def test_hands(self):
"""Test that hands belong to space of landmarks."""
data, labels, _ = data_utils.load_hands()
result = data.shape
n_hands = 52
k_landmarks = 22
dim = 3
expected = (n_hands, k_landmarks, dim)
self.assertAllClose(result, expected)
landmarks_space = Landmarks(ambient_manifold=Euclidean(dim=3),
k_landmarks=k_landmarks)
result = landmarks_space.belongs(data)
self.assertTrue(gs.all(result))
result = gs.logical_and(labels >= 0, labels <= 1)
self.assertTrue(gs.all(result))
def test_load_optical_nerves(self):
"""Test that optical nerves belong to space of landmarks."""
data, labels, monkeys = data_utils.load_optical_nerves()
result = data.shape
n_monkeys = 11
n_eyes_per_monkey = 2
k_landmarks = 5
dim = 3
expected = (n_monkeys * n_eyes_per_monkey, k_landmarks, dim)
self.assertAllClose(result, expected)
landmarks_space = Landmarks(ambient_manifold=Euclidean(dim=dim),
k_landmarks=k_landmarks)
result = landmarks_space.belongs(data)
self.assertTrue(gs.all(result))
result = gs.logical_and(labels >= 0, labels <= 1)
self.assertTrue(gs.all(result))
result = gs.logical_and(monkeys >= 0, monkeys <= 11)
self.assertTrue(gs.all(result))
def setUp(self):
s2 = Hypersphere(dim=2)
r3 = s2.embedding_manifold
initial_point = [0., 0., 1.]
initial_tangent_vec_a = [1., 0., 0.]
initial_tangent_vec_b = [0., 1., 0.]
initial_tangent_vec_c = [-1., 0., 0.]
landmarks_a = s2.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_a)
landmarks_b = s2.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_b)
landmarks_c = s2.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_c)
self.n_sampling_points = 10
sampling_times = gs.linspace(0., 1., self.n_sampling_points)
landmark_set_a = landmarks_a(sampling_times)
landmark_set_b = landmarks_b(sampling_times)
landmark_set_c = landmarks_c(sampling_times)
self.n_landmark_sets = 5
self.times = gs.linspace(0., 1., self.n_landmark_sets)
self.atol = 1e-6
gs.random.seed(1234)
self.space_landmarks_in_euclidean_3d = Landmarks(
ambient_manifold=r3, n_landmarks=self.n_sampling_points)
self.space_landmarks_in_sphere_2d = Landmarks(
ambient_manifold=s2, n_landmarks=self.n_sampling_points)
self.l2_metric_s2 = self.space_landmarks_in_sphere_2d.metric
self.l2_metric_r3 = self.space_landmarks_in_euclidean_3d.metric
self.landmarks_a = landmark_set_a
self.landmarks_b = landmark_set_b
self.landmarks_c = landmark_set_c
class TestLandmarks(geomstats.tests.TestCase):
@geomstats.tests.np_and_pytorch_only
def setUp(self):
s2 = Hypersphere(dim=2)
r3 = s2.embedding_manifold
initial_point = [0., 0., 1.]
initial_tangent_vec_a = [1., 0., 0.]
initial_tangent_vec_b = [0., 1., 0.]
initial_tangent_vec_c = [-1., 0., 0.]
