def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.extrinsic_manifold = Hyperbolic(dimension=self.dimension)
self.ball_manifold = Hyperbolic(dimension=self.dimension,
point_type='ball')
self.intrinsic_manifold = Hyperbolic(dimension=self.dimension,
point_type='intrinsic')
self.half_plane_manifold = Hyperbolic(dimension=self.dimension,
point_type='half-plane')
self.ball_metric = HyperbolicMetric(dimension=self.dimension,
point_type='ball')
self.extrinsic_metric = HyperbolicMetric(dimension=self.dimension,
point_type='extrinsic')
self.n_samples = 10
def __init__(self, n_disks, point_type='ball'):
self.n_disks = n_disks
self.point_type = point_type
list_metrics = []
for i_disk in range(n_disks):
scale_i = (n_disks - i_disk)**0.5
metric_i = HyperbolicMetric(dimension=2,
point_type=point_type,
scale=scale_i)
list_metrics.append(metric_i)
super(PoincarePolydiskMetric, self).__init__(metrics=list_metrics)
def __init__(self, n_disks, coords_type='ball'):
self.n_disks = n_disks
self.coords_type = coords_type
self.default_point_type = 'matrix'
list_metrics = []
for i_disk in range(n_disks):
scale_i = (n_disks - i_disk) ** 0.5
metric_i = HyperbolicMetric(dimension=2,
coords_type=coords_type,
scale=scale_i)
list_metrics.append(metric_i)
super(PoincarePolydiskMetric, self).__init__(
metrics=list_metrics, default_point_type='matrix')
def main():
cluster_1 = gs.random.uniform(low=0.5, high=0.6, size=(20, 2))
cluster_2 = gs.random.uniform(low=0, high=-0.2, size=(20, 2))
ax = plt.gca()
merged_clusters = gs.concatenate((cluster_1, cluster_2), axis=0)
manifold = Hyperbolic(dimension=2, point_type='ball')
metric = HyperbolicMetric(dimension=2, point_type='ball')
visualization.plot(
merged_clusters,
ax=ax,
space='H2_poincare_disk',
marker='.',
color='black',
point_type=manifold.point_type)
kmeans = RiemannianKMeans(
riemannian_metric=metric,
n_clusters=2,
init='random',
)
centroids = kmeans.fit(X=merged_clusters, max_iter=1)
labels = kmeans.predict(X=merged_clusters)
visualization.plot(
centroids,
ax=ax,
space='H2_poincare_disk',
marker='.',
color='red',
point_type=manifold.point_type)
print('Data_labels', labels)
plt.show()
def test_distance_ball_extrinsic_from_extr_5_dim(self):
x_int = gs.array([[10, 0.2, 3, 4]])
y_int = gs.array([[1, 6, 2., 1]])
extrinsic_manifold = Hyperbolic(4, point_type='extrinsic')
ball_metric = HyperbolicMetric(4, point_type='ball')
extrinsic_metric = HyperbolicMetric(4, point_type='extrinsic')
x_extr = extrinsic_manifold.from_coordinates(
x_int, from_point_type='intrinsic')
y_extr = extrinsic_manifold.from_coordinates(
y_int, from_point_type='intrinsic')
x_ball = extrinsic_manifold.to_coordinates(x_extr,
to_point_type='ball')
y_ball = extrinsic_manifold.to_coordinates(y_extr,
to_point_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)
class TestHyperbolicMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.extrinsic_manifold = Hyperbolic(dimension=self.dimension)
self.ball_manifold = Hyperbolic(dimension=self.dimension,
point_type='ball')
self.intrinsic_manifold = Hyperbolic(dimension=self.dimension,
point_type='intrinsic')
self.half_plane_manifold = Hyperbolic(dimension=self.dimension,
point_type='half-plane')
self.ball_metric = HyperbolicMetric(dimension=self.dimension,
point_type='ball')
self.extrinsic_metric = HyperbolicMetric(dimension=self.dimension,
point_type='extrinsic')
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_point_type='extrinsic')
x_b = self.extrinsic_manifold.to_coordinates(x, to_point_type='ball')
x2 = self.ball_manifold.to_coordinates(x_b, to_point_type='extrinsic')
self.assertAllClose(x, x2, atol=1e-8)
@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_point_type='extrinsic')
x_up = self.extrinsic_manifold.to_coordinates(
x, to_point_type='half-plane')
x2 = self.half_plane_manifold.to_coordinates(x_up,
to_point_type='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_point_type='extrinsic')
x_intr2 = self.extrinsic_manifold.to_coordinates(
x_extr, to_point_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_point_type='extrinsic')
x2 = self.extrinsic_manifold.to_coordinates(x_e, to_point_type='ball')
self.assertAllClose(x, x2, atol=1e-10)
@geomstats.tests.np_and_pytorch_only
def test_belongs_ball(self):
x = gs.array([[0.5, 0.2]])
belong = self.ball_manifold.belongs(x)
assert (belong[0])
@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_point_type='extrinsic')
y_extr = self.ball_manifold.to_coordinates(y_ball,
to_point_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)
@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_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')
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)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_extr_5_dim(self):
x_int = gs.array([[10, 0.2, 3, 4]])
y_int = gs.array([[1, 6, 2., 1]])
extrinsic_manifold = Hyperbolic(4, point_type='extrinsic')
ball_metric = HyperbolicMetric(4, point_type='ball')
extrinsic_metric = HyperbolicMetric(4, point_type='extrinsic')
x_extr = extrinsic_manifold.from_coordinates(
x_int, from_point_type='intrinsic')
y_extr = extrinsic_manifold.from_coordinates(
y_int, from_point_type='intrinsic')
x_ball = extrinsic_manifold.to_coordinates(x_extr,
to_point_type='ball')
y_ball = extrinsic_manifold.to_coordinates(y_extr,
to_point_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)
@geomstats.tests.np_and_pytorch_only
def test_log_exp_ball_extrinsic_from_extr(self):
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_and_pytorch_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(y, x)
exp = self.ball_metric.exp(log, x)
self.assertAllClose(exp, y)
@geomstats.tests.np_and_pytorch_only
def test_log_exp_ball_batch(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)
class TestHyperbolicMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.extrinsic_manifold = Hyperbolic(
dimension=self.dimension)
self.ball_manifold = Hyperbolic(
dimension=self.dimension, coords_type='ball')
self.intrinsic_manifold = Hyperbolic(
dimension=self.dimension, coords_type='intrinsic')
self.half_plane_manifold = Hyperbolic(
dimension=self.dimension, coords_type='half-plane')
self.ball_metric = HyperbolicMetric(
dimension=self.dimension, coords_type='ball')
self.extrinsic_metric = HyperbolicMetric(
dimension=self.dimension, coords_type='extrinsic')
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_belongs_half_plane(self):
x_true = gs.array([[0.5, 0.5]])
x_false = gs.array([[0.8, -0.8]])
is_in = self.half_plane_manifold.belongs(x_true)
self.assertTrue(is_in)
is_out = self.half_plane_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 = self.half_plane_manifold.to_coordinates(
x_up, to_coords_type='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)
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)
self.assertAllClose(dst_ball, dst_extr)
@geomstats.tests.np_and_pytorch_only
def test_distance_ball_extrinsic_from_extr_5_dim(self):
x_int = gs.array([[10, 0.2, 3, 4]])
y_int = gs.array([[1, 6, 2., 1]])
extrinsic_manifold = Hyperbolic(4, coords_type='extrinsic')
ball_metric = HyperbolicMetric(4, coords_type='ball')
extrinsic_metric = HyperbolicMetric(4, coords_type='extrinsic')
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)
@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)