class TestPoincareBall(geomstats.tests.TestCase):
def setUp(self):
self.manifold = PoincareBall(2)
self.metric = self.manifold.metric
self.hyperboloid_manifold = Hyperboloid(2)
self.hyperboloid_metric = self.hyperboloid_manifold.metric
def test_squared_dist(self):
point_a = gs.array([-0.3, 0.7])
point_b = gs.array([0.2, 0.5])
distance_a_b = self.metric.dist(point_a, point_b)
squared_distance = self.metric.squared_dist(point_a, point_b)
self.assertAllClose(distance_a_b**2, squared_distance, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_coordinates(self):
point_a = gs.array([-0.3, 0.7])
point_b = gs.array([0.2, 0.5])
point_a_h =\
self.manifold.to_coordinates(point_a, 'extrinsic')
point_b_h =\
self.manifold.to_coordinates(point_b, 'extrinsic')
dist_in_ball =\
self.metric.dist(point_a, point_b)
dist_in_hype =\
self.hyperboloid_metric.dist(point_a_h, point_b_h)
self.assertAllClose(dist_in_ball, dist_in_hype, atol=1e-8)
def test_dist_poincare(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([0.5, -0.5])
dist_a_b =\
self.manifold.metric.dist(point_a, point_b)
result = dist_a_b
expected = 2.887270927429199
self.assertAllClose(result, expected)
def test_dist_vectorization(self):
point_a = gs.array([0.2, 0.5])
point_b = gs.array([[0.3, -0.5], [0.2, 0.2]])
dist_a_b =\
self.manifold.metric.dist(point_a, point_b)
result_vect = dist_a_b
result =\
[self.manifold.metric.dist(point_a, point_b[i])
for i in range(len(point_b))]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
def test_dist_broadcast(self):
point_a = gs.array([[0.2, 0.5], [0.3, 0.1]])
point_b = gs.array([[0.3, -0.5], [0.2, 0.2]])
point_c = gs.array([[0.2, 0.3], [0.5, 0.5], [-0.4, 0.1]])
point_d = gs.array([0.1, 0.2, 0.3])
dist_a_b =\
self.manifold.metric.dist_broadcast(point_a, point_b)
dist_b_c = gs.flatten(
self.manifold.metric.dist_broadcast(point_b, point_c))
result_vect = gs.concatenate((dist_a_b, dist_b_c), axis=0)
result_a_b =\
[self.manifold.metric.dist_broadcast(point_a[i], point_b[i])
for i in range(len(point_b))]
result_b_c = \
[self.manifold.metric.dist_broadcast(point_b[i], point_c[j])
for i in range(len(point_b))
for j in range(len(point_c))
]
result = result_a_b + result_b_c
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
with self.assertRaises(ValueError):
self.manifold.metric.dist_broadcast(point_a, point_d)
@geomstats.tests.np_and_pytorch_only
def test_dist_pairwise(self):
point = gs.array([[0.1, 0.2], [0.3, 0.4], [0.5, 0.5]])
result = self.manifold.metric.dist_pairwise(point)
expected = gs.array([[0., 0.65821943, 1.34682524],
[0.65821943, 0., 0.71497076],
[1.34682524, 0.71497076, 0.]])
self.assertAllClose(result, expected, rtol=1e-3)
def test_mobius_vectorization(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([[0.5, -0.3], [0.3, 0.4]])
dist_a_b =\
self.manifold.metric.mobius_add(point_a, point_b)
result_vect = dist_a_b
result =\
[self.manifold.metric.mobius_add(point_a, point_b[i])
for i in range(len(point_b))]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
dist_a_b =\
self.manifold.metric.mobius_add(point_b, point_a)
result_vect = dist_a_b
result =\
[self.manifold.metric.mobius_add(point_b[i], point_a)
for i in range(len(point_b))]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
def test_log_vectorization(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([[0.5, -0.5], [0.4, 0.4]])
dist_a_b =\
self.manifold.metric.log(point_a, point_b)
result_vect = dist_a_b
result =\
[self.manifold.metric.log(point_a, point_b[i])
for i in range(len(point_b))]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
dist_a_b =\
self.manifold.metric.log(point_b, point_a)
result_vect = dist_a_b
result =\
[self.manifold.metric.log(point_b[i], point_a)
for i in range(len(point_b))]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
def test_exp_vectorization(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([[0.0, 0.0], [0.5, -0.5], [0.4, 0.4]])
dist_a_b =\
self.manifold.metric.exp(point_a, point_b)
result_vect = dist_a_b
result =\
[self.manifold.metric.exp(point_a, point_b[i])
for i in range(len(point_b))]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
dist_a_b =\
self.manifold.metric.exp(point_b, point_a)
result_vect = dist_a_b
result =\
[self.manifold.metric.exp(point_b[i], point_a)
for i in range(len(point_b))]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
def test_log_poincare(self):
point = gs.array([0.3, 0.5])
base_point = gs.array([0.3, 0.3])
result = self.manifold.metric.log(point, base_point)
expected = gs.array([-0.01733576, 0.21958634])
self.manifold.metric.coords_type = 'extrinsic'
self.assertAllClose(result, expected)
def test_belong_true_poincare(self):
point = gs.array([0.3, 0.5])
belong = self.manifold.belongs(point)
self.assertTrue(belong)
def test_belong_false_poincare(self):
point = gs.array([1.2, 0.5])
belong = self.manifold.belongs(point)
self.assertFalse(belong)
def test_projection(self):
point = gs.array([1.2, 0.5])
projected_point = self.manifold.projection(point)
self.assertTrue(gs.sum(projected_point * projected_point) < 1.)
