fixes

src/manifolds/FiberBundle.jl

@@ -157,7 +157,44 @@ the fiber over ``p``, transport ``X`` to fiber over ``q``.
 
 Exact meaning of the operation depends on the fiber bundle, or may even be undefined.
 """
-bundle_transport_to(B::FiberBundle, p, X, q)
+function bundle_transport_to(B::FiberBundle, p, X, q)
+    Y = allocate(X)
+    return bundle_transport_to!(B, Y, p, X, q)
+end
+
+@doc raw"""
+    bundle_transport_tangent_direction(B::FiberBundle, p, X, d)
+
+TODO
+"""
+function bundle_transport_tangent_direction(
+    B::FiberBundle,
+    p,
+    X,
+    d,
+    m::AbstractVectorTransportMethod=default_vector_transport_method(B.manifold),
+)
+    Y = allocate(X)
+    return bundle_transport_tangent_direction!(B, Y, p, X, d, m)
+end
+
+@doc raw"""
+    bundle_transport_tangent_to(B::FiberBundle, p, X, q)
+
+TODO
+
+Ehresmann connection; ``X`` is an element of the vertical bundle ``VF\mathcal M`` from tangent to fiber ``\pi^{-1}({p})``, ``p\in \mathcal M``.
+"""
+function bundle_transport_tangent_to(
+    B::FiberBundle,
+    p,
+    X,
+    q,
+    m::AbstractVectorTransportMethod=default_vector_transport_method(B.manifold),
+)
+    Y = allocate(X)
+    return bundle_transport_tangent_to!(B, Y, p, X, q, m)
+end
 
 """
     bundle_projection(B::FiberBundle, p)
@@ -247,7 +284,7 @@ function get_vector!(
     n = manifold_dimension(M.manifold)
     xp1, xp2 = submanifold_components(M, p)
     Yp1, Yp2 = submanifold_components(M, Y)
-    F = Fiber(M.manifold, M.type, xp1)
+    F = Fiber(M.manifold, xp1, M.type)
     get_vector!(M.manifold, Yp1, xp1, X[1:n], B.data.base_basis)
     get_vector!(F, Yp2, xp2, X[(n + 1):end], B.data.fiber_basis)
     return Y

src/manifolds/VectorBundle.jl

@@ -68,6 +68,28 @@ function bundle_transport_to!(B::TangentBundle, Y, p, X, q)
     return vector_transport_to!(B.manifold, Y, p, X, q, B.vector_transport.method_fiber)
 end
 
+function bundle_transport_tangent_direction!(
+    B::TangentBundle,
+    Y,
+    p,
+    X,
+    d,
+    m::AbstractVectorTransportMethod=default_vector_transport_method(B.manifold),
+)
+    return vector_transport_direction!(B.manifold, Y, p, X, d, m)
+end
+
+function bundle_transport_tangent_to!(
+    B::TangentBundle,
+    Y,
+    p,
+    X,
+    q,
+    m::AbstractVectorTransportMethod=default_vector_transport_method(B.manifold),
+)
+    return vector_transport_to!(B.manifold, Y, p, X, q, m)
+end
+
 function default_inverse_retraction_method(::TangentBundle)
     return FiberBundleInverseProductRetraction()
 end
@@ -100,20 +122,20 @@ end
     inner(B::VectorBundle, p, X, Y)
 
 Inner product of tangent vectors `X` and `Y` at point `p` from the
-vector bundle `B` over manifold `B.fiber` (denoted $\mathcal M$).
+vector bundle `B` over manifold `B.fiber` (denoted ``\mathcal M``).
 
 Notation:
-  * The point $p = (x_p, V_p)$ where $x_p ∈ \mathcal M$ and $V_p$ belongs to the
-    fiber $F=π^{-1}(\{x_p\})$ of the vector bundle $B$ where $π$ is the
-    canonical projection of that vector bundle $B$.
-  * The tangent vector $v = (V_{X,M}, V_{X,F}) ∈ T_{x}B$ where
-    $V_{X,M}$ is a tangent vector from the tangent space $T_{x_p}\mathcal M$ and
-    $V_{X,F}$ is a tangent vector from the tangent space $T_{V_p}F$ (isomorphic to $F$).
-    Similarly for the other tangent vector $w = (V_{Y,M}, V_{Y,F}) ∈ T_{x}B$.
+  * The point ``p = (x_p, V_p)`` where ``x_p ∈ \mathcal M`` and ``V_p`` belongs to the
+    fiber ``F=π^{-1}(\{x_p\})`` of the vector bundle ``B`` where ``π`` is the
+    canonical projection of that vector bundle ``B``.
+  * The tangent vector ``v = (V_{X,M}, V_{X,F}) ∈ T_{x}B`` where
+    ``V_{X,M}`` is a tangent vector from the tangent space ``T_{x_p}\mathcal M`` and
+    ``V_{X,F}`` is a tangent vector from the tangent space ``T_{V_p}F`` (isomorphic to ``F``).
+    Similarly for the other tangent vector ``w = (V_{Y,M}, V_{Y,F}) ∈ T_{x}B``.
 
