def test_extrinsic_half_plane_extrinsic_composition(self, dim, point_intrinsic):
x = Hyperboloid(dim, coords_type="intrinsic").to_coordinates(
point_intrinsic, to_coords_type="extrinsic"
)
x_up = Hyperboloid(dim).to_coordinates(x, to_coords_type="half-space")
x2 = Hyperbolic.change_coordinates_system(x_up, "half-space", "extrinsic")
self.assertAllClose(x, x2)
def test_extrinsic_half_plane_extrinsic(self):
x_in = gs.array([0.5, 7], dtype=gs.float64)
x = self.intrinsic_manifold.to_coordinates(x_in,
to_coords_type="extrinsic")
x_up = self.extrinsic_manifold.to_coordinates(
x, to_coords_type="half-space")
x2 = Hyperbolic.change_coordinates_system(x_up, "half-space",
"extrinsic")
self.assertAllClose(x, x2)
def test_extrinsic_half_plane_extrinsic(self):
x_in = gs.array([0.5, 7])
x = self.intrinsic_manifold.to_coordinates(x_in,
to_coords_type='extrinsic')
x_up = self.extrinsic_manifold.to_coordinates(
x, to_coords_type='half-plane')
x2 = Hyperbolic.change_coordinates_system(x_up, 'half-plane',
'extrinsic')
self.assertAllClose(x, x2, atol=1e-8)
def extrinsic_to_intrinsic_coords(self, point_extrinsic):
"""Convert from extrinsic to intrinsic coordinates.
Parameters
----------
point_extrinsic : array-like, shape=[..., dim_embedding]
Point in the embedded manifold in extrinsic coordinates,
i. e. in the coordinates of the embedding manifold.
"""
belong_point = self.belongs(point_extrinsic)
if not gs.all(belong_point):
raise NameError("Point do not belong to the hyperboloid")
return\
Hyperbolic.change_coordinates_system(point_extrinsic,
'extrinsic',
'intrinsic')
def intrinsic_to_extrinsic_coords(self, point_intrinsic):
"""Convert from intrinsic to extrinsic coordinates.
Parameters
----------
point_intrinsic : array-like, shape=[..., dim]
Point in the embedded manifold in intrinsic coordinates.
"""
if self.dim != point_intrinsic.shape[-1]:
raise NameError("Wrong intrinsic dimension: "
+ str(point_intrinsic.shape[-1]) + " instead of "
+ str(self.dim))
return\
Hyperbolic.change_coordinates_system(point_intrinsic,
'intrinsic',
'extrinsic')
def intrinsic_to_extrinsic_coords(self, point_intrinsic):
"""Convert point from intrinsic to extrensic coordinates.
Convert the parameterization of a point in the hyperbolic space
from its intrinsic coordinates, to its extrinsic coordinates
in Minkowski space.
Parameters
----------
point_intrinsic : array-like, shape=[n_samples, n_disk, dim]
Returns
-------
point_extrinsic : array-like, shape=[n_samples, n_disks, dim + 1]
"""
n_disks = point_intrinsic.shape[1]
point_extrinsic = gs.stack([
Hyperbolic.change_coordinates_system(
point_intrinsic[:, i_disk, ...], 'intrinsic', 'extrinsic')
for i_disk in range(n_disks)
],
axis=1)
return point_extrinsic
