From d6e338127bc610f6b92b0683f242e2decd6c80b9 Mon Sep 17 00:00:00 2001
From: Mateusz Baran <mateuszbaran89@gmail.com>
Date: Fri, 3 Nov 2023 21:34:57 +0100
Subject: [PATCH] fix translate_diff on general unitary

---
 src/groups/general_unitary_groups.jl  | 8 ++++++--
 test/groups/general_unitary_groups.jl | 2 +-
 test/groups/group_operation_action.jl | 1 +
 3 files changed, 8 insertions(+), 3 deletions(-)

diff --git a/src/groups/general_unitary_groups.jl b/src/groups/general_unitary_groups.jl
index 804e6eecea..6f06c6e670 100644
--- a/src/groups/general_unitary_groups.jl
+++ b/src/groups/general_unitary_groups.jl
@@ -306,7 +306,9 @@ function translate_diff!(
     X,
     ::RightForwardAction,
 )
-    return copyto!(G, Y, X)
+    copyto!(G, Y, X)
+    Y .*= -1
+    return Y
 end
 function translate_diff!(
     G::GeneralUnitaryMultiplicationGroup,
@@ -316,7 +318,9 @@ function translate_diff!(
     X,
     ::LeftBackwardAction,
 )
-    return copyto!(G, Y, p * X * inv(G, p))
+    copyto!(G, Y, p * X * inv(G, p))
+    Y .*= -1
+    return Y
 end
 function translate_diff!(
     G::GeneralUnitaryMultiplicationGroup,
diff --git a/test/groups/general_unitary_groups.jl b/test/groups/general_unitary_groups.jl
index d393c07819..7168d59651 100644
--- a/test/groups/general_unitary_groups.jl
+++ b/test/groups/general_unitary_groups.jl
@@ -19,7 +19,7 @@ include("group_utils.jl")
             X2 = log_lie(On, p)
             e = Identity(MultiplicationOperation())
             # They are not yet inverting, p2 is on the “other half”
-            # but taking the log again should also be X ahain
+            # but taking the log again should also be X again
             @test isapprox(On, e, X2, X)
             @test log_lie(On, e) == zeros(n, n)
         end
diff --git a/test/groups/group_operation_action.jl b/test/groups/group_operation_action.jl
index 01f806c559..0f4974805d 100644
--- a/test/groups/group_operation_action.jl
+++ b/test/groups/group_operation_action.jl
@@ -136,5 +136,6 @@ using Manifolds:
 
         @test apply_diff_group(A_right_fwd, a_pts[1], X_pts[1], m_pts[1]) ≈
               -m_pts[1] \ X_pts[1] * m_pts[1]
+        @test apply_diff_group(A_left_back, a_pts[1], X_pts[1], m_pts[1]) ≈ -X_pts[1]
     end
 end