def test_raises(self):
space = self.space
point = space.random_uniform()
with pytest.raises(NotImplementedError):
space.extrinsic_to_spherical(point)
with pytest.raises(NotImplementedError):
space.tangent_extrinsic_to_spherical(point, point)
sphere = Hypersphere(2)
with pytest.raises(ValueError):
sphere.tangent_extrinsic_to_spherical(point)
def test_tangent_extrinsic_to_spherical(self):
"""
Check vectorization of conversion from spherical
to extrinsic coordinates for tangent vectors to the
2-sphere.
"""
dim = 2
sphere = Hypersphere(dim)
base_points_spherical = gs.array([[gs.pi / 2, 0], [gs.pi / 2, 0]])
expected = gs.array([[0.25, 0.5], [0.3, 0.2]])
tangent_vecs = gs.array([[0, 0.5, -0.25], [0, 0.2, -0.3]])
result = sphere.tangent_extrinsic_to_spherical(
tangent_vecs, base_point_spherical=base_points_spherical)
self.assertAllClose(result, expected)
result = sphere.tangent_extrinsic_to_spherical(tangent_vecs[0],
base_point=gs.array(
[1., 0., 0.]))
self.assertAllClose(result, expected[0])
def test_raises(self):
space = self.space
point = space.random_uniform()
self.assertRaises(NotImplementedError,
lambda: space.extrinsic_to_spherical(point))
self.assertRaises(
NotImplementedError,
lambda: space.tangent_extrinsic_to_spherical(point, point))
sphere = Hypersphere(2)
self.assertRaises(ValueError,
lambda: sphere.tangent_extrinsic_to_spherical(point))
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)
