def test_geodesic_with_log_connection(self, dim, point, end_point, n_times,
n_steps, expected, atol):
sphere = Hypersphere(dim)
connection = Connection(dim)
connection.christoffels = sphere.metric.christoffels
geo = connection.geodesic(initial_point=point,
end_point=end_point,
n_steps=n_steps)
times = gs.linspace(0, 1, n_times)
geo = geo(times)
result = geo.shape
self.assertAllClose(result, expected, atol)
def test_exp_connection_metric(self, dim, tangent_vec, base_point):
sphere = Hypersphere(dim)
connection = Connection(dim)
point_ext = sphere.spherical_to_extrinsic(base_point)
vector_ext = sphere.tangent_spherical_to_extrinsic(
tangent_vec, base_point)
connection.christoffels = sphere.metric.christoffels
expected = sphere.metric.exp(vector_ext, point_ext)
result_spherical = connection.exp(tangent_vec,
base_point,
n_steps=50,
step="rk4")
result = sphere.spherical_to_extrinsic(result_spherical)
self.assertAllClose(result, expected)
def test_log_connection_metric(self, dim, point, base_point, atol):
sphere = Hypersphere(dim)
connection = Connection(dim)
connection.christoffels = sphere.metric.christoffels
vector = connection.log(point=point,
base_point=base_point,
n_steps=75,
step="rk4",
tol=1e-10)
result = sphere.tangent_spherical_to_extrinsic(vector, base_point)
p_ext = sphere.spherical_to_extrinsic(base_point)
q_ext = sphere.spherical_to_extrinsic(point)
expected = sphere.metric.log(base_point=p_ext, point=q_ext)
self.assertAllClose(result, expected, atol)
