the default and computationally lighter option. It computes a rough estimate using the Frobenius norm of the operator, making use of the <a class="reference external" href="https://arxiv.org/abs/2010.09649">Hutch++ stochastic algorithm</a>:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using trace method</span>
 <span class="n">op</span><span class="o">.</span><span class="n">lipschitz</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">estimate_lipschitz</span><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="s2">"trace"</span><span class="p">)</span>
 </pre></div>
 </div>
 </li>
-<li><p><strong>SVD Method (``svd``)</strong>: This method computes the spectral norm of the operator and generally provides a tighter Lipschitz constant. However, it can be computationally intensive for large operators. A reduced-accuracy mode is available for quicker but slightly overestimated constants:</p>
+<li><p><strong>SVD Method (</strong><code class="docutils literal notranslate"><span class="pre">svd</span></code><strong>)</strong>: This method computes the spectral norm of the operator and generally provides a tighter Lipschitz constant. However, it can be computationally intensive for large operators. A reduced-accuracy mode is available for quicker but slightly overestimated constants:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using SVD method with reduced accuracy</span>
 <span class="n">op</span><span class="o">.</span><span class="n">lipschitz</span> <span class="o">=</span> <span class="n">op</span><span class="o">.</span><span class="n">estimate_lipschitz</span><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="s2">"svd"</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">)</span>
 </pre></div>
@@ -318,7 +319,7 @@ <h3>Hands-On Example 🎓<a class="headerlink" href="#Hands-On-Example-🎓" tit
 <div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[20]:
 </pre></div>
 </div>
-<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">LinOp</span></a>
+<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pyxu.abc</span> <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">LinOp</span></a>
 <span class="kn">import</span> <a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/index.html#module-numpy" title="numpy"><span class="nn">numpy</span></a> <span class="k">as</span> <span class="nn">np</span>
 
 <span class="n">rand_op</span> <span class="o">=</span> <span class="n">LinOp</span><span class="o">.</span><span class="n">from_array</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.random.html#numpy.random.random" title="numpy.random.random"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">random</span></a><span class="p">((</span><span class="mi">10000</span><span class="p">,</span> <span class="mi">10000</span><span class="p">)))</span>
@@ -426,7 +427,7 @@ <h2>Operator Algebra and Lipschitz Constant Propagation<a class="headerlink" hre
 <span class="o">...</span>
 </pre></div>
 </div>
-<p>More details on this feature can be found in the API reference under <code class="docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic</span></code>.</p>
+<p>More details on this feature can be found in the <a class="reference external" href="../api/index.html">API reference</a> under <code class="docutils literal notranslate"><span class="pre">pyxu.abc.arithmetic</span></code><a class="reference external" href="../api/abc/arithmetic.html#">🔗</a>.</p>
 <blockquote>
 <div><p><strong>Note 📝</strong>: While the propagated constants are usually good enough for step size tuning, they may not always be the tightest estimates.</p>
 </div></blockquote>
diff --git a/guide/lipschitz.ipynb b/guide/lipschitz.ipynb
index f74f0803..0296bebe 100644
--- a/guide/lipschitz.ipynb
+++ b/guide/lipschitz.ipynb
@@ -23,7 +23,7 @@
     "\n",
     "## Accessing Lipschitz Constants\n",
     "\n",
-    "Pyxu operators come equipped with attributes `lipschitz` and `diff_lipschitz` for storing the Lipschitz constants of a map and its derivative (if defined), respectively. These constants are leveraged under the hood by Pyxu to auto-tune the step sizes in various optimization algorithms.\n",
+    "Pyxu operators come equipped with attributes `lipschitz`[🔗](../api/abc.html#pyxu.abc.Map.lipschitz) and `diff_lipschitz`[🔗](../api/abc.html#pyxu.abc.DiffMap.diff_lipschitz) for storing the Lipschitz constants of a map and its derivative (if defined), respectively. These constants are leveraged under the hood by Pyxu to auto-tune the step sizes in various optimization algorithms.\n",
     "\n",
     "```python\n",
     "# Access Lipschitz constant of an operator 'op'\n",
@@ -32,7 +32,7 @@
     "\n",
     "## Estimating Lipschitz Constants\n",
     "\n",
-    "For user-defined or complicated operators where Lipschitz constants are unknown, you can estimate them using Pyxu's `estimate_lipschitz()` method.\n",
+    "For user-defined or complicated operators where Lipschitz constants are unknown, you can estimate them using Pyxu's `estimate_lipschitz()`[🔗](../api/abc.html#pyxu.abc.Map.estimate_lipschitz) method.\n",
     "\n",
     "```python\n",
     "# Estimate Lipschitz constant and update the attribute\n",
@@ -43,7 +43,7 @@
     "\n",
     "Pyxu offers two methods to estimate Lipschitz constants:\n",
     "\n",
-    "1. **Trace Method (`trace`)**: This is the default and computationally lighter option. It computes a rough estimate using the Frobenius norm of the operator, making use of the [Hutch++ stochastic algorithm](https://arxiv.org/abs/2010.09649):\n",
+    "1. **Trace Method (**`trace`**)**: This is the default and computationally lighter option. It computes a rough estimate using the Frobenius norm of the operator, making use of the [Hutch++ stochastic algorithm](https://arxiv.org/abs/2010.09649):\n",
     "\n",
     "    ```python\n",
     "    # Using trace method\n",
@@ -52,7 +52,7 @@
     "    ```\n",
     "\n",
     "\n",
-    "2. **SVD Method (`svd`)**: This method computes the spectral norm of the operator and generally provides a tighter Lipschitz constant. However, it can be computationally intensive for large operators. A reduced-accuracy mode is available for quicker but slightly overestimated constants:\n",
+    "2. **SVD Method (**`svd`**)**: This method computes the spectral norm of the operator and generally provides a tighter Lipschitz constant. However, it can be computationally intensive for large operators. A reduced-accuracy mode is available for quicker but slightly overestimated constants:\n",
     "\n",
     "    ```python\n",
     "    # Using SVD method with reduced accuracy\n",
@@ -208,7 +208,7 @@
     "... \n",
     "```\n",
     "\n",
-    "More details on this feature can be found in the API reference under `pyxu.abc.arithmetic`.\n",
+    "More details on this feature can be found in the [API reference](../api/index.html) under `pyxu.abc.arithmetic`[🔗](../api/abc/arithmetic.html#).\n",
     "\n",
     "> **Note 📝**: While the propagated constants are usually good enough for step size tuning, they may not always be the tightest estimates.\n",
     "\n",
diff --git a/index.html b/index.html
index 9b1503c7..1c3e71ec 100644
--- a/index.html
+++ b/index.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=b76e3c8a" />
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     <link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
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-    <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="_static/documentation_options.js?v=a4a8746c"></script>
