Some issues with allocation on complex manifolds (#677)

* Some issues with allocation on complex manifolds

* minor cleanup, export number_of_coordinates

NEWS.md

@@ -5,6 +5,13 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [0.9.5] - 2023-11-08
+
+### Changed
+
+- `identity_element` now returns a complex matrix for unitary group.
+- `number_of_coordinates` is now exported.
+
 ## [0.9.4] - 2023-11-06
 
 ### Added

Project.toml

@@ -1,7 +1,7 @@
 name = "Manifolds"
 uuid = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
 authors = ["Seth Axen <[email protected]>", "Mateusz Baran <[email protected]>", "Ronny Bergmann <[email protected]>", "Antoine Levitt <[email protected]>"]
-version = "0.9.4"
+version = "0.9.5"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"

src/Manifolds.jl

@@ -856,6 +856,7 @@ export ×,
     norm,
     normal_tvector_distribution,
     number_eltype,
+    number_of_coordinates,
     one,
     power_dimensions,
     parallel_transport_along,

src/groups/general_unitary_groups.jl

@@ -45,6 +45,14 @@ function allocate_result(M::Rotations, ::typeof(rand), ::Identity{Multiplication
     return similar(Matrix{Float64}, representation_size(M)...)
 end
 
+function allocation_promotion_function(
+    ::GeneralUnitaryMultiplicationGroup{<:Any,ℂ},
+    ::typeof(identity_element),
+    args::Tuple,
+)
+    return complex
+end
+
 decorated_manifold(G::GeneralUnitaryMultiplicationGroup) = G.manifold
 
 @doc raw"""

src/groups/group.jl

@@ -244,8 +244,9 @@ end
 
 @trait_function identity_element!(G::AbstractDecoratorManifold, p)
 
-function allocate_result(G::AbstractDecoratorManifold, ::typeof(identity_element))
-    return zeros(representation_size(G)...)
+function allocate_result(G::AbstractDecoratorManifold, f::typeof(identity_element))
+    apf = allocation_promotion_function(G, f, ())
+    return zeros(apf(Float64), representation_size(G)...)
 end
 
 @doc raw"""

src/groups/unitary.jl

@@ -31,7 +31,7 @@ function Unitary(n, 𝔽::AbstractNumbers=ℂ; parameter::Symbol=:type)
 end
 
 @doc raw"""
-    exp_lie(G::Unitary{2,ℂ}, X)
+    exp_lie(G::Unitary{TypeParameter{Tuple{2}},ℂ}, X)
 
 Compute the group exponential map on the [`Unitary(2)`](@ref) group, which is
 

src/manifolds/GeneralUnitaryMatrices.jl

@@ -51,7 +51,7 @@ end
     check_point(M::GeneralUnitaryMatrices, p; kwargs...)
 
 Check whether `p` is a valid point on the [`UnitaryMatrices`](@ref) or [`OrthogonalMatrices`] `M`,
-i.e. that ``p`` has an determinante of absolute value one
+i.e. that ``p`` has a determinant of absolute value one
 
 The tolerance for the last test can be set using the `kwargs...`.
 """
@@ -79,7 +79,7 @@ end
     check_point(M::Rotations, p; kwargs...)
 
 Check whether `p` is a valid point on the [`UnitaryMatrices`](@ref) `M`,
-i.e. that ``p`` has an determinante of absolute value one, i.e. that ``p^{\mathrm{H}}p``
+i.e. that ``p`` has a determinant of absolute value one, i.e. that ``p^{\mathrm{H}}p``
 
 The tolerance for the last test can be set using the `kwargs...`.
 """
@@ -157,7 +157,7 @@ end
 
 4D rotations can be described by two orthogonal planes that are unchanged by
 the action of the rotation (vectors within a plane rotate only within the
-plane). The cosines of the two angles $α,β$ of rotation about these planes may be
+plane). The cosines of the two angles ``α,β`` of rotation about these planes may be
 obtained from the distinct real parts of the eigenvalues of the rotation
 matrix. This function computes these more efficiently by solving the system
 
@@ -329,18 +329,18 @@ end
     get_coordinates(M::OrthogonalMatrices, p, X)
     get_coordinates(M::UnitaryMatrices, p, X)
 
-Extract the unique tangent vector components $X^i$ at point `p` on [`Rotations`](@ref)
-$\mathrm{SO}(n)$ from the matrix representation `X` of the tangent
+Extract the unique tangent vector components ``X^i`` at point `p` on [`Rotations`](@ref)
+``\mathrm{SO}(n)`` from the matrix representation `X` of the tangent
 vector.
 
