def test_inner_product_is_minkowski_inner_product(self, dim, tangent_vec_a,
tangent_vec_b,
base_point):
metric = self.metric(dim)
minkowki_space = Minkowski(dim + 1)
result = metric.inner_product(tangent_vec_a, tangent_vec_b, base_point)
expected = minkowki_space.metric.inner_product(tangent_vec_a,
tangent_vec_b,
base_point)
self.assertAllClose(result, expected)
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 __init__(self, dim, coords_type='extrinsic', scale=1):
super(Hyperboloid,
self).__init__(dim=dim,
scale=scale,
embedding_manifold=Minkowski(dim + 1))
self.coords_type = coords_type
self.point_type = Hyperboloid.default_point_type
self.embedding_metric = self.embedding_manifold.metric
self.metric =\
HyperboloidMetric(self.dim, self.coords_type, self.scale)
def __init__(self, dim, coords_type='extrinsic', scale=1):
# TODO (ninamiolane): Call __init__ from parent classes
# and remove ignore rule of corresponding DeepSource issue
self.scale = scale
self.dim = dim
self.coords_type = coords_type
self.point_type = Hyperboloid.default_point_type
self.embedding_manifold = Minkowski(dim + 1)
self.embedding_metric = self.embedding_manifold.metric
self.metric =\
HyperboloidMetric(self.dim, self.coords_type, self.scale)
def __init__(self, dim, coords_type="extrinsic", scale=1):
minkowski = Minkowski(dim + 1)
super(Hyperboloid, self).__init__(
dim=dim,
embedding_space=minkowski,
submersion=minkowski.metric.squared_norm,
value=-1.0,
tangent_submersion=minkowski.metric.inner_product,
scale=scale,
)
self.coords_type = coords_type
self.point_type = Hyperboloid.default_point_type
self.metric = HyperboloidMetric(self.dim, self.coords_type, self.scale)
def test_inner_product(self):
"""
Test that the inner product between two tangent vectors
is the Minkowski inner product.
"""
minkowski_space = Minkowski(self.dimension + 1)
base_point = gs.array([1.16563816, 0.36381045, -0.47000603, 0.07381469])
tangent_vec_a = self.space.to_tangent(
vector=gs.array([10.0, 200.0, 1.0, 1.0]), base_point=base_point
)
tangent_vec_b = self.space.to_tangent(
vector=gs.array([11.0, 20.0, -21.0, 0.0]), base_point=base_point
)
result = self.metric.inner_product(tangent_vec_a, tangent_vec_b, base_point)
expected = minkowski_space.metric.inner_product(
tangent_vec_a, tangent_vec_b, base_point
)
self.assertAllClose(result, expected)
class MinkowskiMetricTestData(_RiemannianMetricTestData):
n_list = random.sample(range(2, 4), 2)
metric_args_list = [(n, ) for n in n_list]
shape_list = metric_args_list
space_list = [Minkowski(n) for n in n_list]
n_points_list = random.sample(range(1, 3), 2)
n_tangent_vecs_list = random.sample(range(1, 3), 2)
n_points_a_list = random.sample(range(1, 3), 2)
n_points_b_list = [1]
alpha_list = [1] * 2
n_rungs_list = [1] * 2
scheme_list = ["pole"] * 2
def metric_matrix_test_data(self):
smoke_data = [dict(dim=2, expected=[[-1.0, 0.0], [0.0, 1.0]])]
return self.generate_tests(smoke_data)
def inner_product_test_data(self):
smoke_data = [
dict(dim=2,
point_a=[0.0, 1.0],
point_b=[2.0, 10.0],
expected=10.0),
dict(
dim=2,
point_a=[[-1.0, 0.0], [1.0, 0.0], [2.0, math.sqrt(3)]],
point_b=[
[2.0, -math.sqrt(3)],
[4.0, math.sqrt(15)],
[-4.0, math.sqrt(15)],
],
expected=[2.0, -4.0, 14.70820393],
),
]
return self.generate_tests(smoke_data)
def squared_norm_test_data(self):
smoke_data = [dict(dim=2, vector=[-2.0, 4.0], expected=12.0)]
return self.generate_tests(smoke_data)
def squared_dist_test_data(self):
smoke_data = [
dict(
dim=2,
point_a=[2.0, -math.sqrt(3)],
point_b=[4.0, math.sqrt(15)],
expected=27.416407,
)
]
return self.generate_tests(smoke_data)
def exp_test_data(self):
smoke_data = [
dict(
dim=2,
tangent_vec=[2.0, math.sqrt(3)],
base_point=[1.0, 0.0],
expected=[3.0, math.sqrt(3)],
)
]
return self.generate_tests(smoke_data)
def log_test_data(self):
smoke_data = [
dict(
dim=2,
point=[2.0, math.sqrt(3)],
base_point=[-1.0, 0.0],
expected=[3.0, math.sqrt(3)],
)
]
return self.generate_tests(smoke_data)
def exp_shape_test_data(self):
return self._exp_shape_test_data(self.metric_args_list,
self.space_list, self.shape_list)
def log_shape_test_data(self):
return self._log_shape_test_data(
