Some more small things (#611)

examples/notebooks/iterative_sense_reconstruction_radial2D.ipynb

@@ -241,7 +241,7 @@
    "source": [
     "## Set up density compensation operator $W$\n",
     "We create a density compensation operator $W$ for weighting the loss. We use\n",
-    "Voronoi tesselation of the trajectory to calculate the `~mrpro.data.DcfData`.\n",
+    "Voronoi tessellation of the trajectory to calculate the `~mrpro.data.DcfData`.\n",
     "\n",
     "```{note}\n",
     "Using a weighted loss in iterative SENSE is not necessary, and there has been some discussion about\n",

examples/scripts/iterative_sense_reconstruction_radial2D.py

@@ -110,7 +110,7 @@
 # %% [markdown]
 # ## Set up density compensation operator $W$
 # We create a density compensation operator $W$ for weighting the loss. We use
-# Voronoi tesselation of the trajectory to calculate the `~mrpro.data.DcfData`.
+# Voronoi tessellation of the trajectory to calculate the `~mrpro.data.DcfData`.
 #
 # ```{note}
 # Using a weighted loss in iterative SENSE is not necessary, and there has been some discussion about

src/mrpro/algorithms/dcf/dcf_voronoi.py

@@ -19,7 +19,7 @@ def dcf_1d(traj: torch.Tensor) -> torch.Tensor:
     """Calculate sample density compensation function for 1D trajectory.
 
     This function operators on a single `other` sample.
-    See also `~mrpro.data.DCFData` and `mrpro.utils.smap`
+    See also `~mrpro.data.DcfData` and `mrpro.utils.smap`
 
     Parameters
     ----------
@@ -72,7 +72,7 @@ def dcf_2d3d_voronoi(traj: torch.Tensor) -> torch.Tensor:
     DCF is then computed based on the inverse of the area of these regions.
 
     This function operators on a single `other` sample.
-    See also `~mrpro.data.DCFData` and `mrpro.utils.smap`
+    See also `~mrpro.data.DcfData` and `mrpro.utils.smap`
 
     Parameters
     ----------

src/mrpro/algorithms/optimizers/cg.py

@@ -71,7 +71,7 @@ def cg(
     .. [Hestenes1952] Hestenes, M. R., & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems.
        Journal of Research of the National Bureau of Standards , 49(6), 409-436
     .. [Nocedal2006] Nocedal, J. (2006). *Numerical Optimization* (2nd ed.). Springer.
-    .. [WikipediaCG] `Wikipedia: Conjugate Gradient<https://en.wikipedia.org/wiki/Conjugate_gradient>_`
+    .. [WikipediaCG] Wikipedia: Conjugate Gradient https://en.wikipedia.org/wiki/Conjugate_gradient
     """
     if initial_value is not None and (initial_value.shape != right_hand_side.shape):
         raise ValueError(

src/mrpro/algorithms/optimizers/lbfgs.py

@@ -53,11 +53,10 @@ def lbfgs(
     References
     ----------
     .. [NOC1980] Nocedal, J. (1980). "Updating quasi-Newton matrices with limited storage."
-       *Mathematics of Computation*, 35(151), 773-782.
-       `10.1090/S0025-5718-1980-0572855-7<https://doi.org/10.1090/S0025-5718-1980-0572855-7>_`
+       *Mathematics of Computation*, 35(151), 773-782. https://doi.org/10.1090/S0025-5718-1980-0572855-7
     .. [LIU1989] Liu, D. C., & Nocedal, J. (1989). "On the limited memory BFGS method for large scale optimization."
-       *Mathematical Programming*, 45(1-3), 503-528. `10.1007/BF01589116<https://doi.org/10.1007/BF01589116>_`
-    .. [WIKI] Wikipedia: `Limited-memory_BFGS <https://en.wikipedia.org/wiki/Limited-memory_BFGS>`_
+       *Mathematical Programming*, 45(1-3), 503-528. https://doi.org/10.1007/BF01589116
+    .. [WIKI] Wikipedia: Limited-memory_BFGS https://en.wikipedia.org/wiki/Limited-memory_BFGS
 