def test_exp_poincare(self):
point = gs.array([0.3, 0.5])
base_point = gs.array([0.3, 0.3])
tangent_vec = self.manifold.metric.log(point, base_point)
result = self.manifold.metric.exp(tangent_vec, base_point)
self.manifold.metric.coords_type = 'extrinsic'
self.assertAllClose(result, point)
def test_ball_retraction(self):
x = gs.array([[0.5, 0.6], [0.2, -0.1], [0.2, -0.4]])
y = gs.array([[0.3, 0.5], [0.3, -0.6], [0.3, -0.3]])
ball_metric = self.manifold.metric
tangent_vec = ball_metric.log(y, x)
ball_metric.retraction(tangent_vec, x)
class TestPoincareBallMethods(geomstats.tests.TestCase):
def setUp(self):
self.manifold = PoincareBall(2)
self.metric = self.manifold.metric
self.hyperboloid_manifold = Hyperboloid(2)
self.hyperboloid_metric = self.hyperboloid_manifold.metric
def test_squared_dist(self):
point_a = gs.array([-0.3, 0.7])
point_b = gs.array([0.2, 0.5])
distance_a_b = self.metric.dist(point_a, point_b)
squared_distance = self.metric.squared_dist(point_a, point_b)
# TODO(nmiolane):
# Remove this line when poincare ball is properly vectorized
squared_distance = gs.to_ndarray(squared_distance, to_ndim=2, axis=1)
self.assertAllClose(distance_a_b**2, squared_distance, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_coordinates(self):
point_a = gs.array([-0.3, 0.7])
point_b = gs.array([0.2, 0.5])
point_a_h =\
self.manifold.to_coordinates(point_a, 'extrinsic')
point_b_h =\
self.manifold.to_coordinates(point_b, 'extrinsic')
dist_in_ball =\
self.metric.dist(point_a, point_b)
dist_in_hype =\
self.hyperboloid_metric.dist(point_a_h, point_b_h)
# TODO(ninamiolane): Remove this to_ndarray when poincare_ball
# is properly vectorized
dist_in_hype = gs.to_ndarray(dist_in_hype, to_ndim=2, axis=1)
self.assertAllClose(dist_in_ball, dist_in_hype, atol=1e-8)
def test_dist_poincare(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([0.5, -0.5])
dist_a_b =\
self.manifold.metric.dist(point_a, point_b)
result = dist_a_b
expected = gs.array([[2.887270927429199]])
self.assertAllClose(result, expected)
def test_dist_vectorization(self):
point_a = gs.array([0.2, 0.5])
point_b = gs.array([[0.3, -0.5], [0.2, 0.2]])
dist_a_b =\
self.manifold.metric.dist(point_a, point_b)
result_vect = dist_a_b
result =\
[self.manifold.metric.dist(point_a, point_b[i])
for i in range(len(point_b))]
result = gs.concatenate(result, axis=0)
self.assertAllClose(result_vect, result)
def test_mobius_vectorization(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([[0.5, -0.3], [0.3, 0.4]])
dist_a_b =\
self.manifold.metric.mobius_add(point_a, point_b)
result_vect = dist_a_b
result =\
[self.manifold.metric.mobius_add(point_a, point_b[i])
for i in range(len(point_b))]
result = gs.concatenate(result, axis=0)
self.assertAllClose(result_vect, result)
dist_a_b =\
self.manifold.metric.mobius_add(point_b, point_a)
result_vect = dist_a_b
result =\
[self.manifold.metric.mobius_add(point_b[i], point_a)
for i in range(len(point_b))]
result = gs.concatenate(result, axis=0)
self.assertAllClose(result_vect, result)
def test_log_vectorization(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([[0.5, -0.5], [0.4, 0.4]])
dist_a_b =\
self.manifold.metric.log(point_a, point_b)
result_vect = dist_a_b
result =\
[self.manifold.metric.log(point_a, point_b[i])
for i in range(len(point_b))]
result = gs.concatenate(result, axis=0)
self.assertAllClose(result_vect, result)
dist_a_b =\
self.manifold.metric.log(point_b, point_a)
result_vect = dist_a_b
result =\
[self.manifold.metric.log(point_b[i], point_a)
for i in range(len(point_b))]
result = gs.concatenate(result, axis=0)
self.assertAllClose(result_vect, result)
def test_exp_vectorization(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([[0.5, -0.5], [0.4, 0.4]])
dist_a_b =\
self.manifold.metric.exp(point_a, point_b)
result_vect = dist_a_b
result =\
[self.manifold.metric.exp(point_a, point_b[i])
for i in range(len(point_b))]
result = gs.concatenate(result, axis=0)
self.assertAllClose(result_vect, result)
dist_a_b =\
self.manifold.metric.exp(point_b, point_a)
result_vect = dist_a_b
result =\
[self.manifold.metric.exp(point_b[i], point_a)
for i in range(len(point_b))]
result = gs.concatenate(result, axis=0)
self.assertAllClose(result_vect, result)
def test_log_poincare(self):
point = gs.array([[0.3, 0.5]])
base_point = gs.array([[0.3, 0.3]])
result = self.manifold.metric.log(point, base_point)
expected = gs.array([[-0.01733576, 0.21958634]])
self.manifold.metric.coords_type = 'extrinsic'
self.assertAllClose(result, expected)
def test_belong_true_poincare(self):
point = gs.array([[0.3, 0.5]])
belong = self.manifold.belongs(point)
self.assertTrue(belong)
def test_belong_false_poincare(self):
point = gs.array([[1.2, 0.5]])
belong = self.manifold.belongs(point)
self.assertFalse(belong)
def test_exp_poincare(self):
point = gs.array([[0.3, 0.5]])
base_point = gs.array([[0.3, 0.3]])
tangent_vec = self.manifold.metric.log(point, base_point)
result = self.manifold.metric.exp(tangent_vec, base_point)
self.manifold.metric.coords_type = 'extrinsic'
self.assertAllClose(result, point)
def test_ball_retraction(self):
x = gs.array([[0.5, 0.6], [0.2, -0.1], [0.2, -0.4]])
y = gs.array([[0.3, 0.5], [0.3, -0.6], [0.3, -0.3]])
ball_metric = self.manifold.metric
tangent_vec = ball_metric.log(y, x)
ball_metric.retraction(tangent_vec, x)
class TestEM(geomstats.tests.TestCase):
"""Class for testing Expectation Maximization."""