     <script src="_static/doctools.js?v=888ff710"></script>
     <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="_static/clipboard.min.js?v=a7894cd8"></script>
diff --git a/intro/comparison.html b/intro/comparison.html
index 7fd695a5..bbfd2ea8 100644
--- a/intro/comparison.html
+++ b/intro/comparison.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
diff --git a/intro/index.html b/intro/index.html
index 27a63013..7b13225b 100644
--- a/intro/index.html
+++ b/intro/index.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
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     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
diff --git a/intro/installation.html b/intro/installation.html
index b912a1af..466d1ca7 100644
--- a/intro/installation.html
+++ b/intro/installation.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
     <link rel="stylesheet" type="text/css" href="../_static/sphinx-codeautolink.css?v=125d5c1c" />
     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-dataframe.css?v=2082cf3c" />
     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
diff --git a/intro/primer.html b/intro/primer.html
index a94a3b8f..11763908 100644
--- a/intro/primer.html
+++ b/intro/primer.html
@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=fa44fd50" />
+    <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b76e3c8a" />
     <link rel="stylesheet" type="text/css" href="../_static/plot_directive.css?v=7f9a90b1" />
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     <link rel="stylesheet" type="text/css" href="../_static/copybutton.css?v=76b2166b" />
@@ -38,13 +38,13 @@
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     <link rel="stylesheet" type="text/css" href="../_static/sg_gallery-rendered-html.css?v=1277b6f3" />
     <link rel="stylesheet" type="text/css" href="../_static/design-style.1e8bd061cd6da7fc9cf755528e8ffc24.min.css?v=0a3b3ea7" />
-    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=1031a718" />
+    <link rel="stylesheet" type="text/css" href="../_static/css/custom.css?v=14df3d68" />
   
   <!-- Pre-loaded scripts that we'll load fully later -->
   <link rel="preload" as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" />
 <link rel="preload" as="script" href="../_static/scripts/pydata-sphinx-theme.js?digest=e353d410970836974a52" />
 
-    <script src="../_static/documentation_options.js?v=e02fc88f"></script>
+    <script src="../_static/documentation_options.js?v=a4a8746c"></script>
     <script src="../_static/doctools.js?v=888ff710"></script>
     <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
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diff --git a/intro/tomo.html b/intro/tomo.html
index 180c5bfd..7cb2bec5 100644
--- a/intro/tomo.html
+++ b/intro/tomo.html
@@ -18,7 +18,7 @@
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-<link href="../_static/pygments.css?v=fa44fd50" rel="stylesheet" type="text/css"/>
+<link href="../_static/pygments.css?v=b76e3c8a" rel="stylesheet" type="text/css"/>
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 <link href="../_static/copybutton.css?v=76b2166b" rel="stylesheet" type="text/css"/>
@@ -29,11 +29,11 @@
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-<link href="../_static/css/custom.css?v=1031a718" rel="stylesheet" type="text/css"/>
+<link href="../_static/css/custom.css?v=14df3d68" rel="stylesheet" type="text/css"/>
 <!-- Pre-loaded scripts that we'll load fully later -->
 <link as="script" href="../_static/scripts/bootstrap.js?digest=e353d410970836974a52" rel="preload"/>
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-<script src="../_static/documentation_options.js?v=e02fc88f"></script>
+<script src="../_static/documentation_options.js?v=a4a8746c"></script>
 <script src="../_static/doctools.js?v=888ff710"></script>
 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>
 <script src="../_static/clipboard.min.js?v=a7894cd8"></script>
@@ -397,7 +397,7 @@ <h2>Pyxu’s Modularity to the Rescue<a class="headerlink" href="#Pyxu's-Modular
 <span class="kn">import</span> <span class="nn">skimage.transform</span> <span class="k">as</span> <span class="nn">skt</span>
 
 <span class="c1"># Radon Operator (imported from `skt` since Pyxu did not ship with a Radon transform at the time of this writing.)</span>
-<span class="n">Radon</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.interop.html#pyxu.operator.interop.from_source" title="pyxu.operator.interop.from_source"><span class="n">from_source</span></a><span class="p">(</span><span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
+<span class="n">Radon</span> <span class="o">=</span> <a class="sphinx-codeautolink-a" href="../api/operator.interop.html#pyxu.operator.interop.from_source" title="pyxu.operator.interop.from_source"><span class="n">from_source</span></a><span class="p">(</span><span class="bp">cls</span><span class="o">=</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.LinOp" title="pyxu.abc.operator.LinOp"><span class="n">pxa</span><span class="o">.</span><span class="n">LinOp</span></a><span class="p">,</span>
                     <span class="n">shape</span><span class="o">=</span><span class="p">(</span><span class="n">sino</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="n">phantom</span><span class="o">.</span><span class="n">size</span><span class="p">),</span>
                     <span class="n">apply</span><span class="o">=</span><span class="k">lambda</span> <span class="n">_</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="n">skt</span><span class="o">.</span><span class="n">radon</span><span class="p">(</span><span class="n">arr</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">phantom</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span>
                                                    <span class="n">theta</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">180</span><span class="p">,</span> <span class="n">angles</span><span class="p">),</span>
@@ -754,7 +754,7 @@ <h4>Basic Equations<a class="headerlink" href="#Basic-Equations" title="Link to
     <span class="n">arr</span> <span class="o">=</span> <span class="n">arr</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">)</span>
     <span class="k">return</span> <a class="sphinx-codeautolink-a" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.median_filter.html#scipy.ndimage.median_filter" title="scipy.ndimage.median_filter"><span class="n">median_filter</span></a><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="n">wsize</span><span class="p">)</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
 
-<span class="k">class</span> <span class="nc">MedianFilterPnP</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc/operator.html#pyxu.abc.ProxDiffFunc" title="pyxu.abc.operator.ProxDiffFunc"><span class="n">pxa</span><span class="o">.</span><span class="n">ProxDiffFunc</span></a><span class="p">):</span>
+<span class="k">class</span> <span class="nc">MedianFilterPnP</span><span class="p">(</span><a class="sphinx-codeautolink-a" href="../api/abc.html#pyxu.abc.ProxDiffFunc" title="pyxu.abc.operator.ProxDiffFunc"><span class="n">pxa</span><span class="o">.</span><span class="n">ProxDiffFunc</span></a><span class="p">):</span>
     <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arg_shape</span><span class="p">,</span> <span class="n">wsize</span><span class="p">):</span>
