Inverse retraction based distance approximation (#119)

* Inverse retraction based distance approximation

* bump version

Project.toml

@@ -1,7 +1,7 @@
 name = "ManifoldsBase"
 uuid = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
 authors = ["Seth Axen <[email protected]>", "Mateusz Baran <[email protected]>", "Ronny Bergmann <[email protected]>", "Antoine Levitt <[email protected]>"]
-version = "0.13.14"
+version = "0.13.15"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/ManifoldsBase.jl

@@ -283,6 +283,16 @@ If ``\mathcal M`` is not connected, i.e. consists of several disjoint components
 the distance between two points from different components should be ``∞``.
 """
 distance(M::AbstractManifold, p, q) = norm(M, p, log(M, p, q))
+"""
+    distance(M::AbstractManifold, p, q, m::AbstractInverseRetractionMethod)
+
+Approximate distance between points `p` and `q` on manifold `M` using
+[`AbstractInverseRetractionMethod`](@ref) `m`.
+"""
+function distance(M::AbstractManifold, p, q, m::AbstractInverseRetractionMethod)
+    return norm(M, p, inverse_retract(M, p, q, m))
+end
+distance(M::AbstractManifold, p, q, ::LogarithmicInverseRetraction) = distance(M, p, q)
 
 """
     embed(M::AbstractManifold, p)

test/default_manifold.jl

@@ -52,7 +52,7 @@ function ManifoldsBase._retract(M::DefaultManifold, p, X, ::CustomDefinedRetract
     return retract_custom(M, p, X)
 end
 function retract_custom(::DefaultManifold, p::DefaultPoint, X::DefaultTVector)
-    return DefaultPoint(p.value + X.value)
+    return DefaultPoint(2 * p.value + X.value)
 end
 function ManifoldsBase._inverse_retract(
     M::DefaultManifold,
@@ -63,7 +63,7 @@ function ManifoldsBase._inverse_retract(
     return inverse_retract_custom(M, p, q)
 end
 function inverse_retract_custom(::DefaultManifold, p::DefaultPoint, q::DefaultPoint)
-    return DefaultTVector(q.value - p.value)
+    return DefaultTVector(q.value - 2 * p.value)
 end
 struct MatrixVectorTransport{T} <: AbstractVector{T}
     m::Matrix{T}
@@ -210,6 +210,8 @@ Base.size(x::MatrixVectorTransport) = (size(x.m, 2),)
             @test isapprox(M, exp(M, pts[1], tv1, 0), pts[1])
 
             @test distance(M, pts[1], pts[2]) ≈ norm(M, pts[1], tv1)
+            @test distance(M, pts[1], pts[2], LogarithmicInverseRetraction()) ≈
+                  norm(M, pts[1], tv1)
 
             @test mid_point(M, pts[1], pts[2]) == convert(T, [0.5, 0.5, 0.0])
             midp = allocate(pts[1])
@@ -549,7 +551,8 @@ Base.size(x::MatrixVectorTransport) = (size(x.m, 2),)
         @test X3 == log(M, p, q)
         @test log!(M, X3, p, q) == log(M, p, q)
         @test X3 == log(M, p, q)
-        @test inverse_retract(M, p, q, CustomDefinedInverseRetraction()) == -Y
+        @test inverse_retract(M, p, q, CustomDefinedInverseRetraction()) == -2 * Y
+        @test distance(M, p, q, CustomDefinedInverseRetraction()) == 2.0
         X4 = ManifoldsBase.allocate_result(M, inverse_retract, p, q)
         @test inverse_retract!(M, X4, p, q) == inverse_retract(M, p, q)
         @test X4 == inverse_retract(M, p, q)