From ea6ef685bc643699738a62ee62b1befc1282c6df Mon Sep 17 00:00:00 2001
From: Mateusz Baran <mateuszbaran89@gmail.com>
Date: Thu, 1 Aug 2019 14:18:50 +0200
Subject: [PATCH] flat!, sharp! and optimized inner of cotangent vectors for
 metric manifolds

---
 src/Metric.jl       | 59 +++++++++++++++++++++++++++++++++++++++++++++
 src/VectorBundle.jl |  5 +++-
 test/metric_test.jl | 18 ++++++++++++++
 3 files changed, 81 insertions(+), 1 deletion(-)

diff --git a/src/Metric.jl b/src/Metric.jl
index 97dfbae42a..bbf0abebfe 100644
--- a/src/Metric.jl
+++ b/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
diff --git a/src/VectorBundle.jl b/src/VectorBundle.jl
index fe705d83d0..c5f12de9cf 100644
--- a/src/VectorBundle.jl
+++ b/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))
diff --git a/test/metric_test.jl b/test/metric_test.jl
index ad72cce515..eeedbfbbaf 100644
--- a/test/metric_test.jl
+++ b/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