         <a class="sphinx-codeautolink-a" href="https://docs.python.org/3/library/functions.html#super" title="super"><span class="nb">super</span></a><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">(</span><span class="n">arg_shape</span><span class="p">)))</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">_arg_shape</span> <span class="o">=</span> <span class="n">arg_shape</span>
diff --git a/objects.inv b/objects.inv
index 364594f9686fce4a89678c4085f9cafb214ed7ec..d546bf7581bf1e1ecb3d2c1999fad40f440466cf 100644
GIT binary patch
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diff --git a/plot_directive/api/abc-1_00.pdf b/plot_directive/api/abc-1_00.pdf
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diff --git a/plot_directive/api/experimental-1.py b/plot_directive/api/experimental-1.py
deleted file mode 100644
index d5ab99f6..00000000
--- a/plot_directive/api/experimental-1.py
+++ /dev/null
@@ -1,70 +0,0 @@
-import matplotlib.pyplot as plt
-import numpy as np
-import pyxu.experimental.sampler as pxe_sampler
-import pyxu.operator as pxo
-import scipy as sp
-
-f = pxo.SquaredL2Norm(dim=1) / 2  # To sample 1D normal distribution (mean 0, variance 1)
-ula = pxe_sampler.ULA(f=f)  # Sampler with maximum step size
-ula_lb = pxe_sampler.ULA(f=f, gamma=1e-1)  # Sampler with small step size
-
-gen_ula = ula.samples(x0=np.zeros(1))
-gen_ula_lb = ula_lb.samples(x0=np.zeros(1))
-n_burn_in = int(1e3)  # Number of burn-in iterations
-for i in range(n_burn_in):
-    next(gen_ula)
-    next(gen_ula_lb)
-
-# Online statistics objects
-mean_ula = pxe_sampler.OnlineMoment(order=1)
-mean_ula_lb = pxe_sampler.OnlineMoment(order=1)
-var_ula = pxe_sampler.OnlineVariance()
-var_ula_lb = pxe_sampler.OnlineVariance()
-
-n = int(1e4)  # Number of samples
-samples_ula = np.zeros(n)
-samples_ula_lb = np.zeros(n)
-for i in range(n):
-    sample = next(gen_ula)
-    sample_lb = next(gen_ula_lb)
-    samples_ula[i] = sample
-    samples_ula_lb[i] = sample_lb
-    mean = float(mean_ula.update(sample))
-    var = float(var_ula.update(sample))
-    mean_lb = float(mean_ula_lb.update(sample_lb))
-    var_lb = float(var_ula_lb.update(sample_lb))
-
-# Theoretical variances of biased stationary distributions of ULA
-biased_var = 1 / (1 - ula._gamma / 2)
-biased_var_lb = 1 / (1 - ula_lb._gamma / 2)
-
-# Quantify goodness of fit of empirical distribution with theoretical distribution (Cramér-von Mises test)
-cvm = sp.stats.cramervonmises(samples_ula, "norm", args=(0, np.sqrt(biased_var)))
-cvm_lb = sp.stats.cramervonmises(samples_ula_lb, "norm", args=(0, np.sqrt(biased_var_lb)))
-
-# Plots
-grid = np.linspace(-4, 4, 1000)
-
-plt.figure()
-plt.title(
-    f"ULA samples (large step size) \n Empirical mean: {mean:.3f} (theoretical: 0) \n "
-    f"Empirical variance: {var:.3f} (theoretical: {biased_var:.3f}) \n"
-    f"Cramér-von Mises goodness of fit: {cvm.statistic:.3f}"
-)
-plt.hist(samples_ula, range=(min(grid), max(grid)), bins=100, density=True)
-plt.plot(grid, sp.stats.norm.pdf(grid), label=r"$p(x)$")
-plt.plot(grid, sp.stats.norm.pdf(grid, scale=np.sqrt(biased_var)), label=r"$p_{\gamma_1}(x)$")
-plt.legend()
-plt.show()
-
-plt.figure()
-plt.title(
-    f"ULA samples (small step size) \n Empirical mean: {mean_lb:.3f} (theoretical: 0) \n "
-    f"Empirical variance: {var_lb:.3f} (theoretical: {biased_var_lb:.3f}) \n"
-    f"Cramér-von Mises goodness of fit: {cvm_lb.statistic:.3f}"
-)
-plt.hist(samples_ula_lb, range=(min(grid), max(grid)), bins=100, density=True)
-plt.plot(grid, sp.stats.norm.pdf(grid), label=r"$p(x)$")
-plt.plot(grid, sp.stats.norm.pdf(grid, scale=np.sqrt(biased_var_lb)), label=r"$p_{\gamma_2}(x)$")
-plt.legend()
-plt.show()
\ No newline at end of file
diff --git a/plot_directive/api/experimental-1_00_00.hires.png b/plot_directive/api/experimental-1_00_00.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/experimental-sampler-1_00_00.pdf b/plot_directive/api/experimental-sampler-1_00_00.pdf
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diff --git a/plot_directive/api/operator-1.py b/plot_directive/api/operator-1.py
deleted file mode 100644
index 2fb312ed..00000000
--- a/plot_directive/api/operator-1.py
+++ /dev/null
@@ -1,14 +0,0 @@
-import numpy as np
-import pyxu.operator as pxo
-import matplotlib.pyplot as plt
-
-rng = np.random.default_rng(0)
-D, M, N = 1, 2, 3  # D denotes the dimension of the data
-x = np.fmod(rng.normal(size=(M, D)), 2 * np.pi)
-A = pxo.NUFFT.type1(
-    x, N,
-    isign=-1,
-    eps=1e-9
-)
-A.plot_kernel()
-plt.show()
\ No newline at end of file
diff --git a/plot_directive/api/operator-10.hires.png b/plot_directive/api/operator-10.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-10.py b/plot_directive/api/operator-10.py
deleted file mode 100644
index 1f191681..00000000
--- a/plot_directive/api/operator-10.py
+++ /dev/null
@@ -1,29 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import DirectionalDerivative
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-z = peaks(xx, yy)
-directions = np.zeros(shape=(2, z.size))
-directions[0, : z.size // 2] = 1
-directions[1, z.size // 2:] = 1
-dop = DirectionalDerivative(arg_shape=z.shape, order=1, directions=directions)
-out = dop.unravel(dop(z.ravel()))
-dop2 = DirectionalDerivative(arg_shape=z.shape, order=2, directions=directions)
-out2 = dop2.unravel(dop2(z.ravel()))
-fig, axs = plt.subplots(1, 3, figsize=(15, 5))
-axs = np.ravel(axs)
-h = axs[0].pcolormesh(xx, yy, z, shading="auto")
-axs[0].quiver(x, x, directions[1].reshape(xx.shape), directions[0].reshape(xx.shape))
-plt.colorbar(h, ax=axs[0])
-axs[0].set_title("Signal and directions of first derivatives")
-
-h = axs[1].pcolormesh(xx, yy, out.squeeze(), shading="auto")
-plt.colorbar(h, ax=axs[1])
-axs[1].set_title("First-order directional derivatives")
-
-h = axs[2].pcolormesh(xx, yy, out2.squeeze(), shading="auto")
-plt.colorbar(h, ax=axs[2])
-axs[2].set_title("Second-order directional derivative")
\ No newline at end of file
diff --git a/plot_directive/api/operator-11.py b/plot_directive/api/operator-11.py
deleted file mode 100644
index 06c3a954..00000000
--- a/plot_directive/api/operator-11.py
+++ /dev/null
@@ -1,31 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import DirectionalGradient
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-z = peaks(xx, yy)
-directions1 = np.zeros(shape=(2, z.size))
-directions1[0, :z.size // 2] = 1
-directions1[1, z.size // 2:] = 1
-directions2 = np.zeros(shape=(2, z.size))
-directions2[1, :z.size // 2] = -1
-directions2[0, z.size // 2:] = -1
-arg_shape = z.shape
-dop = DirectionalGradient(arg_shape=arg_shape, directions=[directions1, directions2])
-out = dop.unravel(dop(z.ravel()))
-plt.figure()
-h = plt.pcolormesh(xx, yy, z, shading='auto')
-plt.quiver(x, x, directions1[1].reshape(arg_shape), directions1[0].reshape(xx.shape))
-plt.quiver(x, x, directions2[1].reshape(arg_shape), directions2[0].reshape(xx.shape), color='red')
-plt.colorbar(h)
-plt.title(r'Signal $\mathbf{f}$ and directions of derivatives')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[0], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla_{\mathbf{v}_0} \mathbf{f}$')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[1], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla_{\mathbf{v}_1} \mathbf{f}$')
\ No newline at end of file
diff --git a/plot_directive/api/operator-11_00.hires.png b/plot_directive/api/operator-11_00.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-12.py b/plot_directive/api/operator-12.py
deleted file mode 100644
index 8a895bdc..00000000
--- a/plot_directive/api/operator-12.py
+++ /dev/null
@@ -1,27 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import DirectionalLaplacian
