Adapt to default_basis and pass onwards get_coordinates/get_vector (#34)

* adapt to default_basis
* Fix forward of defaults from Lie Group to Lie algebra.
* Fix forward of defaults from Lie Group to Lie algebra.
* add news entry.
* Fix the remaining ambiguities as well.
* Add tests for the new fallbacks.
* increase code coverage.
* Fix date in tutorial.
* Add an entry to the transition page about the second, positional argument of `identity_element`.

---------

Co-authored-by: Mateusz Baran <[email protected]>

Author: kellertuer

NEWS.md

@@ -10,6 +10,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ### Added
 
 * `identity_element` on `TranslationGroup` supports now `StaticArrays.jl` types.
+* introduce `get_vector` in legacy form to work on Lie groups, but they pass on to their Lie algebra.
+* adapt to the new `default_basis` from ManifoldsBase.jl 1.1.
 
 ### Changed
 

Project.toml

@@ -21,7 +21,7 @@ LieGroupsRecursiveArrayToolsExt = "RecursiveArrayTools"
 Aqua = "0.8"
 LinearAlgebra = "1.10"
 Manifolds = "0.10.16"
-ManifoldsBase = "1.0.3"
+ManifoldsBase = "1.1"
 Quaternions = "0.7.6"
 Random = "1.10"
 RecursiveArrayTools = "2, 3"

docs/src/tutorials/transition.md

@@ -58,3 +58,4 @@ The list is alphabetical, but first lists types, then functions
 3. Formerly, both a power manifold of Lie groups as a manifold as well as a Lie group of a power manifold as a Lie group were possible. This is unified to just defining `G^n` as the Lie group on the power manifold with the element-wise group operation.
 4. Formerly, product manifolds were stored as a [`ProductManifold`](@extref) of Lie groups and an indicator for the group operation, that the direct product should be used. This is switched to internally only store a [`ProductManifold`](@extref) as well as a (new) [`ProductGroupOperation`](@ref) that specifies one group operation for every factor.
 5. The last two points achieve one unified modelling aspect of Lie groups: they are now always a manifold `M` together with a group operation `op`, but a Lie group does not store another Lie group (or product of them) internally with one common type they share, a [`LieGroup`](@ref).
+6. Formerly, [`identity_element`](@ref)`(group[, gT])` to provide a materialized version of the [`Identity`](@ref) point on a Lie group accepted either a concrete point `g` on the Lie group _or_ the `Type` `T` of `g`. This is now unified for example with [`zero_vector`](@ref) and only accepts a `Type` as second argument.

src/interface.jl

@@ -280,6 +280,9 @@ function ManifoldsBase.copyto!(
         ),
     )
 end
+
+ManifoldsBase.default_basis(::AbstractLieGroup) = DefaultLieAlgebraOrthogonalBasis()
+
 _doc_diff_conjugate = """
     diff_conjugate(G::AbstractLieGroup, g, h, X)
     diff_conjugate!(G::AbstractLieGroup, Y, g, h, X)
@@ -430,6 +433,29 @@ end
 @doc "$(_doc_exponential)"
 ManifoldsBase.exp!(G::AbstractLieGroup, ::Any, ::Any)
 
+function ManifoldsBase.get_coordinates(
+    G::AbstractLieGroup, g, X, B::AbstractBasis{<:Any,TangentSpaceType}
+)
+    return get_coordinates(LieAlgebra(G), X, B)
+end
+function ManifoldsBase.get_coordinates!(
+    G::AbstractLieGroup, c, g, X, B::AbstractBasis{<:Any,TangentSpaceType}
+)
+    get_coordinates!(LieAlgebra(G), c, X, B)
+    return c
+end
+
+function ManifoldsBase.get_vector(
+    G::AbstractLieGroup, g, c, B::AbstractBasis{<:Any,TangentSpaceType}
+)
+    return get_vector(LieAlgebra(G), c, B)
+end
+function ManifoldsBase.get_vector!(
+    G::AbstractLieGroup, X, g, c, B::AbstractBasis{<:Any,TangentSpaceType}
+)
+    return get_vector!(LieAlgebra(G), X, c, B)
+end
+
 _doc_identity_element = """
     identity_element(G::AbstractLieGroup)
     identity_element(G::AbstractLieGroup, T)

test/test_interface.jl

@@ -69,18 +69,26 @@ end
         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
+        # Similarly: on G they are the same even for p
         X = [1.0, 0.0]
+        @test default_basis(G) == DefaultLieAlgebraOrthogonalBasis()
         @test get_coordinates(𝔤, X, B) == get_coordinates(M, q, X, B)
+        @test get_coordinates(G, p, 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
+        @test get_coordinates!(G, Y, p, 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)
+        @test get_vector(G, p, c, B) == get_vector(M, q, c, B)
         @test get_vector(𝔤, c, B; tangent_vector_type=Vector{Float64}) ==
             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
+        @test get_vector!(G, d, p, c, B) == get_vector!(M, d, q, c, B)
+        @test c == d
         @test project(G, p) == project(M, p)
         @test project(𝔤, X) == project(M, p, X)
         @test project(𝔤, X, X) == project(M, p, X)

tutorials/getstarted.qmd

@@ -311,7 +311,7 @@ Pkg.status()
 #| echo: false
 #| output: asis
 using Dates
-println("This tutorial was last rendered $(Dates.format(now(), "U d, Y, H:M:S")).");
+println("This tutorial was last rendered $(Dates.format(now(), "U d, Y, HH:MM:SS")).");
 ```
 
 ## Literature