finish tests for product and power – extend features to also work on …

…the sphere.

src/manifolds/PowerManifold.jl

@@ -92,10 +92,11 @@ function change_representer!(M::AbstractPowerManifold, Y, G::AbstractMetric, p,
  M.manifold,
  _write(M, rep_size, Y, i),
  G,
- _read(M, rep_size, P, i),
+ _read(M, rep_size, p, i),
  _read(M, rep_size, X, i),
  )
  end
+ return Y
 end
 
 """
@@ -105,7 +106,7 @@ Since the metric on a power manifold decouples, the change of a representer can
 """
 change_metric(M::AbstractPowerManifold, ::AbstractMetric, ::Any, ::Any)
 
-function change_metric!(M::AbstractPowerManifold, Y, ::AbstractMetric, p, X)
+function change_metric!(M::AbstractPowerManifold, Y, G::AbstractMetric, p, X)
  rep_size = representation_size(M.manifold)
  for i in get_iterator(M)
  change_metric!(
@@ -116,6 +117,7 @@ function change_metric!(M::AbstractPowerManifold, Y, ::AbstractMetric, p, X)
  _read(M, rep_size, X, i),
  )
  end
+ return Y
 end
 
 @doc raw"""

src/manifolds/Sphere.jl

@@ -144,7 +144,9 @@ end
 function decorated_manifold(M::AbstractSphere{𝔽}) where {𝔽}
  return Euclidean(representation_size(M)...; field=𝔽)
 end
-get_embedding(M::AbstractSphere{𝔽}) where {𝔽} = decorated_manifold(M)
+
+# Since on every tangent space the Euclidean matric (restricted to this space) is used, this should be fine
+default_metric_dispatch(::AbstractSphere, ::EuclideanMetric) = Val(true)
 
 @doc raw"""
  distance(M::AbstractSphere, p, q)
@@ -226,6 +228,8 @@ function get_coordinates!(
  return Y
 end
 
+get_embedding(M::AbstractSphere{𝔽}) where {𝔽} = decorated_manifold(M)
+
 @doc raw"""
  get_vector(M::AbstractSphere{ℝ}, p, X, B::DefaultOrthonormalBasis)
 

test/manifolds/power_manifold.jl

@@ -413,4 +413,23 @@ end
  @test isapprox(a, a2)
  @test_throws ErrorException get_point(M, A2, p, a2)
  end
+
+ @testset "metric conversion" begin
+ M = SymmetricPositiveDefinite(3)
+ N = PowerManifold(M, NestedPowerRepresentation(), 2)
+ e = EuclideanMetric()
+ p = [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1]
+ q = [2.0 0.0 0.0; 0.0 2.0 0.0; 0.0 0.0 1]
+ P = [p, q]
+ X = [log(M, p, q), log(M, q, p)]
+ Y = change_metric(N, e, P, X)
+ Yc = [change_metric(M, e, p, log(M, p, q)), change_metric(M, e, q, log(M, q, p))]
+ @test norm(N, P, Y .- Yc) ≈ 0
+ Z = change_representer(N, e, P, X)
+ Zc = [
+ change_representer(M, e, p, log(M, p, q)),
+ change_representer(M, e, q, log(M, q, p)),
+ ]
+ @test norm(N, P, Z .- Zc) ≈ 0
+ end
 end

test/manifolds/product_manifold.jl

@@ -648,4 +648,26 @@ end
  p2 = get_point(M, A, p, a)
  @test all(p2.parts .== p.parts)
  end
+
+ @testset "metric conversion" begin
+ M = SymmetricPositiveDefinite(3)
+ N = ProductManifold(M, M)
+ e = EuclideanMetric()
+ p = [1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1]
+ q = [2.0 0.0 0.0; 0.0 2.0 0.0; 0.0 0.0 1]
+ P = ProductRepr(p, q)
+ X = ProductRepr(log(M, p, q), log(M, q, p))
+ Y = change_metric(N, e, P, X)
+ Yc = ProductRepr(
+ change_metric(M, e, p, log(M, p, q)),
+ change_metric(M, e, q, log(M, q, p)),
+ )
+ @test norm(N, P, Y - Yc) ≈ 0
+ Z = change_representer(N, e, P, X)
+ Zc = ProductRepr(
+ change_representer(M, e, p, log(M, p, q)),
+ change_representer(M, e, q, log(M, q, p)),
+ )
+ @test norm(N, P, Z - Zc) ≈ 0
+ end
 end

test/manifolds/sphere.jl

@@ -214,4 +214,13 @@ using ManifoldsBase: TFVector
  end
  end
  end
+
+ @testset "Metric conversion is the identity" begin
+ p = [1.0, 0.0, 0.0]
+ X = [0.0, 1.0, 1.0]
+ Y = change_representer(M, EuclideanMetric(), p, X)
+ @test Y == X
+ Z = change_metric(M, EuclideanMetric(), p, X)
+ @test Z == X
+ end
 end