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-z = peaks(xx, yy)
-directions1 = np.zeros(shape=(2, z.size))
-directions1[0, :z.size // 2] = 1
-directions1[1, z.size // 2:] = 1
-directions2 = np.zeros(shape=(2, z.size))
-directions2[1, :z.size // 2] = -1
-directions2[0, z.size // 2:] = -1
-arg_shape = z.shape
-dop = DirectionalLaplacian(arg_shape=arg_shape, directions=[directions1, directions2])
-out = dop.unravel(dop(z.ravel()))
-plt.figure()
-h = plt.pcolormesh(xx, yy, z, shading='auto')
-plt.quiver(x, x, directions1[1].reshape(arg_shape), directions1[0].reshape(xx.shape))
-plt.quiver(x, x, directions2[1].reshape(arg_shape), directions2[0].reshape(xx.shape), color='red')
-plt.colorbar(h)
-plt.title('Signal and directions of derivatives')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out.squeeze(), shading='auto')
-plt.colorbar(h)
-plt.title('Directional Laplacian')
\ No newline at end of file
diff --git a/plot_directive/api/operator-12_00.hires.png b/plot_directive/api/operator-12_00.hires.png
deleted file mode 100644
index 4775db44b97eed2fadef1f3d9ebee291e3d429b1..0000000000000000000000000000000000000000
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diff --git a/plot_directive/api/operator-13.py b/plot_directive/api/operator-13.py
deleted file mode 100644
index ddc93cd0..00000000
--- a/plot_directive/api/operator-13.py
+++ /dev/null
@@ -1,35 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import DirectionalHessian
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-z = peaks(xx, yy)
-directions1 = np.zeros(shape=(2, z.size))
-directions1[0, :z.size // 2] = 1
-directions1[1, z.size // 2:] = 1
-directions2 = np.zeros(shape=(2, z.size))
-directions2[1, :z.size // 2] = -1
-directions2[0, z.size // 2:] = -1
-arg_shape = z.shape
-d_hess = DirectionalHessian(arg_shape=arg_shape, directions=[directions1, directions2])
-out = d_hess.unravel(d_hess(z.ravel()))
-plt.figure()
-h = plt.pcolormesh(xx, yy, z, shading='auto')
-plt.quiver(x, x, directions1[1].reshape(arg_shape), directions1[0].reshape(xx.shape))
-plt.quiver(x, x, directions2[1].reshape(arg_shape), directions2[0].reshape(xx.shape), color='red')
-plt.colorbar(h)
-plt.title(r'Signal $\mathbf{f}$ and directions of derivatives')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[0], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla^2_{\mathbf{v}_0} \mathbf{f}$')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[1], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla_{\mathbf{v}_0} \nabla_{\mathbf{v}_{1}} \mathbf{f}$')
-plt.figure()
-h = plt.pcolormesh(xx, yy, out[2], shading='auto')
-plt.colorbar(h)
-plt.title(r'$\nabla^2_{\mathbf{v}_1} \mathbf{f}$')
\ No newline at end of file
diff --git a/plot_directive/api/operator-13_00.hires.png b/plot_directive/api/operator-13_00.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-14.py b/plot_directive/api/operator-14.py
deleted file mode 100644
index d7c5085f..00000000
--- a/plot_directive/api/operator-14.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import MovingAverage
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-ma = MovingAverage(arg_shape, size=5)
-out = ma(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/plot_directive/api/operator-15.hires.png b/plot_directive/api/operator-15.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-15.py b/plot_directive/api/operator-15.py
deleted file mode 100644
index 6af655cf..00000000
--- a/plot_directive/api/operator-15.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Gaussian
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-gaussian = Gaussian(arg_shape, sigma=3)
-out = gaussian(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/plot_directive/api/operator-16.hires.png b/plot_directive/api/operator-16.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-16.py b/plot_directive/api/operator-16.py
deleted file mode 100644
index 7650f6fb..00000000
--- a/plot_directive/api/operator-16.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import DoG
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-dog = DoG(arg_shape, low_sigma=3)
-out = dog(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/plot_directive/api/operator-17.hires.png b/plot_directive/api/operator-17.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-17.py b/plot_directive/api/operator-17.py
deleted file mode 100644
index 74ffad5c..00000000
--- a/plot_directive/api/operator-17.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Laplace
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-laplace = Laplace(arg_shape)
-out = laplace(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/plot_directive/api/operator-18.hires.png b/plot_directive/api/operator-18.hires.png
deleted file mode 100644
index 304a30db3fde200df09b9f53b0c72a3788373954..0000000000000000000000000000000000000000
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diff --git a/plot_directive/api/operator-18.py b/plot_directive/api/operator-18.py
deleted file mode 100644
index c6cfdede..00000000
--- a/plot_directive/api/operator-18.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Sobel
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-sobel = Sobel(arg_shape)
-out = sobel(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/plot_directive/api/operator-19.hires.png b/plot_directive/api/operator-19.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-19.py b/plot_directive/api/operator-19.py
deleted file mode 100644
index 4e36ae88..00000000
--- a/plot_directive/api/operator-19.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Prewitt
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-prewitt = Prewitt(arg_shape)
-out = prewitt(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/plot_directive/api/operator-2.hires.png b/plot_directive/api/operator-2.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-2.py b/plot_directive/api/operator-2.py
deleted file mode 100644
index fb8d4844..00000000
--- a/plot_directive/api/operator-2.py
+++ /dev/null
@@ -1,43 +0,0 @@
-import numpy as np
-import pyxu.operator as pxo
-
-rng = np.random.default_rng(2)
-D, M, N = 2, 500, 200
-rnd_points = lambda _: rng.normal(scale=rng.uniform(0.25, 0.5, size=(D,)), size=(_, D))
-rnd_offset = lambda: rng.uniform(-1, 1, size=(D,))
-scale = 20
-x = np.concatenate(
-    [
-        rnd_points(M) + rnd_offset() * scale,
-        rnd_points(M) + rnd_offset() * scale,
-        rnd_points(M) + rnd_offset() * scale,
-        rnd_points(M) + rnd_offset() * scale,
-        rnd_points(M) + rnd_offset() * scale,
-    ],
-    axis=0,
-)
-z = np.concatenate(
-    [
-        rnd_points(N) + rnd_offset() * scale,
-        rnd_points(N) + rnd_offset() * scale,
-        rnd_points(N) + rnd_offset() * scale,
-        rnd_points(N) + rnd_offset() * scale,
-        rnd_points(N) + rnd_offset() * scale,
-    ],
-    axis=0,
-)
-
-kwargs = dict(
-    x=x,
-    z=z,
-    isign=-1,
-    eps=1e-3,
-)
-A = pxo.NUFFT.type3(**kwargs, chunked=True)
-x_chunks, z_chunks = A.auto_chunk(
-    max_mem=.1,
-    max_anisotropy=1,
-)
-A.allocate(x_chunks, z_chunks)
-fig = A.diagnostic_plot('x')
-fig.show()
\ No newline at end of file
diff --git a/plot_directive/api/operator-20.hires.png b/plot_directive/api/operator-20.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-20.py b/plot_directive/api/operator-20.py
deleted file mode 100644
index e2a1b717..00000000
--- a/plot_directive/api/operator-20.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import matplotlib.pyplot as plt
-from pyxu.operator import Scharr
-
-arg_shape = (11, 11)
-image = np.zeros(arg_shape)
-image[5, 5] = 1.
