Replace further arguments.

src/documentation_glossary.jl

@@ -143,9 +143,8 @@ define!(
 # for each variable as a symbol, we store
 # The variable name should be the symbol
 # :default – in positional or keyword arguments
-# :description – a text description of the variable (always functions)
+# :description – a text description of the variable
 # :type a type
-#
 _var(args...; kwargs...) = glossary(:Variable, args...; kwargs...)
 
 #Meta: How to format an argument, a field of a struct, and a keyword
@@ -184,7 +183,25 @@ define!(
     (; M="M", p="p") ->
         "a cost function ``f: $(_tex(:Cal, M))→ ℝ`` implemented as `($M, $p) -> v`",
 )
-define!(:Variable, :f, :type, "Any")
+define!(:Variable, :f, :type, "Function")
+
+define!(
+    :Variable,
+    :grad_f,
+    :description,
+    (; M="M", p="p") ->
+        "the (Riemannian) gradient ``$(_tex(:grad))f``: $(_math(:M, M=M)) → $(_math(:TpM; M=M, p=p)) of f as a function `(M, p) -> X` or a function `(M, X, p) -> X` computing `X` in-place",
+)
+define!(:Variable, :grad_f, :type, "Function")
+
+define!(
+    :Variable,
+    :Hess_f,
+    :description,
+    (; M="M", p="p") ->
+        "the (Riemannian) Hessian ``$(_tex(:Hess))f``: $(_math(:TpM, M=M, p=p)) → $(_math(:TpM; M=M, p=p)) of f as a function `(M, p, X) -> Y` or a function `(M, Y, p, X) -> Y` computing `Y` in-place",
+)
+define!(:Variable, :Hess_f, :type, "Function")
 
 define!(
     :Variable, :M, :description, (; M="M") -> "a Riemannian manifold ``$(_tex(:Cal, M))``"
@@ -297,14 +314,6 @@ _sc(args...; kwargs...) = glossary(:StoppingCriterion, args...; kwargs...)
 # Old strings
 
 # Arguments
-_arg_grad_f = raw"""
-* `grad_f`: the gradient ``\operatorname{grad}f: \mathcal M → T\mathcal M`` of f
-  as a function `(M, p) -> X` or a function `(M, X, p) -> X` computing `X` in-place
-"""
-_arg_Hess_f = """
-* `Hess_f`: the Hessian ``$(_tex(:Hess))_long`` of f
-  as a function `(M, p, X) -> Y` or a function `(M, Y, p, X) -> Y` computing `Y` in-place
-"""
 _arg_sub_problem = "* `sub_problem` a [`AbstractManoptProblem`](@ref) to specify a problem for a solver or a closed form solution function."
 _arg_sub_state = "* `sub_state` a [`AbstractManoptSolverState`](@ref) for the `sub_problem`."
 _arg_subgrad_f = raw"""

src/solvers/FrankWolfe.jl

@@ -185,7 +185,7 @@ use a retraction and its inverse.
 
 $(_var(:Argument, :M; type=true))
 $(_var(:Argument, :f))
-$_arg_grad_f
+$(_var(:Argument, :grad_f))
 $(_var(:Argument, :p))
 
 $(_note(:GradientObjective))

src/solvers/adaptive_regularization_with_cubics.jl

@@ -222,8 +222,8 @@ For more details see [AgarwalBoumalBullinsCartis:2020](@cite).
 
 $(_var(:Argument, :M; type=true))
 $(_var(:Argument, :f))
-$_arg_grad_f
-$_arg_Hess_f
+$(_var(:Argument, :grad_f))
+$(_var(:Argument, :Hess_f))
 $(_var(:Argument, :p))
 
 the cost `f` and its gradient and Hessian might also be provided as a [`ManifoldHessianObjective`](@ref)

src/solvers/augmented_Lagrangian_method.jl

@@ -269,7 +269,7 @@ where ``θ_ρ ∈ (0,1)`` is a constant scaling factor.
 
