def test_inner_product_matrix_matrix(self):
euclidean = Euclidean(3)
minkowski = Minkowski(3)
space = ProductManifold(manifolds=[euclidean, minkowski],
default_point_type='matrix')
point = space.random_uniform(1)
result = space.metric.inner_product_matrix(point)
expected = gs.eye(6)
expected[3, 3] = -1
self.assertAllClose(result, expected)
def test_inner_product_matrix_matrix(self):
space = ProductManifold(manifolds=[
Hypersphere(dimension=2).embedding_manifold,
Hyperbolic(dimension=2).embedding_manifold
],
default_point_type='matrix')
point = space.random_uniform(1)
result = space.metric.inner_product_matrix(point)
expected = gs.identity(6)
expected[3, 3] = -1
self.assertAllClose(result, expected)
class TestProductManifoldMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.space_matrix = ProductManifold(
manifolds=[Hypersphere(dimension=2),
Hyperbolic(dimension=2)],
default_point_type='matrix')
self.space_vector = ProductManifold(
manifolds=[Hypersphere(dimension=2),
Hyperbolic(dimension=5)],
default_point_type='vector')
def test_dimension(self):
expected = 7
result = self.space_vector.dimension
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_random_and_belongs_matrix(self):
n_samples = 5
data = self.space_matrix.random_uniform(n_samples)
result = self.space_matrix.belongs(data)
expected = gs.array([[True] * n_samples]).transpose(1, 0)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_random_and_belongs_vector(self):
n_samples = 5
data = self.space_vector.random_uniform(n_samples)
result = self.space_vector.belongs(data)
expected = gs.array([[True] * n_samples]).transpose(1, 0)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_exp_log_vector(self):
n_samples = 5
expected = self.space_vector.random_uniform(n_samples)
base_point = self.space_vector.random_uniform(n_samples)
logs = self.space_vector.metric.log(expected, base_point)
result = self.space_vector.metric.exp(logs, base_point)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_exp_log_matrix(self):
n_samples = 5
expected = self.space_matrix.random_uniform(n_samples)
base_point = self.space_matrix.random_uniform(n_samples)
logs = self.space_matrix.metric.log(expected, base_point)
result = self.space_matrix.metric.exp(logs, base_point)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_dist_vector(self):
n_samples = 5
point = self.space_vector.random_uniform(n_samples)
base_point = self.space_vector.random_uniform(n_samples)
logs = self.space_vector.metric.log(point, base_point)
logs = gs.einsum('..., ...j->...j',
1. / self.space_vector.metric.norm(logs, base_point),
logs)
point = self.space_vector.metric.exp(logs, base_point)
result = self.space_vector.metric.dist(point, base_point)
expected = gs.ones(n_samples)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_dist_matrix(self):
n_samples = 5
point = self.space_matrix.random_uniform(n_samples)
base_point = self.space_matrix.random_uniform(n_samples)
logs = self.space_matrix.metric.log(point, base_point)
logs = gs.einsum('..., ...j->...j',
1. / self.space_matrix.metric.norm(logs, base_point),
logs)
point = self.space_matrix.metric.exp(logs, base_point)
result = self.space_matrix.metric.dist(point, base_point)
expected = gs.ones((n_samples, 1))
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_inner_product_matrix_matrix(self):
space = ProductManifold(manifolds=[
Hypersphere(dimension=2).embedding_manifold,
Hyperbolic(dimension=2).embedding_manifold
],
default_point_type='matrix')
point = space.random_uniform(1)
result = space.metric.inner_product_matrix(point)
expected = gs.identity(6)
expected[3, 3] = -1
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_inner_product_matrix_vector(self):
space = ProductManifold(manifolds=[
Hypersphere(dimension=2).embedding_manifold,
Hyperbolic(dimension=2).embedding_manifold
],
default_point_type='vector')
point = space.random_uniform(1)
expected = gs.identity(6)
expected[3, 3] = -1