-
-scharr = Scharr(arg_shape)
-out = scharr(image.ravel())
-plt.figure(figsize=(10, 5))
-plt.subplot(121)
-plt.imshow(image)
-plt.colorbar()
-plt.subplot(122)
-plt.imshow(out.reshape(*arg_shape))
-plt.colorbar()
\ No newline at end of file
diff --git a/plot_directive/api/operator-21.py b/plot_directive/api/operator-21.py
deleted file mode 100644
index 9ef935ea..00000000
--- a/plot_directive/api/operator-21.py
+++ /dev/null
@@ -1,45 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import StructureTensor
-from pyxu.util.misc import peaks
-
-# Define input image
-n = 1000
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-nsamples = 2
-arg_shape = image.shape  # (1000, 1000)
-images = np.tile(image, (nsamples, 1, 1)).reshape(nsamples, -1)
-print(images.shape)  # (2, 1000000)
-# Instantiate structure tensor operator
-structure_tensor = StructureTensor(arg_shape=arg_shape)
-
-outputs = structure_tensor(images)
-print(outputs.shape)  # (2, 3000000)
-# Plot
-outputs = structure_tensor.unravel(outputs)
-print(outputs.shape)  # (2, 3, 1000, 1000)
-plt.figure()
-plt.imshow(images[0].reshape(arg_shape))
-plt.colorbar()
-plt.title("Image")
-plt.axis("off")
-
-plt.figure()
-plt.imshow(outputs[0][0].reshape(arg_shape))
-plt.colorbar()
-plt.title(r"$\hat{S}_{xx}$")
-plt.axis("off")
-
-plt.figure()
-plt.imshow(outputs[0][1].reshape(arg_shape))
-plt.colorbar()
-plt.title(r"$\hat{S}_{xy}$")
-plt.axis("off")
-
-plt.figure()
-plt.imshow(outputs[0][2].reshape(arg_shape))
-plt.colorbar()
-plt.title(r"$\hat{S}_{yy}$")
-plt.axis("off")
\ No newline at end of file
diff --git a/plot_directive/api/operator-21_00.hires.png b/plot_directive/api/operator-21_00.hires.png
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diff --git a/plot_directive/api/operator-3.py b/plot_directive/api/operator-3.py
deleted file mode 100644
index 725e0ddf..00000000
--- a/plot_directive/api/operator-3.py
+++ /dev/null
@@ -1,40 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import PartialDerivative
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # Shape of our image
-# Specify derivative order at each direction
-df_dx = (1, 0)  # Compute derivative of order 1 in first dimension
-d2f_dy2 = (0, 2)  # Compute derivative of order 2 in second dimension
-d3f_dxdy2 = (1, 2)  # Compute derivative of order 1 in first dimension and der. of order 2 in second dimension
-# Instantiate derivative operators
-sigma = 2.0
-diff1 = PartialDerivative.gaussian_derivative(order=df_dx, arg_shape=arg_shape, sigma=sigma / np.sqrt(2))
-diff2 = PartialDerivative.gaussian_derivative(order=d2f_dy2, arg_shape=arg_shape, sigma=sigma / np.sqrt(2))
-diff = PartialDerivative.gaussian_derivative(order=d3f_dxdy2, arg_shape=arg_shape, sigma=sigma)
-# Compute derivatives
-out1 = (diff1 * diff2)(image.ravel()).reshape(arg_shape)
-out2 = diff(image.ravel()).reshape(arg_shape)
-# Plot derivatives
-fig, axs = plt.subplots(1, 3, figsize=(15, 4))
-im = axs[0].imshow(image)
-axs[0].axis("off")
-axs[0].set_title("f(x,y)")
-plt.colorbar(im, ax=axs[0])
-axs[1].imshow(out1)
-axs[1].axis("off")
-axs[1].set_title(r"$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$")
-plt.colorbar(im, ax=axs[1])
-
-axs[2].imshow(out2)
-axs[2].axis("off")
-axs[2].set_title(r"$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$")
-plt.colorbar(im, ax=axs[2])
-
-# Test approximation error
-plt.figure()
-plt.imshow(abs(out1 - out2) / abs(out2)), plt.colorbar()
\ No newline at end of file
diff --git a/plot_directive/api/operator-3_00.hires.png b/plot_directive/api/operator-3_00.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-4.py b/plot_directive/api/operator-4.py
deleted file mode 100644
index bfe7ebc3..00000000
--- a/plot_directive/api/operator-4.py
+++ /dev/null
@@ -1,33 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import PartialDerivative
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # Shape of our image
-# Specify derivative order at each direction
-df_dx = (1, 0) # Compute derivative of order 1 in first dimension
-d2f_dy2 = (0, 2) # Compute derivative of order 2 in second dimension
-d3f_dxdy2 = (1, 2) # Compute derivative of order 1 in first dimension and der. of order 2 in second dimension
-# Instantiate derivative operators
-diff1 = PartialDerivative.gaussian_derivative(order=df_dx, arg_shape=arg_shape, sigma=2.0)
-diff2 = PartialDerivative.gaussian_derivative(order=d2f_dy2, arg_shape=arg_shape, sigma=2.0)
-diff = PartialDerivative.gaussian_derivative(order=d3f_dxdy2, arg_shape=arg_shape, sigma=2.0)
-# Compute derivatives
-out1 = (diff1 * diff2)(image.ravel()).reshape(arg_shape)
-out2 = diff(image.ravel()).reshape(arg_shape)
-plt.figure()
-plt.imshow(image),
-plt.axis('off')
-plt.colorbar()
-plt.title('f(x,y)')
-plt.figure()
-plt.imshow(out1.T)
-plt.axis('off')
-plt.title(r'$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$')
-plt.figure()
-plt.imshow(out2.T)
-plt.axis('off')
-plt.title(r'$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$')
\ No newline at end of file
diff --git a/plot_directive/api/operator-4_00.hires.png b/plot_directive/api/operator-4_00.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-5.py b/plot_directive/api/operator-5.py
deleted file mode 100644
index caacd6b1..00000000
--- a/plot_directive/api/operator-5.py
+++ /dev/null
@@ -1,34 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Gradient
-from pyxu.util.misc import peaks
-
-# Define input image
-n = 100
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # (1000, 1000)
-# Instantiate gradient operator
-grad = Gradient(arg_shape=arg_shape)
-
-# Compute gradients
-output = grad(image.ravel()) # shape = (2000000, )
-df_dx, df_dy = grad.unravel(output) # shape = (2, 1000, 1000)
-
-# Plot image
-fig, axs = plt.subplots(1, 3, figsize=(15, 4))
-im = axs[0].imshow(image)
-axs[0].set_title("Image")
-axs[0].axis("off")
-plt.colorbar(im, ax=axs[0])
-
-# Plot gradient
-im = axs[1].imshow(df_dx)
-axs[1].set_title(r"$\partial f/ \partial x$")
-axs[1].axis("off")
-plt.colorbar(im, ax=axs[1])
-im = axs[2].imshow(df_dy)
-axs[2].set_title(r"$\partial f/ \partial y$")
-axs[2].axis("off")
-plt.colorbar(im, ax=axs[2])
\ No newline at end of file
diff --git a/plot_directive/api/operator-6.hires.png b/plot_directive/api/operator-6.hires.png
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diff --git a/plot_directive/api/operator-6.py b/plot_directive/api/operator-6.py
deleted file mode 100644
index 088a74fe..00000000