landmarks_a = s2.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_a)
landmarks_b = s2.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_b)
landmarks_c = s2.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_c)
self.n_sampling_points = 10
sampling_times = gs.linspace(0., 1., self.n_sampling_points)
landmark_set_a = landmarks_a(sampling_times)
landmark_set_b = landmarks_b(sampling_times)
landmark_set_c = landmarks_c(sampling_times)
self.n_landmark_sets = 5
self.times = gs.linspace(0., 1., self.n_landmark_sets)
self.atol = 1e-6
gs.random.seed(1234)
self.space_landmarks_in_euclidean_3d = Landmarks(ambient_manifold=r3)
self.space_landmarks_in_sphere_2d = Landmarks(ambient_manifold=s2)
self.l2_metric_s2 = self.space_landmarks_in_sphere_2d.l2_metric
self.l2_metric_r3 = self.space_landmarks_in_euclidean_3d.l2_metric
self.landmarks_a = landmark_set_a
self.landmarks_b = landmark_set_b
self.landmarks_c = landmark_set_c
@geomstats.tests.np_and_pytorch_only
def test_belongs(self):
result = self.space_landmarks_in_sphere_2d.belongs(self.landmarks_a)
expected = True
self.assertAllClose(result, expected)
# TODO (ninamiolane): Uncomment when belongs is vectorized
# @geomstats.tests.np_and_pytorch_only
# def test_belongs_vectorization(self):
# landmark_sets = gs.array([self.landmarks_a, self.landmarks_b])
# result = self.space_landmarks_in_sphere_2d.belongs(landmark_sets)
# expected = gs.array([True, True])
# self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_l2_metric_log_and_squared_norm_and_dist(self):
"""Test that squared norm of logarithm is squared dist."""
tangent_vec = self.l2_metric_s2.log(landmarks=self.landmarks_b,
base_landmarks=self.landmarks_a)
log_ab = tangent_vec
result = self.l2_metric_s2.squared_norm(vector=log_ab,
base_point=self.landmarks_a)
expected = self.l2_metric_s2.dist(self.landmarks_a,
self.landmarks_b)**2
self.assertAllClose(result, expected)
@geomstats.tests.np_only
def test_l2_metric_log_and_exp(self):
"""Test that exp and log are inverse maps."""
tangent_vec = self.l2_metric_s2.log(landmarks=self.landmarks_b,
base_landmarks=self.landmarks_a)
result = self.l2_metric_s2.exp(tangent_vec=tangent_vec,
base_landmarks=self.landmarks_a)
expected = self.landmarks_b
self.assertAllClose(result, expected, atol=self.atol)
@geomstats.tests.np_only
def test_l2_metric_inner_product_vectorization(self):
"""Test the vectorization inner_product."""
n_samples = self.n_landmark_sets
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_bc = self.l2_metric_s2.geodesic(self.landmarks_b,
self.landmarks_c)
landmarks_ab = landmarks_ab(self.times)
landmarks_bc = landmarks_bc(self.times)
tangent_vecs = self.l2_metric_s2.log(landmarks=landmarks_bc,
base_landmarks=landmarks_ab)
result = self.l2_metric_s2.inner_product(tangent_vecs, tangent_vecs,
landmarks_ab)
self.assertAllClose(gs.shape(result), (n_samples, ))
@geomstats.tests.np_only
def test_l2_metric_dist_vectorization(self):
"""Test the vectorization of dist."""
n_samples = self.n_landmark_sets
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_bc = self.l2_metric_s2.geodesic(self.landmarks_b,
self.landmarks_c)
landmarks_ab = landmarks_ab(self.times)
landmarks_bc = landmarks_bc(self.times)
result = self.l2_metric_s2.dist(landmarks_ab, landmarks_bc)
self.assertAllClose(gs.shape(result), (n_samples, ))
@geomstats.tests.np_and_tf_only
def test_l2_metric_exp_vectorization(self):
"""Test the vectorization of exp."""
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_bc = self.l2_metric_s2.geodesic(self.landmarks_b,
self.landmarks_c)
landmarks_ab = landmarks_ab(self.times)
landmarks_bc = landmarks_bc(self.times)
tangent_vecs = self.l2_metric_s2.log(landmarks=landmarks_bc,
base_landmarks=landmarks_ab)
result = self.l2_metric_s2.exp(tangent_vec=tangent_vecs,
base_landmarks=landmarks_ab)
self.assertAllClose(gs.shape(result), gs.shape(landmarks_ab))
@geomstats.tests.np_only
def test_l2_metric_log_vectorization(self):
"""Test the vectorization of log."""
