Stiefel, SPD, minor fixes

NEWS.md

@@ -18,7 +18,20 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Sizes of all manifolds can now be either encoded in type or stored in a field to avoid over-specialization.
   The default is set to store the size in a field. To obtain the old behavior, pass the `parameter=:type` keyword
   argument to manifold constructor. Related changes:
-  - Statically sized `SpecialEuclidean{N}` is now `SpecialEuclidean{TypeParameter{Tuple{N}}}`, whereas the type of special Euclidean group with field-stored size is `SpecialEuclidean{Tuple{Int}}`. Similar change applies to `GeneralUnitaryMultiplicationGroup{n}`, `Orthogonal{n}`, `SpecialOrthogonal{n}`, `SpecialUnitary{n}`, `SpecialEuclideanManifold{n}`, `TranslationGroup`. For example
+  - Statically sized `SpecialEuclidean{N}` is now `SpecialEuclidean{TypeParameter{Tuple{N}}}`, whereas the type of special Euclidean group with field-stored size is `SpecialEuclidean{Tuple{Int}}`. Similar change applies to:
+    - `CholeskySpace{N}`,
+    - `Euclidean`,
+    - `GeneralUnitaryMultiplicationGroup{n}`,
+    - `Grassmann{n,k}`,
+    - `Orthogonal{n}`,
+    - `SpecialOrthogonal{n}`,
+    - `SpecialUnitary{n}`,
+    - `SpecialEuclideanManifold{n}`,
+    - `Stiefel{n,k}`,
+    - `SymmetricPositiveDefinite{n}`,
+    - `TranslationGroup`.
+
+  For example
 
   ```{julia}
   function Base.show(io::IO, ::SpecialEuclidean{n}) where {n}
@@ -43,10 +56,22 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
   end
   ```
 
-  for groups with size stored in field.
+  for groups with size stored in field. Alternatively, you can use a single generic method like this:
+
+  ```{julia}
+  function Base.show(io::IO, G::SpecialEuclidean{T}) where {T}
+    n = get_n(G)
+    if T <: TypeParameter
+        return print(io, "SpecialEuclidean($(n); parameter=:type)")
+    else
+        return print(io, "SpecialEuclidean($(n))")
+    end
+  end
+  ```
+
 - Argument order for type alias `RotationActionOnVector`: most often dispatched on argument is now first.
 
 ### Removed
 
 - `ProductRepr` is removed; please use `ArrayPartition` instead.
-- Default methods throwing "not implemented" `ErrorException` for some group-related operations.
+- Default methods throwing "not implemented" `ErrorException` for some group-related operations.

src/manifolds/CholeskySpace.jl

@@ -1,19 +1,24 @@
 @doc raw"""
-    CholeskySpace{N} <: AbstractManifold{ℝ}
+    CholeskySpace{T} <: AbstractManifold{ℝ}
 
 The manifold of lower triangular matrices with positive diagonal and
 a metric based on the cholesky decomposition. The formulae for this manifold
 are for example summarized in Table 1 of [Lin:2019](@cite).
 
 # Constructor
 
-    CholeskySpace(n)
+    CholeskySpace(n; parameter::Symbol=:field)
 
 Generate the manifold of $n× n$ lower triangular matrices with positive diagonal.
 """
-struct CholeskySpace{N} <: AbstractManifold{ℝ} end
+struct CholeskySpace{T} <: AbstractManifold{ℝ}
+    size::T
+end
 
-CholeskySpace(n::Int) = CholeskySpace{n}()
+function CholeskySpace(n::Int; parameter::Symbol=:field)
+    size = wrap_type_parameter(parameter, (n,))
+    return CholeskySpace{typeof(size)}(size)
+end
 
 @doc raw"""
     check_point(M::CholeskySpace, p; kwargs...)
@@ -105,6 +110,9 @@ function exp!(::CholeskySpace, q, p, X)
     return q
 end
 
+get_n(::CholeskySpace{TypeParameter{N}}) where {N} = N
+get_n(M::CholeskySpace{Tuple{Int}}) = get_parameter(M.size)[1]
+
 @doc raw"""
     inner(M::CholeskySpace, p, X, Y)
 
@@ -164,16 +172,28 @@ Return the manifold dimension for the [`CholeskySpace`](@ref) `M`, i.e.
     \dim(\mathcal M) = \frac{N(N+1)}{2}.
 ````
 """
-@generated manifold_dimension(::CholeskySpace{N}) where {N} = div(N * (N + 1), 2)
+function manifold_dimension(M::CholeskySpace)
+    N = get_n(M)
+    return div(N * (N + 1), 2)
+end
 
 @doc raw"""
     representation_size(M::CholeskySpace)
 
 Return the representation size for the [`CholeskySpace`](@ref)`{N}` `M`, i.e. `(N,N)`.
 """
-@generated representation_size(::CholeskySpace{N}) where {N} = (N, N)
+function representation_size(M::CholeskySpace)
+    N = get_n(M)
+    return (N, N)
+end
 
-Base.show(io::IO, ::CholeskySpace{N}) where {N} = print(io, "CholeskySpace($(N))")
+function Base.show(io::IO, ::CholeskySpace{TypeParameter{Tuple{n}}}) where {n}
+    return print(io, "CholeskySpace($(n); parameter=:type)")
+end
+function Base.show(io::IO, M::CholeskySpace{Tuple{Int}})
+    n = get_n(M)
+    return print(io, "CholeskySpace($(n))")
+end
 
 # two small helpers for strictly lower and upper triangulars
 strictlyLowerTriangular(p) = LowerTriangular(p) - Diagonal(diag(p))

src/manifolds/Grassmann.jl

@@ -65,7 +65,7 @@ A good overview can be found in[BendokatZimmermannAbsil:2020](@cite).
 
 # Constructor
 
-    Grassmann(n,k,field=ℝ)
+    Grassmann(n, k, field=ℝ, parameter::Symbol=:field)
 
 Generate the Grassmann manifold $\operatorname{Gr}(n,k)$, where the real-valued
 case `field = ℝ` is the default.

src/manifolds/GrassmannStiefel.jl

@@ -28,7 +28,7 @@ end
 ManifoldsBase.@manifold_element_forwards StiefelPoint value
 ManifoldsBase.@manifold_vector_forwards StiefelTVector value
 ManifoldsBase.@default_manifold_fallbacks Stiefel StiefelPoint StiefelTVector value value
-ManifoldsBase.@default_manifold_fallbacks (Stiefel{n,k,ℝ} where {n,k}) StiefelPoint StiefelTVector value value
+ManifoldsBase.@default_manifold_fallbacks (Stiefel{<:Any,ℝ}) StiefelPoint StiefelTVector value value
 ManifoldsBase.@default_manifold_fallbacks Grassmann StiefelPoint StiefelTVector value value
 
 function default_vector_transport_method(::Grassmann, ::Type{<:AbstractArray})

src/manifolds/Rotations.jl

@@ -408,7 +408,8 @@ and that means the inverse has to be appliead to the (Euclidean) Hessian
 to map it into the Lie algebra.
 """
 riemannian_Hessian(M::Rotations, p, G, H, X)
-function riemannian_Hessian!(::Rotations{N}, Y, p, G, H, X) where {N}
+function riemannian_Hessian!(M::Rotations, Y, p, G, H, X)
+    N = get_n(M)
     symmetrize!(Y, G' * p)
     project!(SkewSymmetricMatrices(N), Y, p' * H - X * Y)
     return Y