flat!, sharp! and optimized inner of cotangent vectors for metric man…

…ifolds

src/Metric.jl

@@ -144,6 +144,21 @@ end
  return inner(M.manifold, x, v, w)
 end
 
+@traitfn function inner(B::VectorBundleFibers{<:CotangentSpaceType, MMT}, x, v, w) where {MT<:Manifold,
+ GT<:Metric,
+ MMT<:MetricManifold{MT,GT};
+ !HasMetric{MT,GT}}
+ ginv = inverse_local_metric(B.M, x)
+ return dot(ginv * v, ginv * w)
+end
+
+@traitfn function inner(B::VectorBundleFibers{<:CotangentSpaceType, MMT}, x, v, w) where {MT<:Manifold,
+ GT<:Metric,
+ MMT<:MetricManifold{MT,GT};
+ HasMetric{MT,GT}}
+ return inner(VectorBundleFibers(B.VS, B.M.manifold), x, v, w)
+end
+
 @traitfn function norm(M::MMT, x, v) where {MT<:Manifold,
  GT<:Metric,
  MMT<:MetricManifold{MT,GT};
@@ -457,3 +472,47 @@ end
  HasMetric{MT,GT}}
  return is_tangent_vector(M.manifold, x, v; kwargs...)
 end
+
+@traitfn function flat!(M::MMT,
+ v::FVector{CotangentSpaceType},
+ x,
+ w::FVector{TangentSpaceType}) where {MT<:Manifold,
+ GT<:Metric,
+ MMT<:MetricManifold{MT,GT};
+ !HasMetric{MT,GT}}
+ g = local_metric(M, x)
+ copyto!(v, g*w)
+ return v
+end
+
+@traitfn function flat!(M::MMT,
+ v::FVector{CotangentSpaceType},
+ x,
+ w::FVector{TangentSpaceType}) where {MT<:Manifold,
+ GT<:Metric,
+ MMT<:MetricManifold{MT,GT};
+ HasMetric{MT,GT}}
+ return flat!(M.manifold, v, x, w)
+end
+
+@traitfn function sharp!(M::MMT,
+ v::FVector{TangentSpaceType},
+ x,
+ w::FVector{CotangentSpaceType}) where {MT<:Manifold,
+ GT<:Metric,
+ MMT<:MetricManifold{MT,GT};
+ !HasMetric{MT,GT}}
+ ginv = inverse_local_metric(M, x)
+ copyto!(v, ginv*w)
+ return v
+end
+
+@traitfn function sharp!(M::MMT,
+ v::FVector{TangentSpaceType},
+ x,
+ w::FVector{CotangentSpaceType}) where {MT<:Manifold,
+ GT<:Metric,
+ MMT<:MetricManifold{MT,GT};
+ HasMetric{MT,GT}}
+ return flat!(M.manifold, v, x, w)
+end

src/VectorBundle.jl

@@ -219,7 +219,10 @@ function inner(B::VectorBundleFibers{<:TangentSpaceType}, x, v, w)
 end
 
 function inner(B::VectorBundleFibers{<:CotangentSpaceType}, x, v, w)
- return inner(B.M, x, flat(B, x, v), flat(B, x, w))
+ return inner(B.M,
+ x,
+ sharp(B.M, x, FVector(CotangentSpace, v)).data,
+ sharp(B.M, x, FVector(CotangentSpace, w)).data)
 end
 
 norm(B::VectorBundleFibers, x, v) = sqrt(inner(B, x, v, v))

test/metric_test.jl

@@ -1,3 +1,4 @@
+include("utils.jl")
 
 struct TestEuclidean{N} <: Manifold end
 struct TestEuclideanMetric <: Metric end
@@ -153,6 +154,14 @@ struct BaseManifoldMetric{M} <: Metric end
  Manifolds.exp!(::BaseManifold, y, x, v) = y .= x + 2 * v
  Manifolds.log!(::BaseManifold, v, x, y) = v .= (y - x) / 2
  Manifolds.project_tangent!(::BaseManifold, w, x, v) = w .= 2 .* v
+ function Manifolds.flat!(::BaseManifold, v::FVector{Manifolds.CotangentSpaceType}, x, w::FVector{Manifolds.TangentSpaceType})
+ v.data .= 2 .* w.data
+ return v
+ end
+ function Manifolds.sharp!(::BaseManifold, v::FVector{Manifolds.TangentSpaceType}, x, w::FVector{Manifolds.CotangentSpaceType})
+ v.data .= w.data ./ 2
+ return v
+ end
 
  M = BaseManifold{3}()
  g = BaseManifoldMetric{3}()
@@ -178,4 +187,13 @@ struct BaseManifoldMetric{M} <: Metric end
  @test injectivity_radius(MM) === injectivity_radius(M)
  @test is_manifold_point(MM, x) === is_manifold_point(M, x)
  @test is_tangent_vector(MM, x, v) === is_tangent_vector(M, x, v)
+
+ cov = flat(M, x, FVector(TangentSpace, v))
+ cow = flat(M, x, FVector(TangentSpace, w))
+ @test cov.data ≈ flat(MM, x, FVector(TangentSpace, v)).data
+ cotspace = CotangentBundleFibers(M)
+ @test cov.data ≈ 2 * v
+ @test inner(M, x, v, w) ≈ inner(cotspace, x, cov.data, cow.data)
+ @test inner(MM, x, v, w) ≈ inner(cotspace, x, cov.data, cow.data)
+ @test sharp(M, x, cov).data ≈ v
 end