def test_connection(self):
group = self.matrix_so3
metric = InvariantMetric(group=group)
x, y, z = metric.normal_basis(group.lie_algebra.basis)
result = metric.connection(x, y)
expected = 1.0 / 2**0.5 / 2.0 * z
self.assertAllClose(result, expected)
point = group.random_uniform()
translation_map = group.tangent_translation_map(point)
tan_a = translation_map(x)
tan_b = translation_map(y)
result = metric.connection(tan_a, tan_b, point)
expected = translation_map(expected)
self.assertAllClose(result, expected)
def test_connection(self):
group = self.matrix_so3
lie_algebra = SkewSymmetricMatrices(3)
metric = InvariantMetric(group=group, algebra=lie_algebra)
x, y, z = lie_algebra.orthonormal_basis(metric.metric_mat_at_identity)
result = metric.connection(-z, y)
expected = -1. / 2**.5 / 2. * x
self.assertAllClose(result, expected)
point = group.random_uniform()
translation_map = group.tangent_translation_map(point)
tan_a = translation_map(-z)
tan_b = translation_map(y)
result = metric.connection(tan_a, tan_b, point)
expected = translation_map(expected)
self.assertAllClose(result, expected)
def test_connection_translation_map(self, group, tangent_vec_a,
tangent_vec_b, point, expected):
metric = InvariantMetric(group)
translation_map = group.tangent_translation_map(point)
tan_a = translation_map(tangent_vec_a)
tan_b = translation_map(tangent_vec_b)
result = metric.connection(tan_a, tan_b, point)
expected = translation_map(expected)
self.assertAllClose(result, expected, rtol=1e-3, atol=1e-3)
def test_connection(self, group, tangent_vec_a, tangent_vec_b, expected):
metric = InvariantMetric(group)
self.assertAllClose(metric.connection(tangent_vec_a, tangent_vec_b),
expected)