def powerm(cls, mat, power):
"""
Compute the matrix power.
Parameters
----------
mat : array_like, shape=[..., n, n]
Symmetric matrix with non-negative eigenvalues.
power : float, list
Power at which mat will be raised. If a list of powers is passed,
a list of results will be returned.
Returns
-------
powerm : array_like or list of arrays, shape=[..., n, n]
Matrix power of mat.
"""
if isinstance(power, list):
power_ = [lambda ev, p=p: gs.power(ev, p) for p in power]
else:
def power_(ev):
return gs.power(ev, power)
return cls.apply_func_to_eigvals(mat, power_, check_positive=True)
def diag_inner_product(tangent_vec_a, tangent_vec_b, base_point):
"""Compute the inner product using only diagonal elements.
Parameters
----------
tangent_vec_a : array-like, shape=[..., n, n]
Tangent vector at base point.
tangent_vec_b : array-like, shape=[..., n, n]
Tangent vector at base point.
base_point : array-like, shape=[..., n, n]
Base point.
Returns
-------
ip_diagonal : array-like, shape=[...]
Inner-product.
"""
inv_sqrt_diagonal = gs.power(Matrices.diagonal(base_point), -2)
tangent_vec_a_diagonal = Matrices.diagonal(tangent_vec_a)
tangent_vec_b_diagonal = Matrices.diagonal(tangent_vec_b)
prod = tangent_vec_a_diagonal * tangent_vec_b_diagonal * inv_sqrt_diagonal
ip_diagonal = gs.sum(prod, axis=-1)
return ip_diagonal
def _power(eigvals):
return gs.power(eigvals, power)
The n-dimensional hyperbolic space with Poincare ball model.
Lead author: Hadi Zaatiti.
"""
import geomstats.algebra_utils as utils
import geomstats.backend as gs
from geomstats.geometry._hyperbolic import _Hyperbolic
from geomstats.geometry.base import OpenSet
from geomstats.geometry.euclidean import Euclidean
from geomstats.geometry.riemannian_metric import RiemannianMetric
EPSILON = 1e-6
NORMALIZATION_FACTOR_CST = gs.sqrt(gs.pi / 2)
PI_2_3 = gs.power(gs.array([2.0 * gs.pi]), gs.array([2 / 3]))
SQRT_2 = gs.sqrt(2.0)
class PoincareBall(_Hyperbolic, OpenSet):
"""Class for the n-dimensional Poincare ball.
Class for the n-dimensional Poincaré ball model. For other
representations of hyperbolic spaces see the `Hyperbolic` class.
Parameters
----------
dim : int
Dimension of the hyperbolic space.
scale : int
Scale of the hyperbolic space, defined as the set of points
def test_inner_product_norm(self, m, n, mat):
self.assertAllClose(
self.metric(m, n).inner_product(mat, mat),
gs.power(self.metric(m, n).norm(mat), 2),
)
def power_(ev):
return gs.power(ev, power)
