Some issues with allocation on complex manifolds

NEWS.md

@@ -5,6 +5,12 @@ 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-dd
+
+### Changed
+
+- `identity_element` now returns a complex matrix for unitary group.
+
 ## [0.9.4] - 2023-11-06
 
 ### Added

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"""

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)