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test_spd_matrices_space.py
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test_spd_matrices_space.py
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"""
Unit tests for the manifold of symmetric positive definite matrices.
"""
import warnings
import geomstats.backend as gs
import geomstats.tests
import tests.helper as helper
from geomstats.spd_matrices_space import SPDMatricesSpace
class TestSPDMatricesSpaceMethods(geomstats.tests.TestCase):
_multiprocess_can_split_ = True
def setUp(self):
warnings.simplefilter('ignore', category=ImportWarning)
gs.random.seed(1234)
self.n = 3
self.space = SPDMatricesSpace(n=self.n)
self.metric = self.space.metric
self.n_samples = 4
def test_random_uniform_and_belongs(self):
point = self.space.random_uniform()
result = self.space.belongs(point)
expected = gs.array([[True]])
self.assertAllClose(result, expected)
def test_random_uniform_and_belongs_vectorization(self):
"""
Test that the random uniform method samples
on the hypersphere space.
"""
n_samples = self.n_samples
points = self.space.random_uniform(n_samples=n_samples)
result = self.space.belongs(points)
self.assertAllClose(gs.shape(result), (n_samples, 1))
def vector_from_symmetric_matrix_and_symmetric_matrix_from_vector(self):
sym_mat_1 = gs.array([[1., 0.6, -3.],
[0.6, 7., 0.],
[-3., 0., 8.]])
vector_1 = self.space.vector_from_symmetric_matrix(sym_mat_1)
result_1 = self.space.symmetric_matrix_from_vector(vector_1)
expected_1 = sym_mat_1
self.assertTrue(gs.allclose(result_1, expected_1))
vector_2 = gs.array([1, 2, 3, 4, 5, 6])
sym_mat_2 = self.space.symmetric_matrix_from_vector(vector_2)
result_2 = self.space.vector_from_symmetric_matrix(sym_mat_2)
expected_2 = vector_2
self.assertTrue(gs.allclose(result_2, expected_2))
def vector_and_symmetric_matrix_vectorization(self):
n_samples = self.n_samples
vector = gs.random.rand(n_samples, 6)
sym_mat = self.space.symmetric_matrix_from_vector(vector)
result = self.space.vector_from_symmetric_matrix(sym_mat)
expected = vector
self.assertTrue(gs.allclose(result, expected))
sym_mat = self.space.random_uniform(n_samples)
vector = self.space.vector_from_symmetric_matrix(sym_mat)
result = self.space.symmetric_matrix_from_vector(vector)
expected = sym_mat
self.assertTrue(gs.allclose(result, expected))
def test_log_and_exp(self):
base_point = gs.array([[5., 0., 0.],
[0., 7., 2.],
[0., 2., 8.]])
point = gs.array([[9., 0., 0.],
[0., 5., 0.],
[0., 0., 1.]])
log = self.metric.log(point=point, base_point=base_point)
result = self.metric.exp(tangent_vec=log, base_point=base_point)
expected = helper.to_matrix(point)
self.assertAllClose(result, expected)
def test_exp_and_belongs(self):
n_samples = self.n_samples
base_point = self.space.random_uniform(n_samples=1)
tangent_vec = self.space.random_tangent_vec_uniform(
n_samples=n_samples,
base_point=base_point)
exps = self.metric.exp(tangent_vec, base_point)
result = self.space.belongs(exps)
expected = gs.array([[True]] * n_samples)
self.assertAllClose(result, expected)
def test_exp_vectorization(self):
n_samples = self.n_samples
one_base_point = self.space.random_uniform(n_samples=1)
n_base_point = self.space.random_uniform(n_samples=n_samples)
n_tangent_vec_same_base = self.space.random_tangent_vec_uniform(
n_samples=n_samples,
base_point=one_base_point)
n_tangent_vec = self.space.random_tangent_vec_uniform(
n_samples=n_samples,
base_point=n_base_point)
# Test with the 1 base_point, and several different tangent_vecs
result = self.metric.exp(n_tangent_vec_same_base, one_base_point)
self.assertAllClose(