-The basis on the Lie algebra $𝔰𝔬(n)$ is chosen such that
-for $\mathrm{SO}(2)$, $X^1 = θ = X_{21}$ is the angle of rotation, and
-for $\mathrm{SO}(3)$, $(X^1, X^2, X^3) = (X_{32}, X_{13}, X_{21}) = θ u$ is the
-angular velocity and axis-angle representation, where $u$ is the unit vector
+The basis on the Lie algebra ``𝔰𝔬(n)`` is chosen such that
+for ``\mathrm{SO}(2)``, ``X^1 = θ = X_{21}`` is the angle of rotation, and
+for ``\mathrm{SO}(3)``, ``(X^1, X^2, X^3) = (X_{32}, X_{13}, X_{21}) = θ u`` is the
+angular velocity and axis-angle representation, where ``u`` is the unit vector
 along the axis of rotation.
 
-For $\mathrm{SO}(n)$ where $n ≥ 4$, the additional elements of $X^i$ are
-$X^{j (j - 3)/2 + k + 1} = X_{jk}$, for $j ∈ [4,n], k ∈ [1,j)$.
+For ``\mathrm{SO}(n)`` where ``n ≥ 4``, the additional elements of ``X^i`` are
+``X^{j (j - 3)/2 + k + 1} = X_{jk}``, for ``j ∈ [4,n], k ∈ [1,j)``.
 """
 get_coordinates(::GeneralUnitaryMatrices{<:Any,ℝ}, ::Any...)
 function get_coordinates(
@@ -476,7 +476,7 @@ end
 
 Convert the unique tangent vector components `Xⁱ` at point `p` on [`Rotations`](@ref)
 or [`OrthogonalMatrices`](@ref)
-to the matrix representation $X$ of the tangent vector. See
+to the matrix representation ``X`` of the tangent vector. See
 [`get_coordinates`](@ref get_coordinates(::GeneralUnitaryMatrices, ::Any...)) for the conventions used.
 """
 get_vector(::GeneralUnitaryMatrices{<:Any,ℝ}, ::Any...)
@@ -643,7 +643,7 @@ injectivity_radius(::GeneralUnitaryMatrices) = π
 @doc raw"""
     injectivity_radius(G::GeneralUnitaryMatrices{<:Any,ℂ,DeterminantOneMatrices})
 
-Return the injectivity radius for general complex unitary matrix manifolds, where the determinant is $+1$,
+Return the injectivity radius for general complex unitary matrix manifolds, where the determinant is ``+1``,
 which is[^1]
 
 ```math
@@ -726,7 +726,7 @@ Compute the logarithmic map on the [`Rotations`](@ref) manifold
 \log_p q = \operatorname{log}(p^{\mathrm{T}}q)
 ```
 
-where $\operatorname{Log}$ denotes the matrix logarithm. For numerical stability,
+where ``\operatorname{Log}`` denotes the matrix logarithm. For numerical stability,
 the result is projected onto the set of skew symmetric matrices.
 
 For antipodal rotations the function returns deterministically one of the tangent vectors

test/groups/general_unitary_groups.jl

@@ -89,6 +89,8 @@ include("group_utils.jl")
         @test manifold_volume(Unitary(3)) ≈ sqrt(3) * 2 * π^6
         @test manifold_volume(Unitary(4)) ≈ sqrt(2) * 8 * π^10 / 12
 
+        @test identity_element(U2) isa Matrix{ComplexF64}
+
         for n in [1, 2, 3]
             Un = Unitary(n)
             X = zeros(ComplexF64, n, n)