def setUp(self):
"""Set manifold, data and EM parameters."""
self.n_samples = 5
self.dim = 2
self.space = PoincareBall(dim=self.dim)
self.metric = self.space.metric
self.initialisation_method = 'random'
self.mean_method = 'batch'
cluster_1 = gs.random.uniform(low=0.2,
high=0.6,
size=(self.n_samples, self.dim))
cluster_2 = gs.random.uniform(low=-0.6,
high=-0.2,
size=(self.n_samples, self.dim))
cluster_3 = gs.random.uniform(low=-0.3,
high=0,
size=(self.n_samples, self.dim))
cluster_3 = cluster_3 * gs.array([-1., 1.])
self.n_gaussian = 3
self.data = gs.concatenate((cluster_1, cluster_2, cluster_3), axis=0)
@geomstats.tests.np_only
def test_fit_init_kmeans(self):
"""Test fitting data into a GMM."""
gmm_learning = RiemannianEM(
metric=self.metric,
n_gaussians=self.n_gaussian,
initialisation_method=self.initialisation_method)
means, variances, coefficients = gmm_learning.fit(self.data)
self.assertTrue((coefficients < 1).all() and (coefficients > 0).all())
self.assertTrue((variances < 1).all() and (variances > 0).all())
self.assertTrue(self.space.belongs(means).all())
gmm_learning = RiemannianEM(metric=self.metric,
n_gaussians=self.n_gaussian,
initialisation_method='kmeans')
means, variances, coefficients = gmm_learning.fit(self.data)
self.assertTrue((coefficients < 1).all() and (coefficients > 0).all())
self.assertTrue((variances < 1).all() and (variances > 0).all())
self.assertTrue(self.space.belongs(means).all())
@geomstats.tests.np_only
def test_fit_init_random(self):
"""Test fitting data into a GMM."""
gmm_learning = RiemannianEM(
metric=self.metric,
n_gaussians=self.n_gaussian,
initialisation_method=self.initialisation_method)
means, variances, coefficients = gmm_learning.fit(self.data)
self.assertTrue((coefficients < 1).all() and (coefficients > 0).all())
self.assertTrue((variances < 1).all() and (variances > 0).all())
self.assertTrue(self.space.belongs(means).all())
gmm_learning = RiemannianEM(metric=self.metric,
n_gaussians=self.n_gaussian,
initialisation_method='random')
means, variances, coefficients = gmm_learning.fit(self.data)
self.assertTrue((coefficients < 1).all() and (coefficients > 0).all())
self.assertTrue((variances < 1).all() and (variances > 0).all())
self.assertTrue(self.space.belongs(means).all())
def test_weighted_frechet_mean(self):
"""Test for weighted mean."""
data = gs.array([[0.1, 0.2], [0.25, 0.35]])
weights = gs.array([3., 1.])
mean_o = FrechetMean(metric=self.metric, point_type='vector', lr=1.)
mean_o.fit(data, weights=weights)
result = mean_o.estimate_
expected = self.metric.exp(
weights[1] / gs.sum(weights) * self.metric.log(data[1], data[0]),
data[0])
self.assertAllClose(result, expected)
@geomstats.tests.np_and_pytorch_only
def test_normalization_factor(self):
"""Test for Gaussian distribution normalization factor."""
gmm = RiemannianEM(self.metric)
variances_range, normalization_factor_var, phi_inv_var = \
gmm.normalization_factor_init(
gs.arange(ZETA_LOWER_BOUND, ZETA_UPPER_BOUND, ZETA_STEP))
self.assertAllClose(normalization_factor_var[4], 0.00291884, TOLERANCE)
self.assertAllClose(phi_inv_var[3], 0.00562326, TOLERANCE)
variances_test = gs.array([0.8, 1.2])
norm_factor_test = find_normalization_factor(variances_test,
variances_range,
normalization_factor_var)
norm_factor_verdict = gs.array([0.79577319, 2.3791778])
self.assertAllClose(norm_factor_test, norm_factor_verdict, TOLERANCE)
norm_factor_test2 = self.metric.normalization_factor(variances_test)
self.assertAllClose(norm_factor_test2, norm_factor_verdict, TOLERANCE)
norm_factor_test3, norm_factor_gradient_test = \
self.metric.norm_factor_gradient(variances_test)
norm_factor_gradient_verdict = gs.array([3.0553115709, 2.53770926])
self.assertAllClose(norm_factor_test3, norm_factor_verdict, TOLERANCE)
self.assertAllClose(norm_factor_gradient_test,
norm_factor_gradient_verdict, TOLERANCE)
find_var_test = find_variance_from_index(
gs.array([0.5, 0.4, 0.3, 0.2]), variances_range, phi_inv_var)
find_var_verdict = gs.array([0.481, 0.434, 0.378, 0.311])
self.assertAllClose(find_var_test, find_var_verdict, TOLERANCE)
@geomstats.tests.np_only
def test_fit_init_random_sphere(self):
"""Test fitting data into a GMM."""
