activate more tests that should work

src/Lie_algebra/Lie_algebra_interface.jl

@@ -152,7 +152,13 @@ function ManifoldsBase.zero_vector(𝔤::LieAlgebra)
     # pass to manifold directly
     return ManifoldsBase.zero_vector(𝔤.manifold.manifold, identity_element(𝔤.manifold))
 end
-function ManifoldsBase.zero_vector!(𝔤::LieAlgebra, X)
+function ManifoldsBase.zero_vector(𝔤::LieAlgebra, ::T) where {T}
+    # pass to Lie group
+    return ManifoldsBase.zero_vector(𝔤.manifold, identity_element(𝔤.manifold, T))
+end
+function ManifoldsBase.zero_vector!(𝔤::LieAlgebra, X::T) where {T}
     # pass to manifold directly
-    return ManifoldsBase.zero_vector!(𝔤.manifold.manifold, X, identity_element(𝔤.manifold))
+    return ManifoldsBase.zero_vector!(
+        𝔤.manifold.manifold, X, identity_element(𝔤.manifold, T)
+    )
 end

src/groups/special_euclidean_group.jl

@@ -317,7 +317,7 @@ ManifoldsBase.exp(
 
 @doc "$(_doc_exp_SE2_id)"
 function ManifoldsBase.exp!(
-    G::SpecialEuclideanGroup{ManifoldsBase.TypeParameter{Tuple{2}}},
+    G::SpecialEuclideanGroup{<:ManifoldsBase.TypeParameter{Tuple{2}}},
     g,
     ::Identity{<:SpecialEuclideanOperation},
     X,
@@ -375,15 +375,15 @@ This result can be computed in-place of `g`.
 @doc "$(_doc_exp_SE3_id)"
 ManifoldsBase.exp(
     ::SpecialEuclideanGroup{ManifoldsBase.TypeParameter{Tuple{3}}},
-    ::Identity{SpecialEuclideanOperation},
+    ::Identity{<:SpecialEuclideanOperation},
     ::Any,
 )
 
 @doc "$(_doc_exp_SE3_id)"
 function ManifoldsBase.exp!(
     G::SpecialEuclideanGroup{ManifoldsBase.TypeParameter{Tuple{3}}},
     g,
-    ::Identity{SpecialEuclideanOperation},
+    ::Identity{<:SpecialEuclideanOperation},
     X,
 )
     init_constants!(G, g)
@@ -408,11 +408,12 @@ function ManifoldsBase.exp!(
 end
 
 function ManifoldsBase.exp!(
-    G::SpecialEuclideanGroup,
+    G::SpecialEuclideanGroup{ManifoldsBase.TypeParameter{Tuple{n}}},
     g::AbstractMatrix,
-    ::Identity{SpecialEuclideanOperation},
-    X::AbstractMatrix,
-)
+    ::Identity{<:SpecialEuclideanOperation},
+    X;
+    AbstractMatrix,
+) where {n}
     copyto!(g, exp(X))
     return g
 end
@@ -582,15 +583,15 @@ This result can be computed in-place of `g`.
 @doc "$(_doc_log_SE2_id)"
 ManifoldsBase.log(
     ::SpecialEuclideanGroup{ManifoldsBase.TypeParameter{Tuple{2}}},
-    ::Identity{SpecialEuclideanOperation},
+    ::Identity{<:SpecialEuclideanOperation},
     ::Any,
 )
 
 @doc "$(_doc_log_SE2_id)"
 function ManifoldsBase.log!(
     G::SpecialEuclideanGroup{ManifoldsBase.TypeParameter{Tuple{2}}},
     X,
-    ::Identity{SpecialEuclideanOperation},
+    ::Identity{<:SpecialEuclideanOperation},
     g,
 )
     init_constants!(LieAlgebra(G), X)
@@ -637,15 +638,15 @@ This result can be computed in-place of `g`.
 @doc "$(_doc_log_SE3_id)"
 ManifoldsBase.log(
     ::SpecialEuclideanGroup{ManifoldsBase.TypeParameter{Tuple{3}}},
-    ::Identity{SpecialEuclideanOperation},
+    ::Identity{<:SpecialEuclideanOperation},
     ::Any,
 )
 
 @doc "$(_doc_log_SE3_id)"
 function ManifoldsBase.log!(
     G::SpecialEuclideanGroup{ManifoldsBase.TypeParameter{Tuple{3}}},
     X,
-    ::Identity{SpecialEuclideanOperation},
+    ::Identity{<:SpecialEuclideanOperation},
     g,
 )
     init_constants!(LieAlgebra(G), X)
@@ -669,7 +670,7 @@ end
 function ManifoldsBase.log!(
     ::SpecialEuclideanGroup,
     X::AbstractMatrix,
-    ::Identity{SpecialEuclideanOperation},
+    ::Identity{<:SpecialEuclideanOperation},
     g::AbstractMatrix,
 )
     copyto!(X, log(g))

src/interface.jl

@@ -405,14 +405,25 @@ Implementing the Lie group exponential function introduces a default implementat
 """
 
