def test_dist_log_then_exp_norm(self, manifolds, default_point_type,
n_samples, einsum_str, expected):
space = ProductManifold(manifolds=manifolds,
default_point_type=default_point_type)
point = space.random_point(n_samples)
base_point = space.random_point(n_samples)
logs = space.metric.log(point, base_point)
normalized_logs = gs.einsum(
einsum_str,
1.0 / space.metric.norm(logs, base_point),
logs,
)
point = space.metric.exp(normalized_logs, base_point)
result = space.metric.dist(point, base_point)
self.assertAllClose(result, expected)
def test_inner_product_matrix_vector(self, default_point_type):
euclidean = Euclidean(3)
minkowski = Minkowski(3)
space = ProductManifold(manifolds=[euclidean, minkowski])
point = space.random_point(1)
expected = gs.eye(6)
expected[3, 3] = -1
result = space.metric.metric_matrix(point)
self.assertAllClose(result, expected)
class TestProductManifold(geomstats.tests.TestCase):
def setup_method(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=3)],
default_point_type="vector",
)
def test_dimension(self):
expected = 5
result = self.space_vector.dim
self.assertAllClose(result, expected)
def test_random_and_belongs_matrix(self):
n_samples = 1
data = self.space_matrix.random_point(n_samples)
result = self.space_matrix.belongs(data)
self.assertTrue(result)
n_samples = 5
data = self.space_matrix.random_point(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_point(n_samples)
result = self.space_vector.belongs(data)
expected = gs.array([True] * n_samples)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_autograd_only
def test_exp_log_vector(self):
n_samples = 5
expected = self.space_vector.random_point(n_samples)
base_point = self.space_vector.random_point(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_autograd_and_torch_only
def test_exp_log_matrix(self):
n_samples = 5
expected = self.space_matrix.random_point(n_samples)
base_point = self.space_matrix.random_point(n_samples)
logs = self.space_matrix.metric.log(expected, base_point)
result = self.space_matrix.metric.exp(logs, base_point)
self.assertAllClose(result, expected, atol=1e-5)
@geomstats.tests.np_and_autograd_only
def test_dist_log_exp_norm_vector(self):
n_samples = 5
point = self.space_vector.random_point(n_samples)
base_point = self.space_vector.random_point(n_samples)
logs = self.space_vector.metric.log(point, base_point)
normalized_logs = gs.einsum(
"..., ...j->...j",
1.0 / 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_autograd_and_torch_only
def test_dist_log_exp_norm_matrix(self):
n_samples = 10
point = self.space_matrix.random_point(n_samples)
base_point = self.space_matrix.random_point(n_samples)
logs = self.space_matrix.metric.log(point, base_point)
normalized_logs = gs.einsum(
"..., ...jl->...jl",
1.0 / 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_autograd_and_torch_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_point(1)
result = space.metric.metric_matrix(point)
expected = gs.eye(6)
expected[3, 3] = -1
self.assertAllClose(result, expected)
@geomstats.tests.np_autograd_and_torch_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_point(1)
expected = gs.eye(6)
expected[3, 3] = -1
result = space.metric.metric_matrix(point)
self.assertAllClose(result, expected)
def test_regularize_vector(self):
expected = self.space_vector.random_point(5)
result = self.space_vector.regularize(expected)
self.assertAllClose(result, expected)
def test_regularize_matrix(self):
expected = self.space_matrix.random_point(5)
result = self.space_matrix.regularize(expected)
self.assertAllClose(result, expected)
@geomstats.tests.np_autograd_and_torch_only
def test_inner_product_matrix(self):
n_samples = 1
expected = self.space_matrix.random_point(n_samples)
base_point = self.space_matrix.random_point(n_samples)
logs = self.space_matrix.metric.log(expected, base_point)
result = self.space_matrix.metric.inner_product(logs, logs)
expected = self.space_matrix.metric.squared_dist(base_point, expected)
self.assertAllClose(result, expected)
n_samples = 5
expected = self.space_matrix.random_point(n_samples)
base_point = self.space_matrix.random_point(n_samples)
logs = self.space_matrix.metric.log(expected, base_point)
result = self.space_matrix.metric.inner_product(logs, logs)
expected = self.space_matrix.metric.squared_dist(base_point, expected)
self.assertAllClose(result, expected)
@geomstats.tests.np_autograd_and_torch_only
def test_projection_and_belongs_vector(self):
space = self.space_vector
shape = (2, space.dim + 2)
result = helper.test_projection_and_belongs(space, shape, atol=gs.atol * 100)
for res in result:
self.assertTrue(res)
@geomstats.tests.np_autograd_and_torch_only
def test_projection_and_belongs_matrix(self):
space = self.space_matrix
shape = (2, len(space.manifolds), space.manifolds[0].dim + 1)
result = helper.test_projection_and_belongs(space, shape, atol=gs.atol * 100)
for res in result:
self.assertTrue(res)
def test_to_tangent_is_tangent_vector(self):
space = self.space_vector
result = helper.test_to_tangent_is_tangent(space, atol=gs.atol)
for res in result:
self.assertTrue(res)
def test_to_tangent_is_tangent_matrix(self):
space = self.space_matrix
result = helper.test_to_tangent_is_tangent(space, atol=gs.atol)
for res in result:
self.assertTrue(res)
class TestProductManifold(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 = 1
data = self.space_matrix.random_point(n_samples)
result = self.space_matrix.belongs(data)
self.assertTrue(result)
n_samples = 5
data = self.space_matrix.random_point(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_point(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_point(n_samples)
base_point = self.space_vector.random_point(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_point(n_samples)
base_point = self.space_matrix.random_point(n_samples)
logs = self.space_matrix.metric.log(expected, base_point)
result = self.space_matrix.metric.exp(logs, base_point)
self.assertAllClose(result, expected, atol=1e-5)
@geomstats.tests.np_only
def test_dist_log_exp_norm_vector(self):
n_samples = 5
point = self.space_vector.random_point(n_samples)
base_point = self.space_vector.random_point(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_point(n_samples)
base_point = self.space_matrix.random_point(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_point(1)
result = space.metric.metric_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_point(1)
expected = gs.eye(6)
expected[3, 3] = -1
result = space.metric.metric_matrix(point)
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_regularize_vector(self):
expected = self.space_vector.random_point(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_point(5)
result = self.space_matrix.regularize(expected)
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_inner_product_matrix(self):
n_samples = 1
expected = self.space_matrix.random_point(n_samples)
base_point = self.space_matrix.random_point(n_samples)
logs = self.space_matrix.metric.log(expected, base_point)
result = self.space_matrix.metric.inner_product(logs, logs)
expected = self.space_matrix.metric.squared_dist(base_point, expected)
self.assertAllClose(result, expected)
n_samples = 5
expected = self.space_matrix.random_point(n_samples)
base_point = self.space_matrix.random_point(n_samples)
logs = self.space_matrix.metric.log(expected, base_point)
result = self.space_matrix.metric.inner_product(logs, logs)
expected = self.space_matrix.metric.squared_dist(base_point, expected)
self.assertAllClose(result, expected)