space = Hypersphere(2)
gmm_learning = RiemannianEM(
metric=space.metric,
n_gaussians=2,
initialisation_method=self.initialisation_method)
means = space.random_uniform(2)
cluster_1 = space.random_von_mises_fisher(mu=means[0],
kappa=20,
n_samples=140)
cluster_2 = space.random_von_mises_fisher(mu=means[1],
kappa=20,
n_samples=140)
data = gs.concatenate((cluster_1, cluster_2), axis=0)
means, variances, coefficients = gmm_learning.fit(data)
self.assertTrue((coefficients < 1).all() and (coefficients > 0).all())
self.assertTrue((variances < 1).all() and (variances > 0).all())
self.assertTrue(space.belongs(means).all())
class TestHyperbolicCoords(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.extrinsic_manifold = Hyperboloid(dim=self.dimension)
self.extrinsic_metric = self.extrinsic_manifold.metric
self.ball_manifold = PoincareBall(dim=self.dimension)
self.ball_metric = self.ball_manifold.metric
self.intrinsic_manifold = Hyperboloid(dim=self.dimension,
coords_type="intrinsic")
self.intrinsic_metric = self.intrinsic_manifold.metric
self.n_samples = 10
def test_extrinsic_ball_extrinsic(self):
x_in = gs.array([0.5, 7])
x = self.intrinsic_manifold.to_coordinates(x_in,
to_coords_type="extrinsic")
x_b = self.extrinsic_manifold.to_coordinates(x, to_coords_type="ball")
x2 = self.ball_manifold.to_coordinates(x_b, to_coords_type="extrinsic")
self.assertAllClose(x, x2)
def test_belongs_intrinsic(self):
x_in = gs.array([0.5, 7])
is_in = self.intrinsic_manifold.belongs(x_in)
self.assertTrue(is_in)
def test_belongs_extrinsic(self):
x_true = self.intrinsic_manifold.to_coordinates(
gs.array([0.5, 7]), "extrinsic")
x_false = gs.array([0.5, 7, 3.0])
is_in = self.extrinsic_manifold.belongs(x_true)
self.assertTrue(is_in)
is_out = self.extrinsic_manifold.belongs(x_false)
self.assertFalse(is_out)
def test_belongs_ball(self):
x_true = gs.array([0.5, 0.5])
x_false = gs.array([0.8, 0.8])
is_in = self.ball_manifold.belongs(x_true)
self.assertTrue(is_in)
is_out = self.ball_manifold.belongs(x_false)
self.assertFalse(is_out)
def test_extrinsic_half_plane_extrinsic(self):
x_in = gs.array([0.5, 7], dtype=gs.float64)
x = self.intrinsic_manifold.to_coordinates(x_in,
to_coords_type="extrinsic")
x_up = self.extrinsic_manifold.to_coordinates(
x, to_coords_type="half-space")
x2 = Hyperbolic.change_coordinates_system(x_up, "half-space",
"extrinsic")
self.assertAllClose(x, x2)
def test_intrinsic_extrinsic_intrinsic(self):
x_intr = gs.array([0.5, 7])
x_extr = self.intrinsic_manifold.to_coordinates(
x_intr, to_coords_type="extrinsic")
x_intr2 = self.extrinsic_manifold.to_coordinates(
x_extr, to_coords_type="intrinsic")
self.assertAllClose(x_intr, x_intr2)
def test_ball_extrinsic_ball(self):
x = gs.array([0.5, 0.2])
x_e = self.ball_manifold.to_coordinates(x, to_coords_type="extrinsic")
x2 = self.extrinsic_manifold.to_coordinates(x_e, to_coords_type="ball")
self.assertAllClose(x, x2)
def test_distance_ball_extrinsic_from_ball(self):
x_ball = gs.array([0.7, 0.2])
y_ball = gs.array([0.2, 0.2])
x_extr = self.ball_manifold.to_coordinates(x_ball,
to_coords_type="extrinsic")
y_extr = self.ball_manifold.to_coordinates(y_ball,
to_coords_type="extrinsic")
dst_ball = self.ball_metric.dist(x_ball, y_ball)
dst_extr = self.extrinsic_metric.dist(x_extr, y_extr)
self.assertAllClose(dst_ball, dst_extr)
def test_distance_ball_extrinsic_from_extr(self):
x_int = gs.array([10, 0.2])
y_int = gs.array([1, 6.0])
x_extr = self.intrinsic_manifold.to_coordinates(
x_int, to_coords_type="extrinsic")
y_extr = self.intrinsic_manifold.to_coordinates(
y_int, to_coords_type="extrinsic")
x_ball = self.extrinsic_manifold.to_coordinates(x_extr,
to_coords_type="ball")
y_ball = self.extrinsic_manifold.to_coordinates(y_extr,
to_coords_type="ball")
dst_ball = self.ball_metric.dist(x_ball, y_ball)
dst_extr = self.extrinsic_metric.dist(x_extr, y_extr)
self.assertAllClose(dst_ball, dst_extr)
def test_distance_ball_extrinsic_from_extr_4_dim(self):
x_int = gs.array([10, 0.2, 3, 4])
y_int = gs.array([1, 6, 2.0, 1])
ball_manifold = PoincareBall(4)
extrinsic_manifold = Hyperboloid(4)
ball_metric = ball_manifold.metric
extrinsic_metric = extrinsic_manifold.metric
x_extr = extrinsic_manifold.from_coordinates(
x_int, from_coords_type="intrinsic")
y_extr = extrinsic_manifold.from_coordinates(
y_int, from_coords_type="intrinsic")
x_ball = extrinsic_manifold.to_coordinates(x_extr,
to_coords_type="ball")
y_ball = extrinsic_manifold.to_coordinates(y_extr,
to_coords_type="ball")
dst_ball = ball_metric.dist(x_ball, y_ball)
dst_extr = extrinsic_metric.dist(x_extr, y_extr)
self.assertAllClose(dst_ball, dst_extr)
def test_log_exp_ball_extrinsic_from_extr(self):
"""Compare log exp in different parameterizations."""
