Fix diff_group_apply (#73)

* Fix diff_group_apply

* fix ref name

* fixes and tests

* fix test

* add missing method

Author: mateuszbaran

NEWS.md

@@ -5,6 +5,12 @@ All notable Changes to the Julia package `LieGroups.jl` will be documented in th
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [0.1.6] 2025-10-10
+
+### Fixed
+
+* `diff_group_apply` has corrected documentation and works with `g` equal to `Identity`.
+
 ## [0.1.5] 2025-10-09
 
 ### Changed

Project.toml

@@ -1,7 +1,7 @@
 name = "LieGroups"
 uuid = "6774de46-80ba-43f8-ba42-e41071ccfc5f"
 authors = ["Seth Axen <[email protected]>", "Mateusz Baran <[email protected]>", "Ronny Bergmann <[email protected]>", "Yueh-Hua Tu", "Olivier Verdier <[email protected]>"]
-version = "0.1.5"
+version = "0.1.6"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/group_actions/columnwise_action.jl

@@ -22,3 +22,13 @@ function apply!(a::GroupAction{ColumnwiseGroupAction{LeftMultiplicationGroupActi
     map((qcol, pcol) -> apply!(b, qcol, g, pcol), eachcol(q), eachcol(p))
     return q
 end
+
+function diff_group_apply!(
+        ::GroupAction{ColumnwiseGroupAction{LeftMultiplicationGroupAction}},
+        Y,
+        ::Identity{MatrixMultiplicationGroupOperation},
+        p,
+        X,
+    )
+    return Base.mightalias(Y, X) ? Y .= X * p : mul!(Y, X, p)
+end

src/group_actions/group_action_interface.jl

@@ -277,19 +277,39 @@ function diff_apply! end
 @doc "$(_doc_diff_apply)"
 diff_apply!(A::GroupAction, q, g, p)
 
-_doc_diff_group_apply = """
+_doc_diff_group_apply = raw"""
     diff_group_apply(A::GroupAction, g, p, X)
     diff_group_apply!(A::GroupAction, Y, g, p, X)
 
-Compute the differential ``$(_math(:d))_{$(_tex(:Cal, "G"))} σ_g(p): $(_math(:𝔤)) → $(_math(:𝔤))``,
-where we use the short hand notation ``σ_p(g) = σ(g,p)`` for a left action,
-and for a right action ``τ_p(g) = τ(g,p)``.
+
+Compute the value of differential of action [`GroupAction`](@ref) `A` on vector `X`,
+where element `g` is acting on `p`, with respect to the group element.
+
+Let ``\mathcal G`` be the group acting on manifold ``\mathcal M`` by the action `A`.
+The action is of element ``g ∈ \mathcal G`` on a point ``p ∈ \mathcal M``.
+The differential transforms vector `X` from the tangent space at `a ∈ \mathcal G`,
+``X ∈ T_a \mathcal G`` into a tangent space of the manifold ``\mathcal M``.
+When action on element `p` is written as ``\mathrm{d}τ^p``, with the specified left or right
+convention, the differential transforms vectors
+
+````math
+(\mathrm{d}τ^p) : T_{a} \mathcal G → T_{τ_a p} \mathcal M
+````
+
+# See also
+
+[`apply`](@ref), [`diff_apply`](@ref)
 """
 
 function diff_group_apply end
 @doc "$(_doc_diff_group_apply)"
 function diff_group_apply(A::GroupAction, g, p, X)
-    Y = allocate_result(base_manifold(A), apply, g, X)
+    Y = allocate_result(base_manifold(A), diff_group_apply, g, X)
+    diff_group_apply!(A, Y, g, p, X)
+    return Y
+end
+function diff_group_apply(A::GroupAction, g::Identity, p, X)
+    Y = allocate_on(A.manifold, TangentSpaceType())
     diff_group_apply!(A, Y, g, p, X)
     return Y
 end

src/group_actions/multiplication_action.jl

@@ -26,8 +26,8 @@ end
 function diff_apply!(::GroupAction{LeftMultiplicationGroupAction}, Y, g, p, X)
     return Base.mightalias(Y, X) ? Y .= g * X : mul!(Y, g, X)
 end
+=#
 
