def test_log_after_exp_with_angles_close_to_pi(
self, metric, tangent_vec, base_point
):
"""
Test that the Riemannian left exponential and the
Riemannian left logarithm are inverse.
Expect their composition to give the identity function.
"""
group = SpecialEuclidean(3, "vector")
result = metric.log(metric.exp(tangent_vec, base_point), base_point)
expected = group.regularize_tangent_vec(
tangent_vec=tangent_vec, base_point=base_point, metric=metric
)
inv_expected = gs.concatenate([-expected[:3], expected[3:6]])
norm = gs.linalg.norm(expected)
atol = ATOL
if norm != 0:
atol = ATOL * norm
self.assertTrue(
gs.allclose(result, expected, atol=atol)
or gs.allclose(result, inv_expected, atol=atol)
)
def test_log_after_exp(self, metric, tangent_vec, base_point):
"""
Test that the Riemannian left exponential and the
Riemannian left logarithm are inverse.
Expect their composition to give the identity function.
"""
group = SpecialEuclidean(3, "vector")
result = metric.log(metric.exp(tangent_vec, base_point), base_point)
expected = group.regularize_tangent_vec(
tangent_vec=tangent_vec, base_point=base_point, metric=metric
)
norm = gs.linalg.norm(expected)
atol = ATOL
if norm != 0:
atol = ATOL * norm
self.assertAllClose(result, expected, atol=atol)