 @doc "$_doc_exp"
-function ManifoldsBase.exp(G::LieGroup, g, X, t::Number=1)
+function ManifoldsBase.exp(G::LieGroup, g, X, t::Number)
     h = allocate_result(G, exp, g)
     exp!(G, h, g, X, t)
     return h
 end
+function ManifoldsBase.exp(G::LieGroup, g, X)
+    h = allocate_result(G, exp, g)
+    exp!(G, h, g, X)
+    return h
+end
 
 @doc "$_doc_exp"
 function ManifoldsBase.exp!(G::LieGroup, h, g, X)
+    exp!(G, h, Identity(G), X)
+    compose!(G, h, g, h)
+    return h
+end
+
+function ManifoldsBase.exp!(G::LieGroup, h, g, X, t::Number)
     exp!(G, h, Identity(G), X, t)
     compose!(G, h, g, h)
     return h
@@ -918,8 +929,8 @@ Random.rand(G::LieGroup, T::Type; vector_at=nothing, kwargs...)
 function Random.rand(M::LieGroup, T::Type, d::Integer; kwargs...)
     return [rand(M, T; kwargs...) for _ in 1:d]
 end
-function Random.rand(rng::AbstractRNG, M::LieGroup, T::Type, d::Integer; kwargs...)
-    return [rand(rng, M, T; kwargs...) for _ in 1:d]
+function Random.rand(rng::AbstractRNG, G::LieGroup, T::Type, d::Integer; kwargs...)
+    return [rand(rng, G, T; kwargs...) for _ in 1:d]
 end
 function Random.rand(G::LieGroup, d::Integer; kwargs...)
     return [rand(M; kwargs...) for _ in 1:d]
@@ -948,12 +959,14 @@ function Random.rand!(G::LieGroup, pX; kwargs...)
     return rand!(Random.default_rng(), G, pX; kwargs...)
 end
 
-function Random.rand!(rng::AbstractRNG, G::LieGroup, pX; vector_at=nothing, kwargs...)
+function Random.rand!(
+    rng::AbstractRNG, G::LieGroup, pX::T; vector_at=nothing, kwargs...
+) where {T}
     M = base_manifold(G)
     if vector_at === nothing # for points -> pass to manifold
         rand!(rng, M, pX, kwargs...)
     else # for tangent vectors -> materialize identity, pass to tangent space there.
-        rand!(rng, M, pX; vector_at=identity_element(G), kwargs...)
+        rand!(rng, M, pX; vector_at=identity_element(G, T), kwargs...)
     end
 end
 

test/groups/test_special_euclidean_group.jl

@@ -7,7 +7,7 @@ using LieGroupsTestSuite
 @testset "Special Euclidean" begin
     G = SpecialEuclideanGroup(2)
     g1 = 1 / sqrt(2) .* [1.0 1.0 sqrt(2); -1.0 1.0 0.0; 0.0 0.0 sqrt(2)]
-    g2 = 1 / sqrt(2) .* [0.0 -1.0 0.0; 1.0 0.0 1.0; 0.0 0.0 1.0]
+    g2 = [0.0 -1.0 0.0; 1.0 0.0 1.0; 0.0 0.0 1.0]
     g3 = [1.0 0.0 1.0; 0.0 1.0 1.0; 0.0 0.0 1.0]
     X1 = [0.0 -0.23 0.0; 0.23 0.0 1.0; 0.0 0.0 0.0]
     X2 = [0.0 0.30 1.0; -0.20 0.0 1.0; 0.0 0.0 0.0]
@@ -30,9 +30,9 @@ using LieGroupsTestSuite
             inv,
             # inv_left_compose,
             # inv_right_compose,
-            # is_identity,
+            is_identity,
             # lie_bracket,
-            # log,
+            log,
             rand,
             show,
             vee,
@@ -72,10 +72,10 @@ using LieGroupsTestSuite
             inv,
             # inv_left_compose,
             # inv_right_compose,
-            # is_identity,
+            is_identity,
             # lie_bracket,
-            # log,
-            # rand, TODO: introduce rand(G, T)
+            log,
+            rand,
             show,
             vee,
         ],
@@ -106,7 +106,7 @@ using LieGroupsTestSuite
         :Functions => [
             # adjoint,
             compose,
-            # conjugate,
+            conjugate,
             # diff_inv,
             # diff_left_compose,
             # diff_right_compose,
@@ -116,10 +116,10 @@ using LieGroupsTestSuite
             inv,
             # inv_left_compose,
             # inv_right_compose,
-            # is_identity,
+            is_identity,
             # lie_bracket,
-            # log,
-            # rand, TODO: introduce rand(G, T)
+            log,
+            rand,
             show,
             vee,
         ],