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_bc = self.l2_metric_s2.geodesic(self.landmarks_b,
self.landmarks_c)
landmarks_ab = landmarks_ab(self.times)
landmarks_bc = landmarks_bc(self.times)
tangent_vecs = self.l2_metric_s2.log(landmarks=landmarks_bc,
base_landmarks=landmarks_ab)
result = tangent_vecs
self.assertAllClose(gs.shape(result), gs.shape(landmarks_ab))
@geomstats.tests.np_only
def test_l2_metric_geodesic(self):
"""Test the geodesic method of L2Metric."""
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_bc = self.l2_metric_s2.geodesic(self.landmarks_b,
self.landmarks_c)
landmarks_ab = landmarks_ab(self.times)
landmarks_bc = landmarks_bc(self.times)
result = landmarks_ab
expected = gs.zeros(landmarks_ab.shape)
for k in range(self.n_sampling_points):
geod = self.l2_metric_s2.ambient_metric.geodesic(
initial_point=self.landmarks_a[k, :],
end_point=self.landmarks_b[k, :])
expected[:, k, :] = geod(self.times)
self.assertAllClose(result, expected)
geod = self.l2_metric_s2.geodesic(initial_landmarks=landmarks_ab,
end_landmarks=landmarks_bc)
class TestDataL2Metric(_RiemannianMetricTestData):
dim_list = random.sample(range(2, 4), 2)
n_landmarks_list = random.sample(range(2, 5), 2)
metric_args_list = [
(Hypersphere(dim), n_landmarks)
for dim, n_landmarks in zip(dim_list, n_landmarks_list)
] + [(Euclidean(dim + 1), n_landmarks)
for dim, n_landmarks in zip(dim_list, n_landmarks_list)]
space_list = [Landmarks(*metric_arg) for metric_arg in metric_args_list]
shape_list = [(n_landmark, dim + 1)
for dim, n_landmark in zip(dim_list, n_landmarks_list)] * 2
n_points_list = random.sample(range(2, 5), 2)
n_tangent_vecs_list = random.sample(range(2, 5), 2)
n_points_a_list = random.sample(range(2, 5), 2)
n_points_b_list = [1]
alpha_list = [1] * 4
n_rungs_list = [1] * 4
scheme_list = ["pole"] * 4
s2 = Hypersphere(dim=2)
r3 = s2.embedding_space
initial_point = [0.0, 0.0, 1.0]
initial_tangent_vec_a = [1.0, 0.0, 0.0]
initial_tangent_vec_b = [0.0, 1.0, 0.0]
initial_tangent_vec_c = [-1.0, 0.0, 0.0]
landmarks_a = s2.metric.geodesic(initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_a)
landmarks_b = s2.metric.geodesic(initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_b)
landmarks_c = s2.metric.geodesic(initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_c)
n_sampling_points = 10
sampling_times = gs.linspace(0.0, 1.0, n_sampling_points)
landmark_set_a = landmarks_a(sampling_times)
landmark_set_b = landmarks_b(sampling_times)
landmark_set_c = landmarks_c(sampling_times)
n_landmark_sets = 5
times = gs.linspace(0.0, 1.0, n_landmark_sets)
space_landmarks_in_sphere_2d = Landmarks(ambient_manifold=s2,
k_landmarks=n_sampling_points)
l2_metric_s2 = space_landmarks_in_sphere_2d.metric
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 * 10000,
)
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 * 100,
)
def exp_after_log_test_data(self):
return self._exp_after_log_test_data(
self.metric_args_list,
self.space_list,
self.n_tangent_vecs_list,
rtol=gs.rtol * 1000,
atol=gs.atol * 1000,
)
def log_after_exp_test_data(self):
return self._log_after_exp_test_data(
self.metric_args_list,
self.space_list,
self.shape_list,
self.n_points_list,
amplitude=30,
rtol=gs.rtol * 10000,
