def test_curvature_derivative(self):
group = self.matrix_so3
metric = InvariantMetric(group=group)
x, y, z = metric.normal_basis(group.lie_algebra.basis)
result = metric.curvature_derivative(x, y, z, x)
expected = gs.zeros_like(x)
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)
tan_c = translation_map(z)
result = metric.curvature_derivative(tan_a, tan_b, tan_c, tan_a, point)
expected = gs.zeros_like(x)
self.assertAllClose(result, expected)
def test_curvature_derivative(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.curvature_derivative(x, y, z, x)
expected = gs.zeros_like(x)
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)
tan_c = translation_map(z)
result = metric.curvature_derivative(tan_a, tan_b, tan_c, tan_a, point)
expected = gs.zeros_like(x)
self.assertAllClose(result, expected)
def test_curvature_derivative_tangent_translation_map(
self,
group,
tangent_vec_a,
tangent_vec_b,
tangent_vec_c,
tangent_vec_d,
base_point,
expected,
):
metric = InvariantMetric(group=group)
translation_map = group.tangent_translation_map(base_point)
tan_a = translation_map(tangent_vec_a)
tan_b = translation_map(tangent_vec_b)
tan_c = translation_map(tangent_vec_c)
tan_d = translation_map(tangent_vec_d)
result = metric.curvature_derivative(tan_a, tan_b, tan_c, tan_d,
base_point)
self.assertAllClose(result, expected)