-function diff_group_apply!(::GroupAction{LeftMultiplicationGroupAction}, Y, g, p, X)
+function diff_group_apply!(::GroupAction{LeftMultiplicationGroupAction}, Y, ::Identity{MatrixMultiplicationGroupOperation}, p, X)
     return Base.mightalias(Y, X) ? Y .= X * p : mul!(Y, X, p)
 end
-=#

test/LieGroupsTestSuite.jl/LieGroupsTestSuite.jl

@@ -339,6 +339,8 @@ function test_diff_group_apply(
                 @test isapprox(𝔤, Y1, Y3)
             end
         end
+        e = Identity(G)
+        @test is_vector(G, e, diff_group_apply(A, e, p, X))
         !ismissing(expected) && @test isapprox(𝔤, Y1, expected)
     end
 end

test/actions/test_columnwise_action.jl

@@ -7,7 +7,7 @@ using LieGroupsTestSuite
 
 @testset "Columnwise Actions" begin
     G = SpecialOrthogonalGroup(3)
-    M = Euclidean(3)
+    M = Euclidean(3, 3)
     cga = ColumnwiseGroupAction(LeftMultiplicationGroupAction())
     a = GroupAction(cga, G, M)
     s = 1 / sqrt(2)
@@ -17,5 +17,6 @@ using LieGroupsTestSuite
     @test apply(a, g, p) ≈ gp
     q = similar(p)
     apply!(a, q, g, p)
-
+    X = [0.0 -3.0 2.0; 3.0 0.0 -1.0; -2.0 1.0 0.0]
+    @test diff_group_apply(a, Identity(G), p, X) ≈ X * p
 end

test/actions/test_multiplication_action.jl

@@ -0,0 +1,27 @@
+using LieGroups, Test
+using Manifolds: Euclidean
+
+s = joinpath(@__DIR__, "..", "LieGroupsTestSuite.jl")
+!(s in LOAD_PATH) && (push!(LOAD_PATH, s))
+using LieGroupsTestSuite
+
+@testset "Multiplication Action" begin
+    G = SpecialOrthogonalGroup(3)
+    M = Euclidean(3)
+    a = LeftMultiplicationGroupAction()
+    A = GroupAction(a, G, M)
+
+    g = [0.7620105424968724 -0.01728550575563964 0.6473338739896082; -0.3990906109981697 0.7746993466910932 0.4904769173462713; -0.5099672708485612 -0.6320934531595508 0.583430586390622]
+    p = [4.0, 5.0, 6.0]
+    gp = g * p
+    @test apply(A, g, p) ≈ gp
+    q = similar(p)
+    apply!(A, q, g, p)
+    @test q ≈ gp
+
+    X = [0.0 -3.0 2.0; 3.0 0.0 -1.0; -2.0 1.0 0.0]
+    Z = similar(p)
+    diff_group_apply!(A, Z, Identity(G), p, X)
+    @test Z ≈ X * p
+    @test diff_group_apply(A, Identity(G), p, X) ≈ X * p
+end

test/actions/test_rowwise_action.jl

@@ -7,7 +7,7 @@ using LieGroupsTestSuite
 
 @testset "Rowwise Actions" begin
     G = SpecialOrthogonalGroup(3)
-    M = Euclidean(3)
+    M = Euclidean(3, 3)
     cga = RowwiseGroupAction(LeftMultiplicationGroupAction())
     a = GroupAction(cga, G, M)
     s = 1 / sqrt(2)

test/runtests.jl

@@ -25,6 +25,7 @@ end
         include_test("actions/test_action_interface.jl")
         include_test("actions/test_addition_action.jl")
         include_test("actions/test_operation_action.jl")
+        include_test("actions/test_multiplication_action.jl")
         include_test("actions/test_rotation_around_axis_action.jl")
         include_test("actions/test_columnwise_action.jl")
         include_test("actions/test_rowwise_action.jl")