Unify signatures, fix a few tex typos and improve english on the fact…

…ory info/note.

src/documentation_glossary.jl

@@ -176,10 +176,8 @@ define!(
     (type::String) -> """
 !!! info
     This function generates a [`ManifoldDefaultsFactory`](@ref) for [`$(type)`](@ref).
-    If you do not provide a manifold, the manifold `M` later provided to (usually) generate
-    the corresponding [`AbstractManoptSolverState`](@ref) will be used.
-    This affects all arguments and keyword argumentss with defaults that depend on the manifold,
-    unless provided with a value here.
+    For default values, that depend on the manifold, this factory postpones the construction
+    until the manifold from for example a corresponding [`AbstractManoptSolverState`](@ref) is available.
 """,
 )
 define!(

src/plans/conjugate_gradient_plan.jl

@@ -39,7 +39,7 @@ $(_var(:Field, :vector_transport_method))
 
 # Constructor
 
-    ConjugateGradientState(M; kwargs...)
+    ConjugateGradientState(M::AbstractManifold; kwargs...)
 
 where the last five fields can be set by their names as keyword and the
 `X` can be set to a tangent vector type using the keyword `initial_gradient` which defaults to `zero_vector(M,p)`,

src/plans/gradient_plan.jl

@@ -448,8 +448,8 @@ function (a::AverageGradientRule)(
 end
 
 """
-    AverageGradient(M; kwargs...)
     AverageGradient(; kwargs...)
+    AverageGradient(M::AbstractManifold; kwargs...)
 
 Add an average of gradients to a gradient processor. A set of previous directions (from the
 inner processor) and the last iterate are stored, average is taken after vector transporting
@@ -548,7 +548,7 @@ end
 
 @doc """
     Nesterov(; kwargs...)
-    Nesterov(M; kwargs...)
+    Nesterov(M::AbstractManifold; kwargs...)
 
 Assume ``f`` is ``L``-Lipschitz and ``μ``-strongly convex. Given
 

src/plans/stepsize.jl

@@ -95,7 +95,7 @@ end
     ConstantLength(s; kwargs...)
     ConstantLength(M::AbstractManifold, s; kwargs...)
 
-Specify a [`Stepsize`]  that is constant.
+Specify a [`Stepsize`](@ref) that is constant.
 
 # Input
 
@@ -191,8 +191,8 @@ function show(io::IO, s::DecreasingStepsize)
     )
 end
 """
-    DecreasingLength(M; kwargs...)
     DegreasingLength(; kwargs...)
+    DecreasingLength(M::AbstractManifold; kwargs...)
 
 Specify a [`Stepsize`]  that is decreasing as ``s_k = $(_tex(:frac, "(l - ak)f^i", "(k+s)^e"))
 with the following
@@ -208,7 +208,7 @@ with the following
 * `:relative` – scale the gradient tangent vector ``X`` to ``s_k*X``
 * `:absolute` – scale the gradient to an absolute step length ``s_k``, that is ``$(_tex(:frac, "s_k", _tex(:norm, "X")))X``
 
-$(_note(:ManifoldDefaultFactory, "NesterovRule"))
+$(_note(:ManifoldDefaultFactory, "DecreasingStepsize"))
 """
 function DecreasingLength(args...; kwargs...)
     return ManifoldDefaultsFactory(Manopt.DecreasingStepsize, args...; kwargs...)
@@ -404,11 +404,11 @@ function set_parameter!(a::ArmijoLinesearchStepsize, ::Val{:IncreaseCondition},
 end
 """
     ArmijoLinesearch(; kwargs...)
-    ArmijoLinesearch(M; kwargs...)
+    ArmijoLinesearch(M::AbstractManifold; kwargs...)
 
-Specify a step size that performs an Armijo line search. Given a Function `f:$(_math(:M))→ℝ`
-and its Riemannian Gradient ``$(_tex(:grad))f:$(_math(:M))→$(_math(:TM))`,
-the curent point ``p∈$(_math(:M))`` and a search direction `X∈$(_math(:TpM))``.
+Specify a step size that performs an Armijo line search. Given a Function ``f:$(_math(:M))→ℝ``
+and its Riemannian Gradient ``$(_tex(:grad))f: $(_math(:M))→$(_math(:TM))``,
+the curent point ``p∈$(_math(:M))`` and a search direction ``X∈$(_math(:TpM))``.
 
 Then the step size ``s`` is found by reducing the initial step size ``s`` until
 
@@ -450,6 +450,7 @@ function ArmijoLinesearch(args...; kwargs...)
     return ManifoldDefaultsFactory(Manopt.ArmijoLinesearchStepsize, args...; kwargs...)
 end
 
+
 @doc """
     AdaptiveWNGradientStepsize{I<:Integer,R<:Real,F<:Function} <: Stepsize
 
@@ -569,7 +570,7 @@ function show(io::IO, awng::AdaptiveWNGradientStepsize)
 end
 """
     AdaptiveWNGradient(; kwargs...)
-    AdaptiveWNGradient(M; kwargs...)
+    AdaptiveWNGradient(M::AbstractManifold; kwargs...)
 
 A stepsize based on the adaptive gradient method introduced by [GrapigliaStella:2023](@cite).
 
@@ -1001,7 +1002,7 @@ get_message(a::NonmonotoneLinesearchStepsize) = a.message
 
 @doc """
     NonmonotoneLinesearch(; kwargs...)
-    NonmonotoneLinesearch(M; kwargs...)
+    NonmonotoneLinesearch(M::AbstractManifold; kwargs...)
 
