Improve random tangent generation on complex circle and rotation matr… (

#689)

* Improve random tangent generation on complex circle and rotation matrices

* shorter vectors for tests

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).
 
+## [0.9.8] - 2023-11-17
+
+### Fixed
+
+- Improved distribution of random vector generation for rotation matrices and complex circle.
+
 ## [0.9.7] - 2023-11-14
 
 ### Fixed

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 = "0.9.7"
+version = "0.9.8"
 
 [deps]
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"

src/manifolds/Circle.jl

@@ -465,7 +465,7 @@ function Random.rand(rng::AbstractRNG, M::Circle{ℂ}; vector_at=nothing, σ::Re
         return sign(randn(rng, ComplexF64))
     else
         # written like that to properly handle `vector_at` being a number or a one-element array
-        return map(p -> project(M, p, σ * rand(rng, typeof(p))), vector_at)
+        return map(p -> project(M, p, σ * randn(rng, complex(typeof(p)))), vector_at)
     end
 end
 

src/manifolds/Rotations.jl

@@ -330,7 +330,6 @@ function Random.rand!(
         (manifold_dimension(M) == 0) && return fill!(pX, 0)
         A = σ .* randn(rng, representation_size(M))
         pX .= triu(A, 1) .- transpose(triu(A, 1))
-        normalize!(pX)
     end
     return pX
 end

test/groups/power_group.jl

@@ -21,7 +21,7 @@ include("group_utils.jl")
         @test G isa PowerGroup
         @test is_point(G, rand(Random.GLOBAL_RNG, G))
         pts = [rand(G) for _ in 1:3]
-        X_pts = [rand(G; vector_at=pts[1]) for _ in 1:3]
+        X_pts = [0.5 * rand(G; vector_at=pts[1]) for _ in 1:3]
 
         @test compose(G, pts[1], Identity(G)) == pts[1]
         @test compose(G, Identity(G), pts[1]) == pts[1]