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 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)