 
     Parameters

src/mrpro/data/DcfData.py

@@ -23,7 +23,7 @@ class DcfData(MoveDataMixin):
     """Density compensation data (DcfData) class."""
 
     data: torch.Tensor
-    """Density compensation values. Shape (... other, k2, k1, k0)"""
+    """Density compensation values. Shape `(... other, k2, k1, k0)`"""
 
     @classmethod
     def from_traj_voronoi(cls, traj: KTrajectory) -> Self:

src/mrpro/data/Rotation.py

@@ -1768,8 +1768,8 @@ def align_vectors(
 
         where :math:`w_i`'s are the `weights` corresponding to each vector.
 
-        The rotation is estimated with Kabsch algorithm [1]_, and solves what
-        is known as the "pointing problem", or "Wahba's problem" [2]_.
+        The rotation is estimated with Kabsch algorithm [KAB]_, and solves what
+        is known as the "pointing problem", or "Wahba's problem" [WAH]_.
 
         There are two special cases. The first is if a single vector is given
         for `a` and `b`, in which the shortest distance rotation that aligns
@@ -1781,7 +1781,7 @@ def align_vectors(
         of these two rotations. The result via this process is the same as the
         Kabsch algorithm as the corresponding weight approaches infinity in
         the limit. For a single secondary vector this is known as the
-        "align-constrain" algorithm [3]_.
+        "align-constrain" algorithm [MAG2018]_.
 
         For both special cases (single vectors or an infinite weight), the
         sensitivity matrix does not have physical meaning and an error will be
@@ -1822,12 +1822,10 @@ def align_vectors(
 
         References
         ----------
-        .. [1] https://en.wikipedia.org/wiki/Kabsch_algorithm
-        .. [2] https://en.wikipedia.org/wiki/Wahba%27s_problem
-        .. [3] Magner, Robert,
-                "Extending target tracking capabilities through trajectory and
-                momentum setpoint optimization." Small Satellite Conference,
-                2018.
+        .. [KAB] https://en.wikipedia.org/wiki/Kabsch_algorithm
+        .. [WAH] https://en.wikipedia.org/wiki/Wahba%27s_problem
+        .. [MAG2018] Magner R (2018), Extending target tracking capabilities through trajectory and momentum setpoint
+           optimization. Small Satellite Conference.
         """
         a_tensor = torch.stack([torch.as_tensor(el) for el in a]) if isinstance(a, Sequence) else torch.as_tensor(a)
         b_tensor = torch.stack([torch.as_tensor(el) for el in b]) if isinstance(b, Sequence) else torch.as_tensor(b)

src/mrpro/operators/models/InversionRecovery.py

@@ -36,7 +36,7 @@ def forward(self, m0: torch.Tensor, t1: torch.Tensor) -> tuple[torch.Tensor,]:
 
         Returns
         -------
-            signal with shape `(time *other, coils, z, y, x)`
+            signal with shape `(time, *other, coils, z, y, x)`
         """
         ti = unsqueeze_right(self.ti, m0.ndim - (self.ti.ndim - 1))  # -1 for time
         signal = m0 * (1 - 2 * torch.exp(-(ti / t1)))

src/mrpro/operators/models/MOLLI.py

@@ -50,7 +50,7 @@ def forward(self, a: torch.Tensor, c: torch.Tensor, t1: torch.Tensor) -> tuple[t
 
         Returns
         -------
-            signal with shape `(time *other, coils, z, y, x)`
+            signal with shape `(time, *other, coils, z, y, x)`
         """
         ti = unsqueeze_right(self.ti, a.ndim - (self.ti.ndim - 1))  # -1 for time
         signal = a * (1 - c * torch.exp(ti / t1 * (1 - c)))

src/mrpro/operators/models/MonoExponentialDecay.py

@@ -36,7 +36,7 @@ def forward(self, m0: torch.Tensor, decay_constant: torch.Tensor) -> tuple[torch
 