--- a/plot_directive/api/operator-6.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Jacobian
-from pyxu.util.misc import peaks
-
-x = np.linspace(-2.5, 2.5, 25)
-xx, yy = np.meshgrid(x, x)
-image = np.tile(peaks(xx, yy), (3, 1, 1))
-jac = Jacobian(arg_shape=image.shape[1:], n_channels=image.shape[0])
-out = jac.unravel(jac(image.ravel()))
-fig, axes = plt.subplots(3, 2, figsize=(10, 15))
-for i in range(3):
-    for j in range(2):
-        axes[i, j].imshow(out[i, j].T, cmap=["Reds", "Greens", "Blues"][j])
-        axes[i, j].set_title(f"$\partial I_{{{['R', 'G', 'B'][j]}}}/\partial{{{['x', 'y'][j]}}}$")
-plt.suptitle("Jacobian")
\ No newline at end of file
diff --git a/plot_directive/api/operator-7.hires.png b/plot_directive/api/operator-7.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-7.py b/plot_directive/api/operator-7.py
deleted file mode 100644
index df749166..00000000
--- a/plot_directive/api/operator-7.py
+++ /dev/null
@@ -1,25 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Gradient, Divergence, Laplacian
-from pyxu.util.misc import peaks
-
-n = 100
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # (1000, 1000)
-grad = Gradient(arg_shape=arg_shape)
-div = Divergence(arg_shape=arg_shape)
-# Construct Laplacian via composition
-laplacian1 = div * grad
-# Compare to default Laplacian
-laplacian2 = Laplacian(arg_shape=arg_shape)
-output1 = laplacian1(image.ravel())
-output2 = laplacian2(image.ravel())
-fig, axes = plt.subplots(1, 2, figsize=(10, 5))
-im = axes[0].imshow(np.log(abs(output1)).reshape(*arg_shape))
-axes[0].set_title("Laplacian via composition")
-plt.colorbar(im, ax=axes[0])
-im = axes[1].imshow(np.log(abs(output1)).reshape(*arg_shape))
-axes[1].set_title("Default Laplacian")
-plt.colorbar(im, ax=axes[1])
\ No newline at end of file
diff --git a/plot_directive/api/operator-8.hires.png b/plot_directive/api/operator-8.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-8.py b/plot_directive/api/operator-8.py
deleted file mode 100644
index a64c708c..00000000
--- a/plot_directive/api/operator-8.py
+++ /dev/null
@@ -1,38 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Hessian, PartialDerivative
-from pyxu.util.misc import peaks
-
-n = 100
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-arg_shape = image.shape  # (1000, 1000)
-
-# Instantiate Hessian operator
-hessian = Hessian(arg_shape=arg_shape, directions="all")
-# Compute Hessian
-output = hessian(image.ravel()) # shape = (300000,)
-d2f_dx2, d2f_dxdy, d2f_dy2 = hessian.unravel(output)
-
-# Plot
-fig, axs = plt.subplots(1, 4, figsize=(20, 4))
-im = axs[0].imshow(image)
-plt.colorbar(im, ax=axs[0])
-axs[0].set_title("Image")
-axs[0].axis("off")
-
-im = axs[1].imshow(d2f_dx2)
-plt.colorbar(im, ax=axs[1])
-axs[1].set_title(r"$\partial^{2} f/ \partial x^{2}$")
-axs[1].axis("off")
-
-im = axs[2].imshow(d2f_dxdy)
-plt.colorbar(im, ax=axs[2])
-axs[2].set_title(r"$\partial^{2} f/ \partial x\partial y$")
-axs[2].axis("off")
-
-im = axs[3].imshow(d2f_dy2)
-plt.colorbar(im, ax=axs[3])
-axs[3].set_title(r"$\partial^{2} f/ \partial y^{2}$")
-axs[3].axis("off")
\ No newline at end of file
diff --git a/plot_directive/api/operator-9.hires.png b/plot_directive/api/operator-9.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/operator-9.py b/plot_directive/api/operator-9.py
deleted file mode 100644
index ccb1eef9..00000000
--- a/plot_directive/api/operator-9.py
+++ /dev/null
@@ -1,29 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-from pyxu.operator import Laplacian
-from pyxu.util.misc import peaks
-
-# Define input image
-n = 100
-x = np.linspace(-3, 3, n)
-xx, yy = np.meshgrid(x, x)
-image = peaks(xx, yy)
-
-arg_shape = image.shape  # (1000, 1000)
-# Compute Laplacian
-laplacian = Laplacian(arg_shape=arg_shape)
-output = laplacian(image.ravel())
-output = laplacian.unravel(output) # shape = (1, 1000, 1000)
-# Plot
-fig, axs = plt.subplots(1, 2, figsize=(10, 4))
-im = axs[0].imshow(image)
-plt.colorbar(im, ax=axs[0])
-axs[0].set_title("Image")
-axs[0].axis("off")
-
-im = axs[1].imshow(output.squeeze())
-plt.colorbar(im, ax=axs[1])
-axs[1].set_title(r"$\partial^{2} f/ \partial x^{2}+\partial^{2} f/ \partial y^{2}$")
-axs[1].axis("off")
-
-fig.show()
\ No newline at end of file
diff --git a/plot_directive/api/operator/linop-1.pdf b/plot_directive/api/operator/linop-1.pdf
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diff --git a/plot_directive/api/operator/linop-10_00.pdf b/plot_directive/api/operator/linop-10_00.pdf
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diff --git a/plot_directive/api/operator/linop-10_01.pdf b/plot_directive/api/operator/linop-10_01.pdf
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diff --git a/plot_directive/api/operator/linop-10_02.pdf b/plot_directive/api/operator/linop-10_02.pdf
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diff --git a/plot_directive/api/operator/linop-10_03.pdf b/plot_directive/api/operator/linop-10_03.pdf
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diff --git a/plot_directive/api/operator/linop-11.py b/plot_directive/api/operator/linop-11.py
index 725e0ddf..9b92fec1 100644
--- a/plot_directive/api/operator/linop-11.py
+++ b/plot_directive/api/operator/linop-11.py
@@ -35,6 +35,6 @@
 axs[2].set_title(r"$\frac{\partial^{3} f(x,y)}{\partial x\partial y^{2}}$")
 plt.colorbar(im, ax=axs[2])
 
-# Test approximation error
+# Check approximation error
 plt.figure()
-plt.imshow(abs(out1 - out2) / abs(out2)), plt.colorbar()
\ No newline at end of file
+plt.imshow(abs(out1 - out2)), plt.colorbar()
\ No newline at end of file
diff --git a/plot_directive/api/operator/linop-11_00.pdf b/plot_directive/api/operator/linop-11_00.pdf
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diff --git a/plot_directive/api/operator/linop-11_01.pdf b/plot_directive/api/operator/linop-11_01.pdf
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diff --git a/plot_directive/api/operator/linop-13_01.hires.png b/plot_directive/api/operator/linop-13_01.hires.png
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diff --git a/plot_directive/api/operator/linop-19_02.pdf b/plot_directive/api/operator/linop-19_02.pdf
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diff --git a/plot_directive/api/operator/linop-2.pdf b/plot_directive/api/operator/linop-2.pdf
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diff --git a/plot_directive/api/opt-1.py b/plot_directive/api/opt-1.py