self.metric_args_list,
self.space_list,
)
def squared_dist_is_symmetric_test_data(self):
return self._squared_dist_is_symmetric_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
atol=gs.atol * 1000,
)
def exp_belongs_test_data(self):
return self._exp_belongs_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
belongs_atol=gs.atol * 1000,
)
def log_is_tangent_test_data(self):
return self._log_is_tangent_test_data(
self.metric_args_list,
self.space_list,
self.n_points_list,
is_tangent_atol=gs.atol * 1000,
)
def geodesic_ivp_belongs_test_data(self):
return self._geodesic_ivp_belongs_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_points_list,
belongs_atol=gs.atol * 1000,
)
def geodesic_bvp_belongs_test_data(self):
return self._geodesic_bvp_belongs_test_data(
self.metric_args_list,
self.space_list,
self.n_points_list,
belongs_atol=gs.atol * 1000,
)
def log_then_exp_test_data(self):
return self._log_then_exp_test_data(
self.metric_args_list,
self.space_list,
self.n_points_list,
rtol=gs.rtol * 100,
atol=gs.atol * 10000,
)
def exp_then_log_test_data(self):
return self._exp_then_log_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
rtol=gs.rtol * 100,
atol=gs.atol * 10000,
)
def exp_ladder_parallel_transport_test_data(self):
return self._exp_ladder_parallel_transport_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
self.n_rungs_list,
self.alpha_list,
self.scheme_list,
)
def exp_geodesic_ivp_test_data(self):
return self._exp_geodesic_ivp_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
self.n_points_list,
rtol=gs.rtol * 1000,
atol=gs.atol * 1000,
)
def parallel_transport_ivp_is_isometry_test_data(self):
return self._parallel_transport_ivp_is_isometry_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
is_tangent_atol=gs.atol * 1000,
atol=gs.atol * 1000,
)
def parallel_transport_bvp_is_isometry_test_data(self):
return self._parallel_transport_bvp_is_isometry_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
is_tangent_atol=gs.atol * 1000,
atol=gs.atol * 1000,
)
def dist_is_symmetric_test_data(self):
return self._dist_is_symmetric_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def dist_is_norm_of_log_test_data(self):
return self._dist_is_norm_of_log_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def dist_point_to_itself_is_zero_test_data(self):
return self._dist_point_to_itself_is_zero_test_data(
self.metric_args_list, self.space_list, self.n_points_list)
def inner_product_is_symmetric_test_data(self):
return self._inner_product_is_symmetric_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_tangent_vecs_list,
)
def setUp(self):
self.sphere = Hypersphere(dimension=4)
self.hyperbolic = Hyperbolic(dimension=3)
self.euclidean = Euclidean(dimension=2)
self.minkowski = Minkowski(dimension=2)
from geomstats.geometry.minkowski import Minkowski
from geomstats.geometry.product_manifold import (
NFoldManifold,
NFoldMetric,
ProductManifold,
)
from geomstats.geometry.product_riemannian_metric import ProductRiemannianMetric
from geomstats.geometry.special_orthogonal import SpecialOrthogonal
from tests.conftest import Parametrizer
from tests.data_generation import _ManifoldTestData, _RiemannianMetricTestData
from tests.geometry_test_cases import ManifoldTestCase, RiemannianMetricTestCase
smoke_manifolds_1 = [Hypersphere(dim=2), Hyperboloid(dim=2)]
smoke_metrics_1 = [Hypersphere(dim=2).metric, Hyperboloid(dim=2).metric]
smoke_manifolds_2 = [Euclidean(3), Minkowski(3)]
smoke_metrics_2 = [Euclidean(3).metric, Minkowski(3).metric]
class TestProductManifold(ManifoldTestCase, metaclass=Parametrizer):
space = ProductManifold
skip_test_random_tangent_vec_is_tangent = True
skip_test_projection_belongs = True
class ProductManifoldTestData(_ManifoldTestData):
n_list = random.sample(range(2, 4), 2)
default_point_list = ["vector", "matrix"]
manifolds_list = [[Hypersphere(dim=n),
Hyperboloid(dim=n)] for n in n_list]
space_args_list = [(manifold, None, default_point)
def setUp(self):
gs.random.seed(123)
self.sphere = Hypersphere(dim=4)
self.hyperbolic = Hyperboloid(dim=3)
self.euclidean = Euclidean(dim=2)
self.minkowski = Minkowski(dim=2)