Fix fallbacks, add code cov.

src/Lie_algebra/Lie_algebra_interface.jl

@@ -27,24 +27,22 @@ function LieAlgebra(G::LieGroup{𝔽,O}) where {𝔽,O<:AbstractGroupOperation}
 end
 
 function ManifoldsBase.get_coordinates(𝔤::LieAlgebra, X, B::ManifoldsBase.AbstractBasis)
-    c = ManifoldsBase.allocate_result(B, get_coordinates, X, B)
-    get_coordinates!(𝔤, c, X, B)
-    return X
+    G = 𝔤.manifold
+    return get_coordinates(base_manifold(G), identity_element(G), X, B)
 end
 function ManifoldsBase.get_coordinates!(𝔤::LieAlgebra, c, X, B::ManifoldsBase.AbstractBasis)
     G = 𝔤.manifold
-    get_coordinates!(base_manifold(𝔤), c, identity_element(G), X, B)
+    get_coordinates!(base_manifold(G), c, identity_element(G), X, B)
     return c
 end
 
 function ManifoldsBase.get_vector(𝔤::LieAlgebra, c, B::ManifoldsBase.AbstractBasis)
-    X = zero_vector(𝔤)
-    get_vector!(𝔤, X, c, B)
-    return X
+    G = 𝔤.manifold
+    return get_vector(base_manifold(G), identity_element(G), c, B)
 end
 function ManifoldsBase.get_vector!(𝔤::LieAlgebra, X, c, B::ManifoldsBase.AbstractBasis)
     G = 𝔤.manifold
-    get_vector!(base_manifold(𝔤), X, identity_element(G), c, B)
+    get_vector!(base_manifold(G), X, identity_element(G), c, B)
     return X
 end
 

src/interface.jl

@@ -447,11 +447,13 @@ ManifoldsBase.get_coordinates(G::LieGroup, g, X, B::ManifoldsBase.AbstractBasis)
 ManifoldsBase.get_coordinates!(G::LieGroup, c, g, X, B::ManifoldsBase.AbstractBasis)
 
 function get_coordinates_lie(G::LieGroup, g, X, N)
-    return get_coordinates(G, identity_element(G), X, DefaultOrthogonalBasis(N))
+    return get_coordinates(
+        base_manifold(G), identity_element(G), X, ManifoldsBase.DefaultOrthogonalBasis(N)
+    )
 end
 function get_coordinates_lie!(G::LieGroup, Y, g, X, N)
     return get_coordinates!(
-        base_manifold(G), Y, identity_element(G), X, DefaultOrthogonalBasis(N)
+        base_manifold(G), Y, identity_element(G), X, ManifoldsBase.DefaultOrthogonalBasis(N)
     )
 end
 
@@ -483,11 +485,13 @@ ManifoldsBase.get_vector(G::LieGroup, g, c, B::ManifoldsBase.AbstractBasis)
 ManifoldsBase.get_vector!(G::LieGroup, X, g, c, B::ManifoldsBase.AbstractBasis)
 
 @inline function get_vector_lie(G::LieGroup, g, c, N)
-    return get_vector(base_manifold(G), identity_element(G), c, DefaultOrthogonalBasis(N))
+    return get_vector(
+        base_manifold(G), identity_element(G), c, ManifoldsBase.DefaultOrthogonalBasis(N)
+    )
 end
 @inline function get_vector_lie!(G::LieGroup, Y, g, c, N)
     return get_vector!(
-        base_manifold(G), Y, identity_element(G), c, DefaultOrthogonalBasis(N)
+        base_manifold(G), Y, identity_element(G), c, ManifoldsBase.DefaultOrthogonalBasis(N)
     )
 end
 
@@ -514,15 +518,14 @@ Technically `hat` is a specific case of [`get_vector`](@ref) and is implemented
 
 # function hat end
 @doc "$(_doc_hat)"
-function hat(G::LieGroup, c)
-    X = zero_vector(LieAlgebra(G))
-    return hat!(G, X, c)
+function hat(G::LieGroup{𝔽}, c) where {𝔽}
+    return get_vector_lie(G, Identity(G), c, 𝔽)
 end
 
 # function hat! end
 @doc "$(_doc_hat)"
-function hat!(G::LieGroup, X, c)
-    get_vector!(G, X, identity_element(G), c, LieAlgebraOrthogonalBasis())
+function hat!(G::LieGroup{𝔽}, X, c) where {𝔽}
+    get_vector_lie!(G, X, Identity(G), c, 𝔽)
     return X
 end
 
@@ -845,17 +848,14 @@ Technically `hat` is a specific case of [`get_coordinates`](@ref) and is impleme
 
 # function vee end
 @doc "$(_doc_vee)"
-function vee(G::LieGroup, X)
-    c = ManifoldsBase.allocate_result(G, vee, X)
-    return vee!(G, c, X)
+function vee(G::LieGroup{𝔽}, X) where {𝔽}
+    return get_coordinates_lie(G, Identity(G), X, 𝔽)
 end
 
 # function vee! end
 @doc "$(_doc_vee)"
-function vee!(G::LieGroup, c, X)
-    get_coordinates!(
-        G, c, identity_element(G), X, LieAlgebraOrthogonalBasis(ManifoldsBase.ℝ)
-    )
+function vee!(G::LieGroup{𝔽}, c, X) where {𝔽}
+    get_coordinates_lie!(G, c, Identity(G), X, 𝔽)
     return c
 end
 

test/test_interface.jl

@@ -50,3 +50,25 @@ using LieGroupsTestSuite
         @test_throws MethodError log!(G, X, e, g)
     end
 end
+@testset "Generic Lie Algebra Interface functions" begin
+    M = ManifoldsBase.DefaultManifold(2)
+    op = AdditionGroupOperation()
+    G = LieGroup(M, op)
+    𝔤 = LieAlgebra(G)
+    @testset "Generic get_coordinates/get_vector passthrough on 𝔤" begin
+        B = DefaultOrthonormalBasis()
+        p = [1.0, 2.0]
+        q = [0.0, 0.0]
+        # coordinates and vector on 𝔤 are here the same as the ones on M at 0
+        X = [1.0, 0.0]
+        @test get_coordinates(𝔤, X, B) == get_coordinates(M, q, X, B)
+        Y = copy(X)
+        @test get_coordinates!(𝔤, Y, X, B) == get_coordinates!(M, Y, q, X, B)
+        @test X == Y
+        c = [0.0, 1.0]
+        @test get_vector(𝔤, c, B) == get_vector(M, q, c, B)
+        d = copy(c)
+        @test get_vector!(𝔤, d, c, B) == get_vector!(M, d, q, c, B)
+        @test c == d
+    end
+end