tests

src/groups/rotation_translation_action.jl

@@ -186,7 +186,8 @@ function apply_diff!(
     p,
     X,
 )
-    return mul!(Y, a.x[2], X)
+    mul!(Y, a.x[2], X)
+    return Y
 end
 function apply_diff!(
     ::RotationTranslationActionOnVector{LeftAction},

test/groups/group_operation_action.jl

@@ -156,6 +156,10 @@ using Manifolds:
             RightBackwardAction(),
         )
 
+        Y = similar(X)
+        adjoint_apply_diff_group!(A_right_fwd, Y, a_pts[1], X, m)
+        @test Y ≈ inverse_translate_diff(G, m, a_pts[1], -X, RightBackwardAction())
+
         @test apply_diff_group(A_right_fwd, a_pts[1], X, m) ≈ -m \ X * m
         @test apply_diff_group(A_left_back, a_pts[1], X, m) ≈ -X
     end

test/groups/rotation_translation_action.jl

@@ -69,6 +69,30 @@ include("group_utils.jl")
             apply_diff_group!(A_left, Y, Identity(G), a_X_pts[1], m_pts[1])
             @test Y ≈ a_X_pts[1].x[2] * m_pts[1]
         end
+
+        @testset "apply_diff" begin
+            @test apply_diff(A_left, Identity(G), m_pts[1], X_pts[1]) ≈ X_pts[1]
+            Y = similar(X_pts[1])
+            apply_diff!(A_left, Y, Identity(G), m_pts[1], X_pts[1])
+            @test Y ≈ X_pts[1]
+
+            @test apply_diff(A_left, a_pts[1], m_pts[1], X_pts[1]) ≈
+                  a_pts[1].x[2] * X_pts[1]
+            Y = similar(X_pts[1])
+            apply_diff!(A_left, Y, a_pts[1], m_pts[1], X_pts[1])
+            @test Y ≈ a_pts[1].x[2] * X_pts[1]
+
+            @test apply_diff(A_right, Identity(G), m_pts[1], X_pts[1]) ≈ X_pts[1]
+            Y = similar(X_pts[1])
+            apply_diff!(A_right, Y, Identity(G), m_pts[1], X_pts[1])
+            @test Y ≈ X_pts[1]
+
+            @test apply_diff(A_right, a_pts[1], m_pts[1], X_pts[1]) ≈
+                  a_pts[1].x[2] \ X_pts[1]
+            Y = similar(X_pts[1])
+            apply_diff!(A_right, Y, a_pts[1], m_pts[1], X_pts[1])
+            @test Y ≈ a_pts[1].x[2] \ X_pts[1]
+        end
     end
 end