x_int = gs.array([4.0, 0.2])
y_int = gs.array([3.0, 3])
x_extr = self.intrinsic_manifold.to_coordinates(
x_int, to_coords_type="extrinsic")
y_extr = self.intrinsic_manifold.to_coordinates(
y_int, to_coords_type="extrinsic")
x_ball = self.extrinsic_manifold.to_coordinates(x_extr,
to_coords_type="ball")
y_ball = self.extrinsic_manifold.to_coordinates(y_extr,
to_coords_type="ball")
x_ball_log_exp = self.ball_metric.exp(
self.ball_metric.log(y_ball, x_ball), x_ball)
x_extr_a = self.extrinsic_metric.exp(
self.extrinsic_metric.log(y_extr, x_extr), x_extr)
x_extr_b = self.extrinsic_manifold.from_coordinates(
x_ball_log_exp, from_coords_type="ball")
self.assertAllClose(x_extr_a, x_extr_b, atol=3e-4)
def test_log_exp_ball(self):
x = gs.array([0.1, 0.2])
y = gs.array([0.2, 0.5])
log = self.ball_metric.log(point=y, base_point=x)
exp = self.ball_metric.exp(tangent_vec=log, base_point=x)
self.assertAllClose(exp, y)
def test_log_exp_ball_vectorization(self):
x = gs.array([0.1, 0.2])
y = gs.array([[0.2, 0.5], [0.1, 0.7]])
log = self.ball_metric.log(y, x)
exp = self.ball_metric.exp(log, x)
self.assertAllClose(exp, y)
def test_log_exp_ball_null_tangent(self):
x = gs.array([[0.1, 0.2], [0.1, 0.2]])
tangent_vec = gs.array([[0.0, 0.0], [0.0, 0.0]])
exp = self.ball_metric.exp(tangent_vec, x)
self.assertAllClose(exp, x)
class TestEM(geomstats.tests.TestCase):
"""Class for testing Expectation Maximization."""
@geomstats.tests.np_and_pytorch_only
def setUp(self):
"""Set manifold, data and EM parameters."""
self.n_samples = 5
self.dim = 2
self.space = PoincareBall(dim=self.dim)
self.metric = self.space.metric
self.initialisation_method = 'random'
self.mean_method = 'frechet-poincare-ball'
cluster_1 = gs.random.uniform(low=0.2,
high=0.6,
size=(self.n_samples, self.dim))
cluster_2 = gs.random.uniform(low=-0.6,
high=-0.2,
size=(self.n_samples, self.dim))
cluster_3 = gs.random.uniform(low=-0.3,
high=0,
size=(self.n_samples, self.dim))
cluster_3[:, 0] = -cluster_3[:, 0]
self.n_gaussian = 3
self.data = gs.concatenate((cluster_1, cluster_2, cluster_3), axis=0)
@geomstats.tests.np_only
def test_fit(self):
"""Test fitting data into a GMM."""
gmm_learning = RiemannianEM(
riemannian_metric=self.metric,
n_gaussians=self.n_gaussian,
initialisation_method=self.initialisation_method,
mean_method=self.mean_method)
means, variances, coefficients = gmm_learning.fit(self.data)
self.assertTrue((coefficients < 1).all() and (coefficients > 0).all())
self.assertTrue((variances < 1).all() and (variances > 0).all())
self.assertTrue(self.space.belongs(means).all())
@geomstats.tests.np_only
def test_weighted_frechet_mean(self):
"""Test for weighted mean."""
data = gs.array([[0.1, 0.2], [0.25, 0.35], [-0.1, -0.2], [-0.4, 0.3]])
weights = gs.repeat([0.5], data.shape[0])
mean_o = FrechetMean(metric=self.metric, point_type='vector')
mean_o.fit(data, weights)
mean = mean_o.estimate_
mean_verdict = [-0.03857, 0.15922]
self.assertAllClose(mean, mean_verdict, TOLERANCE)
@geomstats.tests.np_and_pytorch_only
def test_normalization_factor(self):
"""Test for Gaussian distribution normalization factor."""
