def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.space = EuclideanSpace(self.dimension)
self.metric = self.space.metric
self.n_samples = 3
def __init__(self, dimension):
assert isinstance(dimension, int) and dimension > 0
super(Hypersphere,
self).__init__(dimension=dimension,
embedding_manifold=EuclideanSpace(dimension + 1))
self.embedding_metric = self.embedding_manifold.metric
self.metric = HypersphereMetric(dimension)
def __init__(self, n):
assert isinstance(n, int) and n > 1
self.n = n
self.dimension = int((n * (n - 1)) / 2 + n)
super(SpecialEuclideanGroup, self).__init__(
dimension=self.dimension,
identity=gs.zeros(self.dimension))
# TODO(nina): keep the names rotations and translations here?
self.rotations = SpecialOrthogonalGroup(n=n)
self.translations = EuclideanSpace(dimension=n)
self.point_representation = 'vector' if n == 3 else 'matrix'
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.space = EuclideanSpace(self.dimension)
self.metric = self.space.metric
self.n_samples = 3
self.one_point_a = gs.array([0., 1.])
self.one_point_b = gs.array([2., 10.])
self.n_points_a = gs.array([[2., 1.], [-2., -4.], [-5., 1.]])
self.n_points_b = gs.array([[2., 10.], [8., -1.], [-3., 6.]])
def __init__(self, n):
assert n > 1
if n is not 3:
raise NotImplementedError('Only SE(3) is implemented.')
self.n = n
self.dimension = int((n * (n - 1)) / 2 + n)
super(SpecialEuclideanGroup, self).__init__(
dimension=self.dimension,
identity=np.zeros(self.dimension))
# TODO(nina): keep the names rotations and translations here?
self.rotations = SpecialOrthogonalGroup(n=n)
self.translations = EuclideanSpace(dimension=n)
def __init__(self, n, point_type=None):
assert isinstance(n, int) and n > 1
self.n = n
self.dimension = int((n * (n - 1)) / 2 + n)
self.default_point_type = point_type
if point_type is None:
self.default_point_type = 'vector' if n == 3 else 'matrix'
super(SpecialEuclideanGroup, self).__init__(dimension=self.dimension)
# TODO(nina): keep the names rotations and translations here?
self.rotations = SpecialOrthogonalGroup(n=n)
self.translations = EuclideanSpace(dimension=n)
def __init__(self, n, point_type=None, epsilon=0.):
assert isinstance(n, int) and n > 1
self.n = n
self.dimension = int((n * (n - 1)) / 2 + n)
self.epsilon = epsilon
self.default_point_type = point_type
if point_type is None:
self.default_point_type = 'vector' if n == 3 else 'matrix'
super(SpecialEuclideanGroup, self).__init__(dimension=self.dimension)
self.rotations = SpecialOrthogonalGroup(n=n, epsilon=epsilon)
self.translations = EuclideanSpace(dimension=n)
"""
Parameterized manifold.
"""
import math
import numpy as np
import geomstats.backend as gs
from geomstats.embedded_manifold import EmbeddedManifold
from geomstats.euclidean_space import EuclideanMetric
from geomstats.euclidean_space import EuclideanSpace
from geomstats.riemannian_metric import RiemannianMetric
R2 = EuclideanSpace(dimension=2)
R3 = EuclideanSpace(dimension=3)
def get_mask_i_float(i, n):
range_n = gs.arange(n)
i_float = gs.cast(gs.array([i]), gs.int32)[0]
mask_i = gs.equal(range_n, i_float)
mask_i_float = gs.cast(mask_i, gs.float32)
return mask_i_float
class DiscretizedCurvesSpace(EmbeddedManifold):
"""
Space of discretized curves sampled at points in embedding_manifold.
"""