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 = HyperbolicSpace(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 TestHyperbolicSpaceMethods(geomstats.tests.TestCase):
def setUp(self):
gs.random.seed(1234)
self.dimension = 2
self.extrinsic_manifold = HyperbolicSpace(dimension=self.dimension)
self.ball_manifold = HyperbolicSpace(dimension=self.dimension,
point_type='ball')
self.intrinsic_manifold = HyperbolicSpace(dimension=self.dimension,
point_type='intrinsic')
self.half_plane_manifold = HyperbolicSpace(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 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)
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)
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)
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)
def test_belongs_ball(self):
x = gs.array([[0.5, 0.2]])
belong = self.ball_manifold.belongs(x)
assert (belong[0])
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)
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)
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 = HyperbolicSpace(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)
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)
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)
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)