add permanent check from Mateusz' example

Author: dehann

test/manifolds/manifolddiff.jl

@@ -2,7 +2,9 @@
 # using Revise
 using Test
 using LinearAlgebra
+using ManifoldsBase
 using Manifolds, Manopt
+using Optim
 using FiniteDifferences, ManifoldDiff
 
 ##
@@ -44,4 +46,74 @@ end
 ##
 end
 
+
+@testset "Optim.jl ManifoldWrapper example from mateuszbaran (copied to catch issues on future changes)" begin
+# Example modified from: https://gist.github.com/mateuszbaran/0354c0edfb9cdf25e084a2b915816a09
+##
+
+"""
+    ManifoldWrapper{TM<:AbstractManifold} <: Optim.Manifold
+    
+Adapts Manifolds.jl manifolds for use in Optim.jl
+"""
+struct ManifoldWrapper{TM<:AbstractManifold} <: Optim.Manifold
+    M::TM
+end
+
+function Optim.retract!(M::ManifoldWrapper, x)
+    ManifoldsBase.embed_project!(M.M, x, x)
+    return x
+end
+
+function Optim.project_tangent!(M::ManifoldWrapper, g, x)
+    ManifoldsBase.embed_project!(M.M, g, x, g)
+    return g
+end
+
+# example usage of Manifolds.jl manifolds in Optim.jl
+M = Manifolds.Sphere(2)
+x0 = [1.0, 0.0, 0.0]
+q = [0.0, 1.0, 0.0]
+
+f(p) = 0.5 * distance(M, p, q)^2
+
+# manual gradient
+function g!(X, p)
+    log!(M, X, p, q)
+    X .*= -1
+    println(p, X)
+end
+
+##
+
+sol = optimize(f, g!, x0, ConjugateGradient(; manifold=ManifoldWrapper(M)))
+@test isapprox([0,1,0.], sol.minimizer; atol=1e-8)
+
+
+## finitediff gradient (non-manual)
+
+r_backend = ManifoldDiff.TangentDiffBackend(
+    ManifoldDiff.FiniteDifferencesBackend()
+)
+function g_FD!(X,p)
+  X .= ManifoldDiff.gradient(M, f, p, r_backend)
+  X
+end
+
+#
+x0 = [1.0, 0.0, 0.0]
+
+sol = optimize(f, g_FD!, x0, ConjugateGradient(; manifold=ManifoldWrapper(M)))
+@test isapprox([0,1,0.], sol.minimizer; atol=1e-8)
+
+##
+
+# x0 = [1.0, 0.0, 0.0]
+# # internal ForwardDfif doesnt work out the box on Manifolds
+# sol = optimize(f, x0, ConjugateGradient(; manifold=ManifoldWrapper(M)); autodiff=:forward )
+# @test isapprox([0,1,0.], sol.minimizer; atol=1e-8)
+
+##
+end
+
 ##