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 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 setUp(self):
gs.random.seed(1234)
self.sphere = Hypersphere(dimension=2)
self.hyperbolic = Hyperbolic(dimension=5)
self.space = ProductManifold(manifolds=[self.sphere, self.hyperbolic])
def regularize_test_data(self):
smoke_data = [
dict(
manifold=smoke_manifolds_1,
default_point_type="vector",
point=ProductManifold(
smoke_manifolds_1,
default_point_type="vector").random_point(5),
),
dict(
manifold=smoke_manifolds_1,
default_point_type="matrix",
point=ProductManifold(
smoke_manifolds_1,
default_point_type="matrix").random_point(5),
),
]
return self.generate_tests(smoke_data)
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)
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)
def inner_product_matrix_test_data(self):
smoke_data = [
dict(
metric=smoke_metrics_2,
default_point_type="vector",
point=ProductManifold(
smoke_manifolds_1,
default_point_type="vector").random_point(5),
base_point=ProductManifold(
smoke_manifolds_1,
default_point_type="vector").random_point(5),
),
dict(
manifold=smoke_metrics_2,
default_point_type="matrix",
point=ProductManifold(
smoke_manifolds_2,
default_point_type="matrix").random_point(5),
base_point=ProductManifold(
smoke_manifolds_2,
default_point_type="matrix").random_point(5),
),
]
return self.generate_tests(smoke_data)
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)
class ProductRiemannianMetricTestData(_RiemannianMetricTestData):
n_list = random.sample(range(2, 3), 1)
default_point_list = ["vector", "matrix"]
manifolds_list = [[Hypersphere(dim=n),
Hyperboloid(dim=n)] for n in n_list]
metrics_list = [[Hypersphere(dim=n).metric,
Hyperboloid(dim=n).metric] for n in n_list]
metric_args_list = list(zip(metrics_list, default_point_list))
shape_list = [(n + 1, n + 1) if default_point == "matrix" else
(2 * (n + 1), )
for n, default_point in zip(n_list, default_point_list)]
space_list = [
ProductManifold(manifolds, None, default_point_type) for manifolds,
default_point_type in zip(manifolds_list, default_point_list)
]
n_points_list = random.sample(range(2, 5), 1)
n_tangent_vecs_list = random.sample(range(2, 5), 1)
n_points_a_list = random.sample(range(2, 5), 1)
n_points_b_list = [1]
alpha_list = [1] * 1
n_rungs_list = [1] * 1
scheme_list = ["pole"] * 1
def inner_product_matrix_test_data(self):
smoke_data = [
dict(
metric=smoke_metrics_2,
default_point_type="vector",
point=ProductManifold(
smoke_manifolds_1,
default_point_type="vector").random_point(5),
base_point=ProductManifold(
smoke_manifolds_1,
default_point_type="vector").random_point(5),
),
dict(
manifold=smoke_metrics_2,
default_point_type="matrix",
point=ProductManifold(
smoke_manifolds_2,
default_point_type="matrix").random_point(5),
base_point=ProductManifold(
smoke_manifolds_2,
default_point_type="matrix").random_point(5),
),
]
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=1e-1,
)
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 * 1000,
atol=1e-1,
)
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,
amplitude=10,
rtol=gs.rtol * 1000,
atol=1e-1,
)
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 * 100000,
atol=gs.atol * 100000,
)
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_positive_test_data(self):
return self._dist_is_positive_test_data(
self.metric_args_list,
self.space_list,
self.n_points_a_list,
self.n_points_b_list,
)
def squared_dist_is_positive_test_data(self):
return self._squared_dist_is_positive_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 inner_product_matrix_vector_test_data(self):
random_data = [
dict(default_point_type="matrix"),
dict(default_point_type="vector"),
]
return self.generate_tests([], random_data)
def dist_log_then_exp_norm_test_data(self):
smoke_data = [
dict(
space=smoke_manifolds_1,
default_point_type="vector",
n_samples=10,
einsum_str="..., ...j->...j",
expected=gs.ones(10),
),
dict(
space=smoke_manifolds_1,
default_point_type="matrix",
n_samples=10,
einsum_str="..., ...jl->...jl",
expected=gs.ones(10, ),
),
]
return self.generate_tests(smoke_data)