variances_range,\
normalization_factor_var,\
phi_inv_var = \
self.metric.normalization_factor_init(gs.arange(
ZETA_LOWER_BOUND, ZETA_UPPER_BOUND, ZETA_STEP))
self.assertAllClose(normalization_factor_var[4], 0.00291884, TOLERANCE)
self.assertAllClose(phi_inv_var[3], 0.00562326, TOLERANCE)
variances_test = gs.array([0.8, 1.2])
norm_factor_test = self.metric.find_normalization_factor(
variances_test, variances_range, normalization_factor_var)
norm_factor_verdict = gs.array([0.79577319, 2.3791778])
self.assertAllClose(norm_factor_test, norm_factor_verdict, TOLERANCE)
norm_factor_test2 = self.metric.normalization_factor(variances_test)
self.assertAllClose(norm_factor_test2, norm_factor_verdict, TOLERANCE)
norm_factor_test3, norm_factor_gradient_test = \
self.metric.norm_factor_gradient(variances_test)
norm_factor_gradient_verdict = gs.array([3.0553115709, 2.53770926])
self.assertAllClose(norm_factor_test3, norm_factor_verdict, TOLERANCE)
self.assertAllClose(norm_factor_gradient_test,
norm_factor_gradient_verdict, TOLERANCE)
find_var_test = self.metric.find_variance_from_index(
gs.array([0.5, 0.4, 0.3, 0.2]), variances_range, phi_inv_var)
find_var_verdict = gs.array([0.481, 0.434, 0.378, 0.311])
self.assertAllClose(find_var_test, find_var_verdict, TOLERANCE)
class TestHyperbolicMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.extrinsic_manifold = Hyperboloid(
dim=self.dimension)
self.extrinsic_metric = self.extrinsic_manifold.metric
self.ball_manifold = PoincareBall(
dim=self.dimension)
self.ball_metric = self.ball_manifold.metric
self.intrinsic_manifold = Hyperboloid(
dim=self.dimension, coords_type='intrinsic')
self.intrinsic_metric = self.intrinsic_manifold.metric
self.n_samples = 10
@geomstats.tests.np_and_pytorch_only
def test_extrinsic_ball_extrinsic(self):
x_in = gs.array([[0.5, 7]])
x = self.intrinsic_manifold.to_coordinates(
x_in, to_coords_type='extrinsic')
x_b = self.extrinsic_manifold.to_coordinates(x, to_coords_type='ball')
x2 = self.ball_manifold.to_coordinates(x_b, to_coords_type='extrinsic')
self.assertAllClose(x, x2, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_belongs_intrinsic(self):
x_in = gs.array([[0.5, 7]])
is_in = self.intrinsic_manifold.belongs(x_in)
self.assertTrue(is_in)
@geomstats.tests.np_and_pytorch_only
def test_belongs_extrinsic(self):
x_true = self.intrinsic_manifold.to_coordinates(gs.array([[0.5, 7]]),
'extrinsic')
x_false = gs.array([[0.5, 7, 3.]])
is_in = self.extrinsic_manifold.belongs(x_true)
self.assertTrue(is_in)
is_out = self.extrinsic_manifold.belongs(x_false)
self.assertFalse(is_out)
@geomstats.tests.np_and_pytorch_only
def test_belongs_ball(self):
x_true = gs.array([[0.5, 0.5]])
x_false = gs.array([[0.8, 0.8]])
is_in = self.ball_manifold.belongs(x_true)
self.assertTrue(is_in)
is_out = self.ball_manifold.belongs(x_false)
self.assertFalse(is_out)
@geomstats.tests.np_and_pytorch_only
def test_extrinsic_half_plane_extrinsic(self):
x_in = gs.array([[0.5, 7]])
x = self.intrinsic_manifold.to_coordinates(
x_in, to_coords_type='extrinsic')
x_up = self.extrinsic_manifold.to_coordinates(
x, to_coords_type='half-plane')
x2 = Hyperbolic.change_coordinates_system(x_up,
"half-plane",
"extrinsic")
self.assertAllClose(x, x2, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_intrinsic_extrinsic_intrinsic(self):
x_intr = gs.array([[0.5, 7]])
x_extr = self.intrinsic_manifold.to_coordinates(
x_intr, to_coords_type='extrinsic')
x_intr2 = self.extrinsic_manifold.to_coordinates(
x_extr, to_coords_type='intrinsic')
self.assertAllClose(x_intr, x_intr2, atol=1e-8)
@geomstats.tests.np_and_pytorch_only
def test_ball_extrinsic_ball(self):
x = gs.array([[0.5, 0.2]])
x_e = self.ball_manifold.to_coordinates(x, to_coords_type='extrinsic')
x2 = self.extrinsic_manifold.to_coordinates(x_e, to_coords_type='ball')
self.assertAllClose(x, x2, atol=1e-10)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_ball(self):
x_ball = gs.array([[0.7, 0.2]])
y_ball = gs.array([[0.2, 0.2]])
x_extr = self.ball_manifold.to_coordinates(
x_ball, to_coords_type='extrinsic')
y_extr = self.ball_manifold.to_coordinates(
y_ball, to_coords_type='extrinsic')
dst_ball = self.ball_metric.dist(x_ball, y_ball)
dst_extr = self.extrinsic_metric.dist(x_extr, y_extr)
# TODO(nmiolane): Remove this when ball is properly vectorized
dst_extr = gs.to_ndarray(dst_extr, to_ndim=2, axis=1)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_extr(self):
x_int = gs.array([[10, 0.2]])
y_int = gs.array([[1, 6.]])