deleted file mode 100644
index 982b2492..00000000
--- a/plot_directive/api/opt-1.py
+++ /dev/null
@@ -1,31 +0,0 @@
-import matplotlib.pyplot as plt
-import numpy as np
-import pyxu.operator as pxo
-from pyxu.experimental._dev import DownSampling, FirstDerivative
-from pyxu.opt.solver import CV
-
-x = np.repeat(np.asarray([0, 2, 1, 3, 0, 2, 0]), 10)
-N = x.size
-
-D = FirstDerivative(size=N, kind="forward")
-D.lipschitz = D.estimate_lipschitz()
-
-downsample = DownSampling(size=N, downsampling_factor=3)
-y = downsample(x)
-loss = (1 / 2) * pxo.SquaredL2Norm(y.size).argshift(-y)
-F = loss * downsample
-F.diff_lipschitz = F.estimate_diff_lipschitz()
-
-cv = CV(f=F, g=0.01 * pxo.L1Norm(N), h=0.1 * pxo.L1Norm(N), K=D)
-x0, z0 = np.zeros((2, N))
-cv.fit(x0=x0, z0=z0)
-x_recons = cv.solution()[0]
-
-plt.figure()
-plt.stem(x, linefmt="C0-", markerfmt="C0o")
-mask_ids = np.where(downsample.downsampling_mask)[0]
-markerline, stemlines, baseline = plt.stem(mask_ids, y, linefmt="C3-", markerfmt="C3o")
-markerline.set_markerfacecolor("none")
-plt.stem(x_recons, linefmt="C1--", markerfmt="C1s")
-plt.legend(["Ground truth", "Observation", "CV Estimate"])
-plt.show()
\ No newline at end of file
diff --git a/plot_directive/api/opt-2.hires.png b/plot_directive/api/opt-2.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/opt-2.py b/plot_directive/api/opt-2.py
deleted file mode 100644
index 50219928..00000000
--- a/plot_directive/api/opt-2.py
+++ /dev/null
@@ -1,31 +0,0 @@
-import matplotlib.pyplot as plt
-import numpy as np
-import pyxu.operator as pxo
-from pyxu.experimental._dev import DownSampling, FirstDerivative
-from pyxu.opt.solver import PD3O
-
-x = np.repeat(np.asarray([0, 2, 1, 3, 0, 2, 0]), 10)
-N = x.size
-
-D = FirstDerivative(size=N, kind="forward")
-D.lipschitz = D.estimate_lipschitz()
-
-downsample = DownSampling(size=N, downsampling_factor=3)
-y = downsample(x)
-loss = (1 / 2) * pxo.SquaredL2Norm(y.size).argshift(-y)
-F = loss * downsample
-F.diff_lipschitz = F.estimate_diff_lipschitz()
-
-pd3o = PD3O(f=F, g=0.01 * pxo.L1Norm(N), h=0.1 * pxo.L1Norm(N), K=D)
-x0, z0 = np.zeros((2, N))
-pd3o.fit(x0=x0, z0=z0)
-x_recons = pd3o.solution()[0]
-
-plt.figure()
-plt.stem(x, linefmt="C0-", markerfmt="C0o")
-mask_ids = np.where(downsample.downsampling_mask)[0]
-markerline, stemlines, baseline = plt.stem(mask_ids, y, linefmt="C3-", markerfmt="C3o")
-markerline.set_markerfacecolor("none")
-plt.stem(x_recons, linefmt="C1--", markerfmt="C1s")
-plt.legend(["Ground truth", "Observation", "PD3O Estimate"])
-plt.show()
\ No newline at end of file
diff --git a/plot_directive/api/opt-3.hires.png b/plot_directive/api/opt-3.hires.png
deleted file mode 100644
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diff --git a/plot_directive/api/opt-3.py b/plot_directive/api/opt-3.py
deleted file mode 100644
index 2b58eeeb..00000000
--- a/plot_directive/api/opt-3.py
+++ /dev/null
@@ -1,58 +0,0 @@
-import matplotlib.pyplot as plt
-import numpy as np
-import pyxu.abc as pxa
-import pyxu.operator as pxo
-import scipy as sp
-from pyxu.opt.solver import ADMM
-
-N = 100  # Dimension of the problem
-
-# Generate piecewise-linear ground truth
-x_gt = np.array([10, 25, 60, 90])  # Knot locations
-a_gt = np.array([2, -4, 3, -2])  # Amplitudes of the knots
-gt = np.zeros(N)  # Ground-truth signal
-for n in range(len(x_gt)):
-    gt[x_gt[n] :] += a_gt[n] * np.arange(N - x_gt[n]) / N
-
-# Generate data (noisy samples at random locations)
-M = 20  # Number of data points
-rng = np.random.default_rng(seed=0)
-x_samp = rng.choice(np.arange(N // M), size=M) + np.arange(N, step=N // M)  # sampling locations
-sigma = 2 * 1e-2  # noise variance
-y = gt[x_samp] + sigma * rng.standard_normal(size=M)  # noisy data points
-
-# Data-fidelity term
-subsamp_mat = sp.sparse.lil_matrix((M, N))
-for i in range(M):
-    subsamp_mat[i, x_samp[i]] = 1
-G = pxa.LinOp.from_array(subsamp_mat.tocsr())
-F = 1 / 2 * pxo.SquaredL2Norm(dim=y.size).argshift(-y) * G
-F.diff_lipschitz = F.estimate_diff_lipschitz(method="svd")
-
-# Regularization term (promotes sparse second derivatives)
-deriv_mat = sp.sparse.diags(diagonals=[1, -2, 1], offsets=[0, 1, 2], shape=(N - 2, N))
-D = pxa.LinOp.from_array(deriv_mat)
-_lambda = 1e-1  # regularization parameter
-H = _lambda * pxo.L1Norm(dim=D.codim)
-
-# Solver for ADMM
-tau = 1 / _lambda  # internal ADMM parameter
-# Inverse operator to solve the linear system
-A_inv = sp.linalg.inv(G.gram().asarray() + (1 / tau) * D.gram().asarray())
-
-def solver_ADMM(arr, tau):
-    b = (1 / tau) * D.adjoint(arr) + G.adjoint(y)
-    return A_inv @ b.squeeze()
-
-
-# Solve optimization problem
-admm = ADMM(f=F, h=H, K=D, solver=solver_ADMM,show_progress=False)  # with solver
-admm.fit(x0=np.zeros(N), tau=tau)
-x_opt = admm.solution()  # reconstructed signal
-
-# Plots
-plt.figure()
-plt.plot(np.arange(N), gt, label="Ground truth")
-plt.plot(x_samp, y, "kx", label="Noisy data points")
-plt.plot(np.arange(N), x_opt, label="Reconstructed signal")
-plt.legend()
\ No newline at end of file
diff --git a/plot_directive/api/opt-solver-1.pdf b/plot_directive/api/opt-solver-1.pdf
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diff --git a/plot_directive/api/opt-solver-3.pdf b/plot_directive/api/opt-solver-3.pdf
index 7f6968b95a6df2d2ddcbae9bcf4285fda604f9ca..46984fa4550d9fbc06be62b47630b769812da261 100644
GIT binary patch
delta 20
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delta 20
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diff --git a/plot_directive/api/opt-solver-3.png b/plot_directive/api/opt-solver-3.png
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 <span class="label"><span class="fn-bracket">[</span>ProxAdam<span class="fn-bracket">]</span></span>
 <p>Melchior, Joseph, Moolekamp. “Proximal Adam: Robust Adaptive Update Scheme for Constrained Optimization” (2020).</p>
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 <p>Rockafellar, R. Tyrrell. “Monotone operators and the proximal point algorithm.” SIAM journal on control and optimization 14.5 (1976): 877-898.</p>
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 <p>Alain Durmus, Éric Moulines, and Marcelo Pereyra, “Efficient Bayesian Computation by Proximal Markov Chain Monte Carlo: When Langevin Meets Moreau”, SIAM Journal of Imaging Science, 2018</p>
