def test_exp_after_log(self, metric, point, base_point):
"""
Test that the Riemannian right exponential and the
Riemannian right logarithm are inverse.
Expect their composition to give the identity function.
"""
group = SpecialEuclidean(3, "vector")
result = metric.exp(metric.log(point, base_point), base_point)
expected = group.regularize(point)
expected = gs.cast(expected, gs.float64)
norm = gs.linalg.norm(expected)
atol = ATOL
if norm != 0:
atol = ATOL * norm
self.assertAllClose(result, expected, atol=atol)
def test_exp_after_log_right_with_angles_close_to_pi(
self, metric, point, base_point):
group = SpecialEuclidean(3, "vector")
result = metric.exp(metric.log(point, base_point), base_point)
expected = group.regularize(point)
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_regularize_extreme_cases(self, point, expected):
group = SpecialEuclidean(3, "vector")
result = group.regularize(point)
self.assertAllClose(result, expected)