x_extr = self.intrinsic_manifold.to_coordinates(
x_int, to_coords_type='extrinsic')
y_extr = self.intrinsic_manifold.to_coordinates(
y_int, to_coords_type='extrinsic')
x_ball = self.extrinsic_manifold.to_coordinates(
x_extr, to_coords_type='ball')
y_ball = self.extrinsic_manifold.to_coordinates(
y_extr, to_coords_type='ball')
dst_ball = self.ball_metric.dist(x_ball, y_ball)
dst_extr = self.extrinsic_metric.dist(x_extr, y_extr)
# TODO(nmiolane): Remove this when ball is properly vectorized
dst_extr = gs.to_ndarray(dst_extr, to_ndim=2, axis=1)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_extr_4_dim(self):
x_int = gs.array([[10, 0.2, 3, 4]])
y_int = gs.array([[1, 6, 2., 1]])
ball_manifold = PoincareBall(4)
extrinsic_manifold = Hyperboloid(4)
ball_metric = ball_manifold.metric
extrinsic_metric = extrinsic_manifold.metric
x_extr = extrinsic_manifold.from_coordinates(
x_int, from_coords_type='intrinsic')
y_extr = extrinsic_manifold.from_coordinates(
y_int, from_coords_type='intrinsic')
x_ball = extrinsic_manifold.to_coordinates(
x_extr, to_coords_type='ball')
y_ball = extrinsic_manifold.to_coordinates(
y_extr, to_coords_type='ball')
dst_ball = ball_metric.dist(x_ball, y_ball)
dst_extr = extrinsic_metric.dist(x_extr, y_extr)
# TODO(nmiolane): Remove this when ball is properly vectorized
dst_extr = gs.to_ndarray(dst_extr, to_ndim=2, axis=1)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_log_exp_ball_extrinsic_from_extr(self):
"""Compare log exp in different parameterizations."""
# TODO(Hazaatiti): Fix this test
# x_int = gs.array([[4., 0.2]])
# y_int = gs.array([[3., 3]])
# x_extr = self.intrinsic_manifold.to_coordinates(
# x_int, to_point_type='extrinsic')
# y_extr = self.intrinsic_manifold.to_coordinates(
# y_int, to_point_type='extrinsic')
# x_ball = self.extrinsic_manifold.to_coordinates(
# x_extr, to_point_type='ball')
# y_ball = self.extrinsic_manifold.to_coordinates(
# y_extr, to_point_type='ball')
# x_ball_log_exp = self.ball_metric.exp(
# self.ball_metric.log(y_ball, x_ball), x_ball)
# x_extr_a = self.extrinsic_metric.exp(
# self.extrinsic_metric.log(y_extr, x_extr), x_extr)
# x_extr_b = self.extrinsic_manifold.from_coordinates(
# x_ball_log_exp, from_point_type='ball')
# self.assertAllClose(x_extr_a, x_extr_b, atol=1e-4)
@geomstats.tests.np_only
def test_log_exp_ball(self):
x = gs.array([[0.1, 0.2]])
y = gs.array([[0.2, 0.5]])
log = self.ball_metric.log(point=y, base_point=x)
exp = self.ball_metric.exp(tangent_vec=log, base_point=x)
self.assertAllClose(exp, y, atol=1e-1)
@geomstats.tests.np_only
def test_log_exp_ball_vectorization(self):
x = gs.array([[0.1, 0.2]])
y = gs.array([[0.2, 0.5], [0.1, 0.7]])
log = self.ball_metric.log(y, x)
exp = self.ball_metric.exp(log, x)
self.assertAllClose(exp, y, atol=1e-1)
@geomstats.tests.np_only
def test_log_exp_ball_null_tangent(self):
x = gs.array([[0.1, 0.2], [0.1, 0.2]])
tangent_vec = gs.array([[0.0, 0.0], [0.0, 0.0]])
exp = self.ball_metric.exp(tangent_vec, x)
self.assertAllClose(exp, x, atol=1e-10)
class TestPoincareBall(geomstats.tests.TestCase):
def setUp(self):
self.manifold = PoincareBall(2)
self.metric = self.manifold.metric
self.hyperboloid_manifold = Hyperboloid(2)
self.hyperboloid_metric = self.hyperboloid_manifold.metric
def test_squared_dist(self):
point_a = gs.array([-0.3, 0.7])
point_b = gs.array([0.2, 0.5])
distance_a_b = self.metric.dist(point_a, point_b)
squared_distance = self.metric.squared_dist(point_a, point_b)
self.assertAllClose(distance_a_b ** 2, squared_distance)
def test_coordinates(self):
point_a = gs.array([-0.3, 0.7])
point_b = gs.array([0.2, 0.5])
point_a_h = self.manifold.to_coordinates(point_a, "extrinsic")
point_b_h = self.manifold.to_coordinates(point_b, "extrinsic")
dist_in_ball = self.metric.dist(point_a, point_b)
dist_in_hype = self.hyperboloid_metric.dist(point_a_h, point_b_h)
self.assertAllClose(dist_in_ball, dist_in_hype)
def test_dist_poincare(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([0.5, -0.5])
dist_a_b = self.manifold.metric.dist(point_a, point_b)
result = dist_a_b
expected = 2.887270927429199
self.assertAllClose(result, expected)
def test_dist_vectorization(self):
point_a = gs.array([0.2, 0.5])
point_b = gs.array([[0.3, -0.5], [0.2, 0.2]])
dist_a_b = self.manifold.metric.dist(point_a, point_b)
result_vect = dist_a_b
result = [
self.manifold.metric.dist(point_a, point_b[i]) for i in range(len(point_b))
]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
