def test_curvature_derivative_at_identity(self):
group = self.matrix_so3
metric = InvariantMetric(group=group)
basis = metric.normal_basis(group.lie_algebra.basis)
result = True
for x in basis:
for i, y in enumerate(basis):
for z in basis[i:]:
for t in basis:
nabla_r = metric.curvature_derivative_at_identity(x, y, z, t)
if not gs.all(gs.isclose(nabla_r, 0.0)):
print(nabla_r)
result = False
self.assertTrue(result)
def test_curvature_derivative_at_identity(self):
group = self.matrix_so3
lie_algebra = SkewSymmetricMatrices(3)
metric = InvariantMetric(group=group, algebra=lie_algebra)
basis = lie_algebra.orthonormal_basis(metric.metric_mat_at_identity)
result = True
for x in basis:
for i, y in enumerate(basis):
for z in basis[i:]:
for t in basis:
nabla_r = metric.curvature_derivative_at_identity(
x, y, z, t)
if not gs.all(gs.isclose(nabla_r, 0., atol=1e-5)):
print(nabla_r)
result = False
self.assertTrue(result)