result = space.metric.inner_product_matrix(point)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_regularize_vector(self):
expected = self.space_vector.random_uniform(5)
result = self.space_vector.regularize(expected)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_regularize_matrix(self):
expected = self.space_matrix.random_uniform(5)
result = self.space_matrix.regularize(expected)
self.assertAllClose(result, expected)
class TestProductManifoldMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.space_matrix = ProductManifold(
manifolds=[Hypersphere(dim=2),
Hyperboloid(dim=2)],
default_point_type='matrix')
self.space_vector = ProductManifold(
manifolds=[Hypersphere(dim=2),
Hyperboloid(dim=5)],
default_point_type='vector')
def test_dimension(self):
expected = 7
result = self.space_vector.dim
self.assertAllClose(result, expected)
def test_random_and_belongs_matrix(self):
n_samples = 5
data = self.space_matrix.random_uniform(n_samples)
result = self.space_matrix.belongs(data)
expected = gs.array([True] * n_samples)
self.assertAllClose(result, expected)
def test_random_and_belongs_vector(self):
n_samples = 5
data = self.space_vector.random_uniform(n_samples)
result = self.space_vector.belongs(data)
expected = gs.array([True] * n_samples)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_exp_log_vector(self):
n_samples = 5
expected = self.space_vector.random_uniform(n_samples)
base_point = self.space_vector.random_uniform(n_samples)
logs = self.space_vector.metric.log(expected, base_point)
result = self.space_vector.metric.exp(logs, base_point)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_exp_log_matrix(self):
n_samples = 5
expected = self.space_matrix.random_uniform(n_samples)
base_point = self.space_matrix.random_uniform(n_samples)
logs = self.space_matrix.metric.log(expected, base_point)
result = self.space_matrix.metric.exp(logs, base_point)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_dist_log_exp_norm_vector(self):
n_samples = 5
point = self.space_vector.random_uniform(n_samples)
base_point = self.space_vector.random_uniform(n_samples)
logs = self.space_vector.metric.log(point, base_point)
normalized_logs = gs.einsum(
'..., ...j->...j',
1. / self.space_vector.metric.norm(logs, base_point), logs)
point = self.space_vector.metric.exp(normalized_logs, base_point)
result = self.space_vector.metric.dist(point, base_point)
expected = gs.ones(n_samples)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_dist_log_exp_norm_matrix(self):
n_samples = 10
point = self.space_matrix.random_uniform(n_samples)
base_point = self.space_matrix.random_uniform(n_samples)
logs = self.space_matrix.metric.log(point, base_point)
normalized_logs = gs.einsum(
'..., ...jl->...jl',
1. / self.space_matrix.metric.norm(logs, base_point), logs)
point = self.space_matrix.metric.exp(normalized_logs, base_point)
result = self.space_matrix.metric.dist(point, base_point)
expected = gs.ones((n_samples, ))
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_inner_product_matrix_matrix(self):
euclidean = Euclidean(3)
minkowski = Minkowski(3)
space = ProductManifold(manifolds=[euclidean, minkowski],
default_point_type='matrix')
point = space.random_uniform(1)
result = space.metric.inner_product_matrix(point)
expected = gs.eye(6)
expected[3, 3] = -1
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_inner_product_matrix_vector(self):
euclidean = Euclidean(3)
minkowski = Minkowski(3)
space = ProductManifold(manifolds=[euclidean, minkowski],
default_point_type='vector')
point = space.random_uniform(1)
expected = gs.eye(6)
expected[3, 3] = -1
result = space.metric.inner_product_matrix(point)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_regularize_vector(self):
expected = self.space_vector.random_uniform(5)
result = self.space_vector.regularize(expected)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_regularize_matrix(self):
expected = self.space_matrix.random_uniform(5)
result = self.space_matrix.regularize(expected)
self.assertAllClose(result, expected)