atol=gs.atol * 100000,
)
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 * 100,
)
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 * 100,
atol=gs.atol * 100,
)
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 triangle_inequality_of_dist_test_data(self):
return self._triangle_inequality_of_dist_test_data(
self.metric_args_list, self.space_list, self.n_points_list)
def l2_metric_inner_product_vectorization_test_data(self):
smoke_data = [
dict(
l2_metric=self.l2_metric_s2,
times=self.times,
landmark_sets=self.n_landmark_sets,
landmarks_a=self.landmark_set_a,
landmarks_b=self.landmark_set_b,
landmarks_c=self.landmark_set_c,
)
]
return self.generate_tests(smoke_data)
def l2_metric_exp_vectorization_test_data(self):
smoke_data = [
dict(
l2_metric=self.l2_metric_s2,
times=self.times,
landmarks_a=self.landmark_set_a,
landmarks_b=self.landmark_set_b,
landmarks_c=self.landmark_set_c,
)
]
return self.generate_tests(smoke_data)
def l2_metric_log_vectorization_test_data(self):
smoke_data = [
dict(
l2_metric=self.l2_metric_s2,
times=self.times,
landmarks_a=self.landmark_set_a,
landmarks_b=self.landmark_set_b,
landmarks_c=self.landmark_set_c,
)
]
return self.generate_tests(smoke_data)
def l2_metric_geodesic_test_data(self):
smoke_data = [
dict(
l2_metric=self.l2_metric_s2,
times=self.times,
n_sampling_points=self.n_sampling_points,
landmarks_a=self.landmark_set_a,
landmarks_b=self.landmark_set_b,
)
]
return self.generate_tests(smoke_data)
class TestLandmarks(geomstats.tests.TestCase):
def setup_method(self):
s2 = Hypersphere(dim=2)
r3 = s2.embedding_space
initial_point = [0.0, 0.0, 1.0]
initial_tangent_vec_a = [1.0, 0.0, 0.0]
initial_tangent_vec_b = [0.0, 1.0, 0.0]
initial_tangent_vec_c = [-1.0, 0.0, 0.0]
landmarks_a = s2.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_a)
landmarks_b = s2.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_b)
landmarks_c = s2.metric.geodesic(
initial_point=initial_point,
initial_tangent_vec=initial_tangent_vec_c)
self.n_sampling_points = 10
sampling_times = gs.linspace(0.0, 1.0, self.n_sampling_points)
landmark_set_a = landmarks_a(sampling_times)
landmark_set_b = landmarks_b(sampling_times)
landmark_set_c = landmarks_c(sampling_times)
self.n_landmark_sets = 5
self.times = gs.linspace(0.0, 1.0, self.n_landmark_sets)
gs.random.seed(1234)
self.space_landmarks_in_euclidean_3d = Landmarks(
ambient_manifold=r3, k_landmarks=self.n_sampling_points)
self.space_landmarks_in_sphere_2d = Landmarks(
ambient_manifold=s2, k_landmarks=self.n_sampling_points)
self.l2_metric_s2 = self.space_landmarks_in_sphere_2d.metric
self.l2_metric_r3 = self.space_landmarks_in_euclidean_3d.metric
self.landmarks_a = landmark_set_a
self.landmarks_b = landmark_set_b
self.landmarks_c = landmark_set_c
def test_belongs(self):
result = self.space_landmarks_in_sphere_2d.belongs(self.landmarks_a)
expected = True
self.assertAllClose(result, expected)
def test_belongs_vectorization(self):
landmark_sets = gs.array([self.landmarks_a, self.landmarks_b])
result = self.space_landmarks_in_sphere_2d.belongs(landmark_sets)
expected = gs.array([True, True])
self.assertAllClose(result, expected)
def test_l2_metric_log_and_squared_norm_and_dist(self):
"""Test that squared norm of logarithm is squared dist."""