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[[57, "ecosystem"]], "Governance and Team": [[57, "governance-and-team"]], "Steering Council": [[57, "steering-council"]], "Contributors": [[57, "contributors"]], "Partners & Sponsors": [[57, "partners-sponsors"]], "Getting Started": [[59, "getting-started"]], "What Makes Pyxu Special?": [[59, "what-makes-pyxu-special"]], "Why is Pyxu Necessary?": [[59, "why-is-pyxu-necessary"]], "Get Started Now!": [[59, "get-started-now"]], "Join Our Community": [[59, "join-our-community"]], "User Guide": [[55, "user-guide"]], "Comparison with other Frameworks": [[58, "comparison-with-other-frameworks"]], "Main Contenders": [[58, "main-contenders"]], "Comparative Analysis": [[58, "comparative-analysis"]], "Features and Maturity": [[58, "features-and-maturity"]], "Feature Maturity Comparison": [[58, "id2"]], "Ease-of-Use": [[58, "ease-of-use"]], "Support for HPC Computing": [[58, "support-for-hpc-computing"]], "HPC Features Comparison": [[58, "id3"]], "SCICO: A Closer Look": [[58, "scico-a-closer-look"]], "DeepInv: A Note on Usability": [[58, "deepinv-a-note-on-usability"]], "Conclusion": [[58, "conclusion"]], "Lipschitz Constants and Automatic Step Size Tuning": [[56, "Lipschitz-Constants-and-Automatic-Step-Size-Tuning"]], "Introduction to Lipschitz Constants": [[56, "Introduction-to-Lipschitz-Constants"]], "Accessing Lipschitz Constants": [[56, "Accessing-Lipschitz-Constants"]], "Estimating Lipschitz Constants": [[56, "Estimating-Lipschitz-Constants"]], "Supported Backends \ud83c\udf9b\ufe0f": [[56, "Supported-Backends-\ud83c\udf9b\ufe0f"]], "Hands-On Example \ud83c\udf93": [[56, "Hands-On-Example-\ud83c\udf93"]], "Operator Algebra and Lipschitz Constant Propagation": [[56, "Operator-Algebra-and-Lipschitz-Constant-Propagation"]], "Convolution with Pyxu": [[25, "Convolution-with-Pyxu"]], "0) Install dependencies": [[25, "0)-Install-dependencies"]], "1) Prepare data": [[25, "1)-Prepare-data"]], "Create input image": [[25, "Create-input-image"]], "Create blurring 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"pyxu.math": [[9, "module-pyxu.math"], [5, "pyxu-math"]], "pyxu.info.ptype": [[7, "module-pyxu.info.ptype"], [5, "pyxu-info-ptype"]], "API Reference": [[5, "api-reference"]], "pyxu.abc": [[5, "pyxu-abc"], [1, "pyxu-abc"]], "Operator-related": [[5, "operator-related"]], "Solver-related": [[5, "solver-related"]], "Arithmetic Rules (low-level)": [[5, "arithmetic-rules-low-level"]], "pyxu.experimental.sampler": [[5, "pyxu-experimental-sampler"], [4, "module-pyxu.experimental.sampler"]], "pyxu.info.warning": [[5, "pyxu-info-warning"], [8, "module-pyxu.info.warning"]], "pyxu.operator.interop": [[5, "pyxu-operator-interop"], [10, "pyxu-operator-interop"]], "General": [[5, "general"], [10, "general"]], "SciPy": [[5, "scipy"], [10, "scipy"]], "JAX": [[5, "jax"], [10, "jax"]], "PyTorch": [[5, "pytorch"], [10, "pytorch"]], "pyxu.operator": [[5, "pyxu-operator"], [13, "pyxu-operator"]], "Functionals": [[5, "functionals"]], "Norms & Loss Functions": [[5, "norms-loss-functions"], [12, "norms-loss-functions"]], "Indicator Functions": [[5, "indicator-functions"], [12, "indicator-functions"]], "Linear Operators": [[5, "linear-operators"]], "Basic Operators": [[5, "basic-operators"], [14, "basic-operators"]], "Transforms": [[5, "transforms"], [14, "transforms"]], "Stencils & Convolutions": [[5, "stencils-convolutions"], [14, "stencils-convolutions"]], "Filters": [[5, "filters"], [14, "filters"]], "Derivatives": [[5, "derivatives"], [14, "derivatives"]], "Tensor Products": [[5, "tensor-products"], [14, "tensor-products"]], "Block-defined Operators": [[5, "block-defined-operators"]], "pyxu.util": [[5, "pyxu-util"], [21, "pyxu-util"]], "Array Backend-Related": [[5, "array-backend-related"]], "Complex Number Handling": [[5, "complex-number-handling"]], "Operator-Related": [[5, "id2"]], "Differential operators in Pyxu": [[24, "Differential-operators-in-Pyxu"]], "1. Partial derivatives": [[24, "1.-Partial-derivatives"]], "1.1. Parameters": [[24, "1.1.-Parameters"]], "1.2. Finite differences": [[24, "1.2.-Finite-differences"]], "1.3.Gaussian derivative": [[24, "1.3.Gaussian-derivative"]], "1.4. How to choose?": [[24, "1.4.-How-to-choose?"]], "2. Stacks of partial derivatives": [[24, "2.-Stacks-of-partial-derivatives"]], "2.1. Parameters": [[24, "2.1.-Parameters"]], "2.2. Gradient": [[24, "2.2.-Gradient"]], "2.3. 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"installation-with-optional-dependencies"]], "Developer Installation": [[60, "developer-installation"]], "Interoperation with Deep Learning Frameworks": [[60, "interoperation-with-deep-learning-frameworks"]], "You\u2019re All Set!": [[60, "you-re-all-set"]], "Hands-on Example: Computerized Tomography with Pyxu": [[62, "Hands-on-Example:-Computerized-Tomography-with-Pyxu"]], "Tomographic Reconstruction in a Nutshell": [[62, "Tomographic-Reconstruction-in-a-Nutshell"]], "A Non-Ideal Parallel-beam Tomographic Setup": [[62, "A-Non-Ideal-Parallel-beam-Tomographic-Setup"]], "Naive Application of Filtered-Back Projection": [[62, "Naive-Application-of-Filtered-Back-Projection"]], "Pyxu\u2019s Modularity to the Rescue": [[62, "Pyxu's-Modularity-to-the-Rescue"]], "Image Reconstruction with Pyxu": [[62, "Image-Reconstruction-with-Pyxu"]], "Pseudoinverse Solution": [[62, "Pseudoinverse-Solution"]], "Bayesian Inversion": [[62, "Bayesian-Inversion"]], "Plug-and-Play Reconstruction Schemes": [[62, 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"Computational-Imaging-in-a-Nutshell"]], "The Multi-faceted Realm of Computational Imaging": [[58, "The-Multi-faceted-Realm-of-Computational-Imaging"]], "The Dawn of Computational Imaging": [[58, "The-Dawn-of-Computational-Imaging"]], "Bayesian Computational Imaging": [[58, "Bayesian-Computational-Imaging"]], "The Deep Learning Revolution": [[58, "The-Deep-Learning-Revolution"]], "The Adoptability and Usability Crisis of Computational Imaging": [[58, "The-Adoptability-and-Usability-Crisis-of-Computational-Imaging"]], "Pyxu: High-Performance Computational Imaging with Python": [[58, "Pyxu:-High-Performance-Computational-Imaging-with-Python"]], "Installation": [[57, "installation"]], "Basic Installation": [[57, "basic-installation"]], "Installation with Optional Dependencies": [[57, "installation-with-optional-dependencies"]], "Developer Installation": [[57, "developer-installation"]], "Interoperation with Deep Learning Frameworks": [[57, "interoperation-with-deep-learning-frameworks"]], 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\ No newline at end of file