 $(_var(:Argument, :M; type=true))
 $(_var(:Argument, :f))
-$_arg_grad_f
+$(_var(:Argument, :grad_f))
 
 # Optional (if not called with the [`ConstrainedManifoldObjective`](@ref) `cmo`)
 

src/solvers/conjugate_gradient_descent.jl

@@ -71,7 +71,7 @@ $(_doc_update_delta_k)
 
 $(_var(:Argument, :M; type=true))
 $(_var(:Argument, :f))
-$(_arg_grad_f)
+$(_var(:Argument, :grad_f))
 $(_var(:Argument, :p))
 
 # Keyword arguments

src/solvers/exact_penalty_method.jl

@@ -214,7 +214,7 @@ $(_doc_EMP_ρ_update)
 
 $(_var(:Argument, :M; type=true))
 $(_var(:Argument, :f))
-$(_arg_grad_f)
+$(_var(:Argument, :grad_f))
 $(_var(:Argument, :p))
 
 # Keyword arguments

src/solvers/gradient_descent.jl

@@ -131,7 +131,7 @@ The algorithm can be performed in-place of `p`.
 
 $(_var(:Argument, :M; type=true))
 $(_var(:Argument, :f))
-$_arg_grad_f
+$(_var(:Argument, :grad_f))
 $(_var(:Argument, :p))
 
 $(_note(:GradientObjective))

src/solvers/interior_point_Newton.jl

@@ -37,11 +37,11 @@ the constraints are further fulfilled.
 
 # Input
 
-* `M`:      a manifold ``$(_math(:M))``
-* `f`:      a cost function ``f : $(_math(:M)) → ℝ`` to minimize
-* `grad_f`: the gradient ``$(_tex(:grad)) f : $(_math(:M)) → T $(_math(:M))`` of ``f``
-* `Hess_f`: the Hessian ``$(_tex(:Hess))f(p): T_p$(_math(:M)) → T_p$(_math(:M))``, ``X ↦ $(_tex(:Hess))f(p)[X] = ∇_X$(_tex(:grad))f(p)``
-$(_var(:Field, :p))
+$(_var(:Argument, :M))
+$(_var(:Argument, :f))
+$(_var(:Argument, :grad_f))
+$(_var(:Argument, :Hess_f))
+$(_var(:Argument, :p))
 
 or a [`ConstrainedManifoldObjective`](@ref) `cmo` containing `f`, `grad_f`, `Hess_f`, and the constraints
 

src/solvers/quasi_Newton.jl

@@ -196,7 +196,7 @@ The ``k``th iteration consists of
 
 $(_var(:Argument, :M; type=true))
 $(_var(:Argument, :f))
-$(_arg_grad_f)
+$(_var(:Argument, :grad_f))
 $(_var(:Argument, :p))
 
 # Keyword arguments

src/solvers/truncated_conjugate_gradient_descent.jl

@@ -431,8 +431,8 @@ see [AbsilBakerGallivan:2006, ConnGouldToint:2000](@cite).
 
 $(_var(:Argument, :M; type=true))
 $(_var(:Argument, :f))
-$(_arg_grad_f)
-$(_arg_Hess_f)
+$(_var(:Argument, :grad_f))
+$(_var(:Argument, :Hess_f))
 $(_var(:Argument, :p))
 $(_var(:Argument, :X))
 

src/solvers/trust_regions.jl

@@ -271,8 +271,8 @@ by default the [`truncated_conjugate_gradient_descent`](@ref) is used.
 
 $(_var(:Argument, :M; type=true))
 $(_var(:Argument, :f))
-$(_arg_grad_f)
-$(_arg_Hess_f)
+$(_var(:Argument, :grad_f))
+$(_var(:Argument, :Hess_f))
 $(_var(:Argument, :p))
 
 # Keyword arguments