gs.shape(result), (n_samples, self.space.n, self.space.n))
# Test with the same number of base_points and tangent_vecs
result = self.metric.exp(n_tangent_vec, n_base_point)
self.assertAllClose(
gs.shape(result), (n_samples, self.space.n, self.space.n))
def test_log_vectorization(self):
n_samples = self.n_samples
one_base_point = self.space.random_uniform(n_samples=1)
n_base_point = self.space.random_uniform(n_samples=n_samples)
one_point = self.space.random_uniform(n_samples=1)
n_point = self.space.random_uniform(n_samples=n_samples)
# Test with different points, one base point
result = self.metric.log(n_point, one_base_point)
self.assertAllClose(
gs.shape(result), (n_samples, self.space.n, self.space.n))
# Test with the same number of points and base points
result = self.metric.log(n_point, n_base_point)
self.assertAllClose(
gs.shape(result), (n_samples, self.space.n, self.space.n))
# Test with the one point and n base points
result = self.metric.log(one_point, n_base_point)
self.assertAllClose(
gs.shape(result), (n_samples, self.space.n, self.space.n))
def test_geodesic_and_belongs(self):
initial_point = self.space.random_uniform()
initial_tangent_vec = self.space.random_tangent_vec_uniform(
n_samples=1,
base_point=initial_point)
geodesic = self.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec)
n_points = 10
t = gs.linspace(start=0., stop=1., num=n_points)
points = geodesic(t)
result = self.space.belongs(points)
expected = gs.array([[True]] * n_points)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_squared_dist_is_symmetric(self):
n_samples = self.n_samples
point_1 = self.space.random_uniform(n_samples=1)
point_2 = self.space.random_uniform(n_samples=1)
sq_dist_1_2 = self.metric.squared_dist(point_1, point_2)
sq_dist_2_1 = self.metric.squared_dist(point_2, point_1)
self.assertAllClose(sq_dist_1_2, sq_dist_2_1)
point_1 = self.space.random_uniform(n_samples=1)
point_2 = self.space.random_uniform(n_samples=n_samples)
sq_dist_1_2 = self.metric.squared_dist(point_1, point_2)
sq_dist_2_1 = self.metric.squared_dist(point_2, point_1)
self.assertAllClose(sq_dist_1_2, sq_dist_2_1)
point_1 = self.space.random_uniform(n_samples=n_samples)
point_2 = self.space.random_uniform(n_samples=1)
sq_dist_1_2 = self.metric.squared_dist(point_1, point_2)
sq_dist_2_1 = self.metric.squared_dist(point_2, point_1)
self.assertAllClose(sq_dist_1_2, sq_dist_2_1)
point_1 = self.space.random_uniform(n_samples=n_samples)
point_2 = self.space.random_uniform(n_samples=n_samples)
sq_dist_1_2 = self.metric.squared_dist(point_1, point_2)
sq_dist_2_1 = self.metric.squared_dist(point_2, point_1)
self.assertAllClose(sq_dist_1_2, sq_dist_2_1)
def test_squared_dist_vectorization(self):
n_samples = self.n_samples
point_1 = self.space.random_uniform(n_samples=n_samples)
point_2 = self.space.random_uniform(n_samples=n_samples)
result = self.metric.squared_dist(point_1, point_2)
self.assertAllClose(gs.shape(result), (n_samples, 1))
point_1 = self.space.random_uniform(n_samples=1)
point_2 = self.space.random_uniform(n_samples=n_samples)
result = self.metric.squared_dist(point_1, point_2)
self.assertAllClose(gs.shape(result), (n_samples, 1))
point_1 = self.space.random_uniform(n_samples=n_samples)
point_2 = self.space.random_uniform(n_samples=1)
result = self.metric.squared_dist(point_1, point_2)
self.assertAllClose(gs.shape(result), (n_samples, 1))
point_1 = self.space.random_uniform(n_samples=1)
point_2 = self.space.random_uniform(n_samples=1)
result = self.metric.squared_dist(point_1, point_2)
self.assertAllClose(gs.shape(result), (1, 1))
if __name__ == '__main__':
geomstats.tests.main()