tangent_vec = self.l2_metric_s2.log(point=self.landmarks_b,
base_point=self.landmarks_a)
log_ab = tangent_vec
result = self.l2_metric_s2.squared_norm(vector=log_ab,
base_point=self.landmarks_a)
expected = self.l2_metric_s2.dist(self.landmarks_a,
self.landmarks_b)**2
self.assertAllClose(result, expected)
def test_l2_metric_log_and_exp(self):
"""Test that exp and log are inverse maps."""
tangent_vec = self.l2_metric_s2.log(point=self.landmarks_b,
base_point=self.landmarks_a)
result = self.l2_metric_s2.exp(tangent_vec=tangent_vec,
base_point=self.landmarks_a)
expected = self.landmarks_b
self.assertAllClose(result, expected)
@geomstats.tests.np_autograd_and_tf_only
def test_l2_metric_inner_product_vectorization(self):
"""Test the vectorization inner_product."""
n_samples = self.n_landmark_sets
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_bc = self.l2_metric_s2.geodesic(self.landmarks_b,
self.landmarks_c)
landmarks_ab = landmarks_ab(self.times)
landmarks_bc = landmarks_bc(self.times)
tangent_vecs = self.l2_metric_s2.log(point=landmarks_bc,
base_point=landmarks_ab)
result = self.l2_metric_s2.inner_product(tangent_vecs, tangent_vecs,
landmarks_ab)
self.assertAllClose(gs.shape(result), (n_samples, ))
@geomstats.tests.np_autograd_and_tf_only
def test_l2_metric_dist_vectorization(self):
"""Test the vectorization of dist."""
n_samples = self.n_landmark_sets
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_bc = self.l2_metric_s2.geodesic(self.landmarks_b,
self.landmarks_c)
landmarks_ab = landmarks_ab(self.times)
landmarks_bc = landmarks_bc(self.times)
result = self.l2_metric_s2.dist(landmarks_ab, landmarks_bc)
self.assertAllClose(gs.shape(result), (n_samples, ))
@geomstats.tests.np_autograd_and_tf_only
def test_l2_metric_exp_vectorization(self):
"""Test the vectorization of exp."""
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_bc = self.l2_metric_s2.geodesic(self.landmarks_b,
self.landmarks_c)
landmarks_ab = landmarks_ab(self.times)
landmarks_bc = landmarks_bc(self.times)
tangent_vecs = self.l2_metric_s2.log(point=landmarks_bc,
base_point=landmarks_ab)
result = self.l2_metric_s2.exp(tangent_vec=tangent_vecs,
base_point=landmarks_ab)
self.assertAllClose(gs.shape(result), gs.shape(landmarks_ab))
@geomstats.tests.np_autograd_and_tf_only
def test_l2_metric_log_vectorization(self):
"""Test the vectorization of log."""
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_bc = self.l2_metric_s2.geodesic(self.landmarks_b,
self.landmarks_c)
landmarks_ab = landmarks_ab(self.times)
landmarks_bc = landmarks_bc(self.times)
tangent_vecs = self.l2_metric_s2.log(point=landmarks_bc,
base_point=landmarks_ab)
result = tangent_vecs
self.assertAllClose(gs.shape(result), gs.shape(landmarks_ab))
@geomstats.tests.np_autograd_and_tf_only
def test_l2_metric_geodesic(self):
"""Test the geodesic method of L2Metric."""
landmarks_ab = self.l2_metric_s2.geodesic(self.landmarks_a,
self.landmarks_b)
landmarks_ab = landmarks_ab(self.times)
result = landmarks_ab
expected = []
for k in range(self.n_sampling_points):
geod = self.l2_metric_s2.ambient_metric.geodesic(
initial_point=self.landmarks_a[k, :],
end_point=self.landmarks_b[k, :])
expected.append(geod(self.times))
expected = gs.stack(expected, axis=1)
self.assertAllClose(result, expected)