class TestGrassmannianCanonicalMetric(RiemannianMetricTestCase, metaclass=Parametrizer):
metric = connection = GrassmannianCanonicalMetric
skip_test_log_after_exp = True
skip_test_exp_geodesic_ivp = True
skip_test_log_is_tangent = not np_backend()
testing_data = GrassmannianCanonicalMetricTestData()
def test_exp(self, n, k, tangent_vec, base_point, expected):
self.assertAllClose(
self.metric(n, k).exp(gs.array(tangent_vec), gs.array(base_point)),
gs.array(expected),
)
class TestMinkowskiMetric(RiemannianMetricTestCase, metaclass=Parametrizer):
connection = metric = MinkowskiMetric
skip_test_parallel_transport_ivp_is_isometry = True
skip_test_parallel_transport_bvp_is_isometry = True
skip_test_exp_geodesic_ivp = True
skip_test_dist_is_positive = True
skip_test_squared_dist_is_positive = True
skip_test_dist_is_norm_of_log = not np_backend()
skip_test_dist_is_symmetric = not np_backend()
skip_test_triangle_inequality_of_dist = True
testing_data = MinkowskiMetricTestData()
def test_metric_matrix(self, dim, expected):
metric = self.metric(dim)
self.assertAllClose(metric.metric_matrix(), gs.array(expected))
def test_inner_product(self, dim, point_a, point_b, expected):
metric = self.metric(dim)
self.assertAllClose(
metric.inner_product(gs.array(point_a), gs.array(point_b)),
gs.array(expected),
)
def test_squared_norm(self, dim, point, expected):
metric = self.metric(dim)
self.assertAllClose(metric.squared_norm(gs.array(point)), gs.array(expected))
def test_exp(self, dim, tangent_vec, base_point, expected):
result = self.metric(dim).exp(gs.array(tangent_vec), gs.array(base_point))
self.assertAllClose(result, gs.array(expected))
def test_log(self, dim, point, base_point, expected):
result = self.metric(dim).log(gs.array(point), gs.array(base_point))
self.assertAllClose(result, gs.array(expected))
def test_squared_dist(self, dim, point_a, point_b, expected):
result = self.metric(dim).squared_dist(gs.array(point_a), gs.array(point_b))
self.assertAllClose(result, gs.array(expected))
class TestMinkowskiMetric(RiemannianMetricTestCase, metaclass=Parametrizer):
connection = metric = MinkowskiMetric
skip_test_parallel_transport_ivp_is_isometry = True
skip_test_parallel_transport_bvp_is_isometry = True
skip_test_exp_geodesic_ivp = True
skip_test_dist_is_positive = True
skip_test_squared_dist_is_positive = True
skip_test_dist_is_norm_of_log = not np_backend()
skip_test_dist_is_symmetric = not np_backend()
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,
)
testing_data = MinkowskiMetricTestData()
def test_metric_matrix(self, dim, expected):
metric = self.metric(dim)
self.assertAllClose(metric.metric_matrix(), gs.array(expected))
def test_inner_product(self, dim, point_a, point_b, expected):
metric = self.metric(dim)
self.assertAllClose(
metric.inner_product(gs.array(point_a), gs.array(point_b)),
gs.array(expected),
)
def test_squared_norm(self, dim, point, expected):
metric = self.metric(dim)
self.assertAllClose(metric.squared_norm(gs.array(point)),
gs.array(expected))
def test_exp(self, dim, tangent_vec, base_point, expected):
result = self.metric(dim).exp(gs.array(tangent_vec),
gs.array(base_point))
self.assertAllClose(result, gs.array(expected))
def test_log(self, dim, point, base_point, expected):
result = self.metric(dim).log(gs.array(point), gs.array(base_point))
self.assertAllClose(result, gs.array(expected))
def test_squared_dist(self, dim, point_a, point_b, expected):
result = self.metric(dim).squared_dist(gs.array(point_a),
gs.array(point_b))
self.assertAllClose(result, gs.array(expected))
class TestGrassmannianCanonicalMetric(RiemannianMetricTestCase,
metaclass=Parametrizer):
metric = connection = GrassmannianCanonicalMetric
skip_test_exp_then_log = True
skip_test_exp_geodesic_ivp = True
skip_test_log_is_tangent = not np_backend()
class GrassmannianCanonicalMetricTestData(_RiemannianMetricTestData):
n_list = random.sample(range(3, 5), 2)
k_list = [random.sample(range(2, n), 1)[0] for n in n_list]
metric_args_list = list(zip(n_list, k_list))
shape_list = [(n, n) for n in n_list]
space_list = [Grassmannian(n, p) for n, p in metric_args_list]
n_points_list = random.sample(range(1, 5), 2)
n_points_a_list = random.sample(range(1, 5), 2)
n_points_b_list = [1]
n_tangent_vecs_list = random.sample(range(1, 5), 2)
alpha_list = [1] * 2
n_rungs_list = [1] * 2
scheme_list = ["pole"] * 2
def exp_test_data(self):
smoke_data = [
dict(
n=3,
k=2,
tangent_vec=Matrices.bracket(pi_2 * r_y,
gs.array([p_xy, p_yz])),
base_point=gs.array([p_xy, p_yz]),
expected=gs.array([p_yz, p_xy]),
),
dict(
n=3,
k=2,
tangent_vec=Matrices.bracket(pi_2 * gs.array([r_y, r_z]),
gs.array([p_xy, p_yz])),
base_point=gs.array([p_xy, p_yz]),
expected=gs.array([p_yz, p_xz]),
),
]
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 * 10000,
)
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 * 10000,
)
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 * 10000,
atol=gs.atol * 10000,
)
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,
atol=gs.atol * 1000,
)
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,
atol=gs.atol * 1000,
)
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,
)
testing_data = GrassmannianCanonicalMetricTestData()
def test_exp(self, n, k, tangent_vec, base_point, expected):
self.assertAllClose(
self.metric(n, k).exp(gs.array(tangent_vec), gs.array(base_point)),
gs.array(expected),
)