def test_exp_and_log_right_metrics(self):
"""
Test that the Riemannian exponential and the
Riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
# General case for the reference point
base_point = self.point_2
# For right metric: point and point_small
result = helper.log_then_exp(self.right_metric, self.point_1, base_point)
expected = self.point_1
self.assertAllClose(result, expected, atol=1e-4)
result = helper.log_then_exp(self.right_metric, self.point_small, base_point)
expected = self.point_small
self.assertAllClose(result, expected)
def test_exp_and_log_right_diag_metrics(self):
"""
Test that the riemannian exponential and the
riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
# General case for the reference point
base_point = self.point_2
# For right diagonal metric: point and point_small
result = helper.log_then_exp(self.right_diag_metric,
base_point, self.point_1)
expected = self.group.regularize(self.point_1)
# self.assertAllClose(result, expected)
result = helper.log_then_exp(self.right_diag_metric,
base_point, self.point_small)
expected = self.group.regularize(self.point_small)
def test_exp_and_log_left_metrics(self):
"""
Test that the riemannian exponential and the
riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
# General case for the reference point
base_point = self.point_2
# For left metric: point and point_small
result = helper.log_then_exp(self.left_metric, base_point,
self.point_1)
expected = self.point_1
# self.assertTrue(gs.allclose(result, expected))
result = helper.log_then_exp(self.left_metric, base_point,
self.point_small)
expected = self.point_small
def test_exp_and_log_right_diag_metrics(self):
"""
Test that the Riemannian exponential and the
Riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
# FIXME: lower numerical accuracy with tensorflow
# General case for the reference point
base_point = self.point_2
# For right diagonal metric: point and point_small
result = helper.log_then_exp(
self.right_diag_metric, self.point_1, base_point)
expected = self.group.regularize(self.point_1)
self.assertAllClose(result, expected, atol=1e-4, rtol=1e-4)
result = helper.log_then_exp(
self.right_diag_metric, self.point_small, base_point)
expected = self.group.regularize(self.point_small)
self.assertAllClose(result, expected, atol=1e-4, rtol=1e-4)
def test_exp_and_log_left_diag_metrics(self):
"""
Test that the riemannian exponential and the
riemannian logarithm are inverse.
Expect their composition to give the identity function.
"""
# General case for the reference point
base_point = self.point_2
# General point
result = helper.log_then_exp(self.left_diag_metric, base_point,
self.point_1)
expected = self.group.regularize(self.point_1)
# self.assertTrue(gs.allclose(result, expected))
# Edge case, small angle
result = helper.log_then_exp(self.left_diag_metric, base_point,
self.point_small)
expected = self.group.regularize(self.point_small)