         Returns
         -------
-            signal with shape `(time *other, coils, z, y, x)`
+            signal with shape `(time, *other, coils, z, y, x)`
         """
         decay_time = unsqueeze_right(self.decay_time, m0.ndim - (self.decay_time.ndim - 1))  # -1 for time
         signal = m0 * torch.exp(-(decay_time / decay_constant))

src/mrpro/operators/models/SaturationRecovery.py

@@ -36,7 +36,7 @@ def forward(self, m0: torch.Tensor, t1: torch.Tensor) -> tuple[torch.Tensor,]:
 
         Returns
         -------
-            signal with shape `(time *other, coils, z, y, x)`
+            signal with shape `(time, *other, coils, z, y, x)`
         """
         ti = unsqueeze_right(self.ti, m0.ndim - (self.ti.ndim - 1))  # -1 for time
         signal = m0 * (1 - torch.exp(-(ti / t1)))

src/mrpro/operators/models/TransientSteadyStateWithPreparation.py

@@ -24,7 +24,7 @@ class TransientSteadyStateWithPreparation(SignalModel[torch.Tensor, torch.Tensor
 
     - Part B: Commonly after an inversion pulse a strong spoiler gradient is played out to compensate for non-perfect
       inversion. During this time the magnetization :math:`M_z(t)` follows the signal model:
-      :math:`M_z(t) = M_0 + (s * M_0 - M_0)e^{(-t / T1)}` where :math:`s` is ``m0_scaling_preparation``.
+      :math:`M_z(t) = M_0 + (s * M_0 - M_0)e^{(-t / T1)}` where :math:`s` is `m0_scaling_preparation`.
 
     - Part C: After the spoiler gradient the data acquisition starts and the magnetization :math:`M_z(t)` can be
       described by the signal model: :math:`M_z(t) = M_0^* + (M_{init} - M_0^*)e^{(-t / T1^*)}`
@@ -101,7 +101,7 @@ def forward(self, m0: torch.Tensor, t1: torch.Tensor, flip_angle: torch.Tensor)
 
         Returns
         -------
-            signal with shape `(time *other, coils, z, y, x)`
+            signal with shape `(time, *other, coils, z, y, x)`
         """
         m0_ndim = m0.ndim
 

src/mrpro/operators/models/WASABI.py

@@ -79,7 +79,7 @@ def forward(
 
         Returns
         -------
-            signal with shape `(offsets *other, coils, z, y, x)`
+            signal with shape `(offsets, *other, coils, z, y, x)`
         """
         offsets = unsqueeze_right(self.offsets, b0_shift.ndim - (self.offsets.ndim - 1))  # -1 for offset
         delta_b0 = offsets - b0_shift

src/mrpro/operators/models/WASABITI.py

@@ -79,7 +79,7 @@ def forward(self, b0_shift: torch.Tensor, relative_b1: torch.Tensor, t1: torch.T
 
         Returns
         -------
-            signal with shape `(offsets *other, coils, z, y, x)`
+            signal with shape `(offsets, *other, coils, z, y, x)`
         """
         delta_ndim = b0_shift.ndim - (self.offsets.ndim - 1)  # -1 for offset
         offsets = unsqueeze_right(self.offsets, delta_ndim)

src/mrpro/utils/reshape.py

@@ -31,7 +31,7 @@ def unsqueeze_left(x: torch.Tensor, n: int) -> torch.Tensor:
     """Unsqueze multiple times in the leftmost dimension.
 
     Example:
-        tensor with shape `(1,2,3) `and `n=2` would result in tensor with shape `(1,1,1,2,3)`
+        tensor with shape `(1,2,3)` and `n=2` would result in tensor with shape `(1,1,1,2,3)`
 
 
     Parameters