def test_dist_broadcast(self):
point_a = gs.array([[0.2, 0.5], [0.3, 0.1]])
point_b = gs.array([[0.3, -0.5], [0.2, 0.2]])
point_c = gs.array([[0.2, 0.3], [0.5, 0.5], [-0.4, 0.1]])
point_d = gs.array([0.1, 0.2, 0.3])
dist_a_b = self.manifold.metric.dist_broadcast(point_a, point_b)
dist_b_c = gs.flatten(self.manifold.metric.dist_broadcast(point_b, point_c))
result_vect = gs.concatenate((dist_a_b, dist_b_c), axis=0)
result_a_b = [
self.manifold.metric.dist_broadcast(point_a[i], point_b[i])
for i in range(len(point_b))
]
result_b_c = [
self.manifold.metric.dist_broadcast(point_b[i], point_c[j])
for i in range(len(point_b))
for j in range(len(point_c))
]
result = result_a_b + result_b_c
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
with self.assertRaises(ValueError):
self.manifold.metric.dist_broadcast(point_a, point_d)
def test_dist_pairwise(self):
point = gs.array([[0.1, 0.2], [0.3, 0.4], [0.5, 0.5]])
result = self.manifold.metric.dist_pairwise(point)
expected = gs.array(
[
[0.0, 0.65821943, 1.34682524],
[0.65821943, 0.0, 0.71497076],
[1.34682524, 0.71497076, 0.0],
]
)
self.assertAllClose(result, expected, rtol=1e-3)
def test_mobius_vectorization(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([[0.5, -0.3], [0.3, 0.4]])
dist_a_b = self.manifold.metric.mobius_add(point_a, point_b)
result_vect = dist_a_b
result = [
self.manifold.metric.mobius_add(point_a, point_b[i])
for i in range(len(point_b))
]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
dist_a_b = self.manifold.metric.mobius_add(point_b, point_a)
result_vect = dist_a_b
result = [
self.manifold.metric.mobius_add(point_b[i], point_a)
for i in range(len(point_b))
]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
def test_log_vectorization(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([[0.5, -0.5], [0.4, 0.4]])
dist_a_b = self.manifold.metric.log(point_a, point_b)
result_vect = dist_a_b
result = [
self.manifold.metric.log(point_a, point_b[i]) for i in range(len(point_b))
]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
dist_a_b = self.manifold.metric.log(point_b, point_a)
result_vect = dist_a_b
result = [
self.manifold.metric.log(point_b[i], point_a) for i in range(len(point_b))
]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
def test_exp_vectorization(self):
point_a = gs.array([0.5, 0.5])
point_b = gs.array([[0.0, 0.0], [0.5, -0.5], [0.4, 0.4]])
dist_a_b = self.manifold.metric.exp(point_a, point_b)
result_vect = dist_a_b
result = [
self.manifold.metric.exp(point_a, point_b[i]) for i in range(len(point_b))
]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
dist_a_b = self.manifold.metric.exp(point_b, point_a)
result_vect = dist_a_b
result = [
self.manifold.metric.exp(point_b[i], point_a) for i in range(len(point_b))
]
result = gs.stack(result, axis=0)
self.assertAllClose(result_vect, result)
def test_log_poincare(self):
point = gs.array([0.3, 0.5])
base_point = gs.array([0.3, 0.3])
result = self.manifold.metric.log(point, base_point)
expected = gs.array([-0.01733576, 0.21958634])
self.manifold.metric.coords_type = "extrinsic"
self.assertAllClose(result, expected)
def test_belong_true_poincare(self):
point = gs.array([0.3, 0.5])
belong = self.manifold.belongs(point)
self.assertTrue(belong)
def test_belong_false_poincare(self):
point = gs.array([1.2, 0.5])
belong = self.manifold.belongs(point)
self.assertFalse(belong)
def test_projection(self):
point = gs.array([1.2, 0.5])
projected_point = self.manifold.projection(point)
self.assertTrue(gs.sum(projected_point * projected_point) < 1.0)
def test_exp_poincare(self):
point = gs.array([0.3, 0.5])
base_point = gs.array([0.3, 0.3])
tangent_vec = self.manifold.metric.log(point, base_point)
result = self.manifold.metric.exp(tangent_vec, base_point)
self.manifold.metric.coords_type = "extrinsic"
self.assertAllClose(result, point)
def test_ball_retraction(self):
x = gs.array([[0.5, 0.6], [0.2, -0.1], [0.2, -0.4]])
y = gs.array([[0.3, 0.5], [0.3, -0.6], [0.3, -0.3]])
ball_metric = self.manifold.metric
tangent_vec = ball_metric.log(y, x)
ball_metric.retraction(tangent_vec, x)
def test_ball_geodesic(self):
path_function = self.manifold.metric.geodesic(
gs.array([0.1, 0.1]), gs.array([0.2, 0.2])
)
steps = gs.array(gs.linspace(-1000.0, 1000.0, 10000))
path_function(steps)
def test_mobius_out_of_the_ball(self):
x, y = gs.array([0.7, 0.9]), gs.array([0.2, 0.2])
with self.assertRaises(ValueError):
self.manifold.metric.mobius_add(x, y, project_first=False)