 A functor representing a nonmonotone line search using the Barzilai-Borwein step size [IannazzoPorcelli:2017](@cite).
 
@@ -1021,10 +1022,10 @@ where ``α_{k-1}`` is the step size computed in the last iteration and ``$(_math
 Then the Barzilai—Borwein step size is
 
 ```math
-α_k^{$(_tex(:text, "BB"))} = \begin{cases}
-$(_tex(:min))(α_{$(_tex(:text, "max"))}, $(_tex(:max))(α_{$(_tex(:text, "min"))}, τ_{k})), & $(_tex(:text, "if")) ⟨s_{k}, y_{k}⟩_{p_k} > 0,\\
-α_{$(_tex(:text, "max"))}, & \text{else,}
-\end{cases}
+α_k^{$(_tex(:text, "BB"))} = $(_tex(:cases,
+"$(_tex(:min))(α_{$(_tex(:text, "max"))}, $(_tex(:max))(α_{$(_tex(:text, "min"))}, τ_{k})), & $(_tex(:text, "if")) ⟨s_{k}, y_{k}⟩_{p_k} > 0,",
+"α_{$(_tex(:text, "max"))}, & $(_tex(:text, "else,"))"
+))
 ```
 
 where
@@ -1065,7 +1066,7 @@ $(_var(:Keyword, :p; add="to store an interim result"))
 * `bb_max_stepsize=1e3`: upper bound for the Barzilai-Borwein step size greater than min_stepsize
 $(_var(:Keyword, :retraction_method))
 * `strategy=direct`: defines if the new step size is computed using the `:direct`, `:indirect` or `:alternating` strategy
-* `storage=[`StoreStateAction`](@ref)`(M; store_fields=[:Iterate, :Gradient])``: increase efficiency by using a [`StoreStateAction`](@ref) for `:Iterate` and `:Gradient`
+* `storage=`[`StoreStateAction`](@ref)`(M; store_fields=[:Iterate, :Gradient])`: increase efficiency by using a [`StoreStateAction`](@ref) for `:Iterate` and `:Gradient`.
 * `stepsize_reduction=0.5`:  step size reduction factor contained in the interval ``(0,1)``
 * `sufficient_decrease=1e-4`: sufficient decrease parameter contained in the interval ``(0,1)``
 * `stop_when_stepsize_less=0.0`: smallest stepsize when to stop (the last one before is taken)
@@ -1129,7 +1130,7 @@ function show(io::IO, ps::PolyakStepsize)
 end
 """
     Polyak(; kwargs...)
-    Polyak(M; kwargs...)
+    Polyak(M::AbstractManifold; kwargs...)
 
 Compute a step size according to a method propsed by Polyak, cf. the Dynamic step size
 discussed in Section 3.2 of [Bertsekas:2015](@cite).
@@ -1326,7 +1327,7 @@ function status_summary(a::WolfePowellLinesearchStepsize)
 end
 """
     WolfePowellLinesearch(; kwargs...)
-    WolfePowellLinesearch(M; kwargs...)
+    WolfePowellLinesearch(M::AbstractManifold; kwargs...)
 
 Perform a lineseach to fulfull both the Armijo-Goldstein conditions
 ```math
@@ -1501,7 +1502,7 @@ Then the following Algorithm is performed similar to Algorithm 7 from [Huang:201
 
 """
     WolfePowellBinaryLinesearch(; kwargs...)
-    WolfePowellBinaryLinesearch(M; kwargs...)
+    WolfePowellBinaryLinesearch(M::AbstractManifold; kwargs...)
 
 Perform a lineseach to fulfull both the Armijo-Goldstein conditions
 for some given sufficient decrease coefficient ``c_1`` and some sufficient curvature condition coefficient``c_2``.

src/solvers/DouglasRachford.jl

@@ -21,7 +21,7 @@ $(_var(:Field, :stopping_criterion, "stop"))
 
 # Constructor
 
-    DouglasRachfordState(M; kwargs...)
+    DouglasRachfordState(M::AbstractManifold; kwargs...)
 
 # Input
 

src/solvers/NelderMead.jl

@@ -73,7 +73,7 @@ $(_var(:Field, :retraction_method))
 
 # Constructors
 
-    NelderMeadState(M; kwargs...)
+    NelderMeadState(M::AbstractManifold; kwargs...)
 
 Construct a Nelder-Mead Option with a default population (if not provided) of set of
 `dimension(M)+1` random points stored in [`NelderMeadSimplex`](@ref).

src/solvers/alternating_gradient_descent.jl

@@ -20,7 +20,7 @@ $(_var(:Field, :X; add=[:as_Gradient]))
 
 # Constructors
 
-    AlternatingGradientDescentState(M; kwargs...)
+    AlternatingGradientDescentState(M::AbstractManifold; kwargs...)
 
 # Keyword arguments
 * `inner_iterations=5`

src/solvers/gradient_descent.jl

@@ -16,7 +16,7 @@ $(_var(:Field, :retraction_method))
 
 # Constructor
 
-    GradientDescentState(M; kwargs...)
+    GradientDescentState(M::AbstractManifold; kwargs...)
 
 Initialize the gradient descent solver state, where
 

src/solvers/stochastic_gradient_descent.jl

@@ -17,7 +17,7 @@ $(_var(:Field, :retraction_method))
 
 # Constructor
 
-    StochasticGradientDescentState(M; kwargs...)
+    StochasticGradientDescentState(M::AbstractManifold; kwargs...)
 
 Create a `StochasticGradientDescentState` with start point `p`.