def test_spherical_to_extrinsic_and_inverse(self):
dim = 2
n_samples = 5
sphere = Hypersphere(dim)
points = gs.random.rand(n_samples, 2) * gs.pi * gs.array([1., 2.
])[None, :]
extrinsic = sphere.spherical_to_extrinsic(points)
result = sphere.extrinsic_to_spherical(extrinsic)
self.assertAllClose(result, points)
points_extrinsic = sphere.random_uniform(n_samples)
spherical = sphere.extrinsic_to_spherical(points_extrinsic)
result = sphere.spherical_to_extrinsic(spherical)
self.assertAllClose(result, points_extrinsic)
def test_extrinsic_to_spherical_vectorization(self):
dim = 2
sphere = Hypersphere(dim)
expected = gs.array([[gs.pi / 2, 0], [gs.pi / 6, gs.pi / 4]])
point_extrinsic = gs.array([
[1.0, 0.0, 0.0],
[gs.sqrt(2.0) / 4.0,
gs.sqrt(2.0) / 4.0,
gs.sqrt(3.0) / 2.0],
])
result = sphere.extrinsic_to_spherical(point_extrinsic)
self.assertAllClose(result, expected)
def test_extrinsic_to_spherical(self):
"""
Check vectorization of conversion from spherical
to extrinsic coordinates on the 2-sphere.
"""
dim = 2
sphere = Hypersphere(dim)
points_extrinsic = gs.array([1.0, 0.0, 0.0])
result = sphere.extrinsic_to_spherical(points_extrinsic)
expected = gs.array([gs.pi / 2, 0])
self.assertAllClose(result, expected)
def test_tangent_spherical_and_extrinsic_inverse(self):
dim = 2
n_samples = 5
sphere = Hypersphere(dim)
points = gs.random.rand(n_samples, 2) * gs.pi * gs.array([1., 2.
])[None, :]
tangent_spherical = gs.random.rand(n_samples, 2)
tangent_extrinsic = sphere.tangent_spherical_to_extrinsic(
tangent_spherical, points)
result = sphere.tangent_extrinsic_to_spherical(
tangent_extrinsic, base_point_spherical=points)
self.assertAllClose(result, tangent_spherical)
points_extrinsic = sphere.random_uniform(n_samples)
vector = gs.random.rand(n_samples, dim + 1)
tangent_extrinsic = sphere.to_tangent(vector, points_extrinsic)
tangent_spherical = sphere.tangent_extrinsic_to_spherical(
tangent_extrinsic, base_point=points_extrinsic)
spherical = sphere.extrinsic_to_spherical(points_extrinsic)
result = sphere.tangent_spherical_to_extrinsic(tangent_spherical,
spherical)
self.assertAllClose(result, tangent_extrinsic)