 The inner product is calculated as
 
-$⟨X, Y⟩_p = ⟨V_{X,M}, V_{Y,M}⟩_{x_p} + ⟨V_{X,F}, V_{Y,F}⟩_{V_p}.$
+``⟨X, Y⟩_p = ⟨V_{X,M}, V_{Y,M}⟩_{x_p} + ⟨V_{X,F}, V_{Y,F}⟩_{V_p}.``
 """
 function inner(B::FiberBundle, p, X, Y)
     px, Vx = submanifold_components(B.manifold, p)
@@ -354,7 +376,7 @@ function vector_transport_to!(
     VYM, VYF = submanifold_components(M.manifold, Y)
     qx, qVx = submanifold_components(M.manifold, q)
     vector_transport_to!(M.manifold, VYM, px, VXM, qx, m.method_point)
-    vector_transport_to!(M.manifold, VYF, px, VXF, qx, m.method_fiber)
+    bundle_transport_tangent_to!(M, VYF, px, VXF, qx, m.method_fiber)
     return Y
 end
 
@@ -370,7 +392,7 @@ function _vector_transport_direction(
     dx, dVx = submanifold_components(M.manifold, d)
     return ArrayPartition(
         vector_transport_direction(M.manifold, px, VXM, dx, m.method_point),
-        vector_transport_direction(M.fiber, px, VXF, dx, m.method_fiber),
+        bundle_transport_tangent_direction(M, px, VXF, dx, m.method_fiber),
     )
 end
 
@@ -386,7 +408,7 @@ function _vector_transport_to(
     qx, qVx = submanifold_components(M.manifold, q)
     return ArrayPartition(
         vector_transport_to(M.manifold, px, VXM, qx, m.method_point),
-        vector_transport_to(M.manifold, px, VXF, qx, m.method_fiber),
+        bundle_transport_tangent_to(M, px, VXF, qx, m.method_fiber),
     )
 end
 

test/manifolds/vector_bundle.jl

@@ -103,26 +103,8 @@ struct TestVectorSpaceType <: VectorSpaceType end
             Xir = allocate(pts_tb[1])
             inverse_retract!(TB, Xir, pts_tb[1], pts_tb[2], m_prod_invretr)
             @test isapprox(TB, pts_tb[1], Xir, X12_prod)
-            @test isapprox(
-                norm(TB.fiber, pts_tb[1][TB, :point], pts_tb[1][TB, :vector]),
-                sqrt(
-                    inner(
-                        TB.fiber,
-                        pts_tb[1][TB, :point],
-                        pts_tb[1][TB, :vector],
-                        pts_tb[1][TB, :vector],
-                    ),
-                ),
-            )
-            @test isapprox(
-                distance(
-                    TB.fiber,
-                    pts_tb[1][TB, :point],
-                    pts_tb[1][TB, :vector],
-                    [0.0, 2.0, 3.0],
-                ),
-                5.0,
-            )
+            F = Fiber(M, pts_tb[1][TB, :point], TangentSpaceType())
+            @test isapprox(distance(F, pts_tb[1][TB, :vector], [0.0, 2.0, 3.0]), 5.0)
             Xir2 = allocate(pts_tb[1])
             vector_transport_to!(
                 TB,
@@ -175,7 +157,7 @@ struct TestVectorSpaceType <: VectorSpaceType end
         @test vector_space_dimension(Sphere(3), TT) == 9
         @test base_manifold(Fiber(Sphere(2), [1.0, 0.0, 0.0], TT)) == M
         @test sprint(show, Fiber(Sphere(2), [1.0, 0.0, 0.0], TT)) ==
-              "VectorSpaceFiber(TensorProductType(TangentSpaceType(), TangentSpaceType()), Sphere(2, ℝ))"
+              "VectorSpaceFiber{ℝ, Sphere{TypeParameter{Tuple{2}}, ℝ}, Manifolds.TensorProductType{Tuple{TangentSpaceType, TangentSpaceType}}, Vector{Float64}}(Sphere(2, ℝ), [1.0, 0.0, 0.0], TensorProductType(TangentSpaceType(), TangentSpaceType()))"
     end
 
     @testset "Error messages" begin
@@ -215,7 +197,7 @@ struct TestVectorSpaceType <: VectorSpaceType end
         tbvt = Manifolds.FiberBundleProductVectorTransport(ppt, ppt)
         @test TangentBundle(M, tbvt).vector_transport === tbvt
         @test CotangentBundle(M, tbvt).vector_transport === tbvt
-        @test VectorBundle(TangentSpace, M, tbvt).vector_transport === tbvt
+        @test TangentBundle(M, tbvt).vector_transport === tbvt
     end
 
     @testset "Extended flatness tests" begin