def test_exp_after_log_intrinsic_ball_extrinsic( self, dim, x_intrinsic, y_intrinsic ): intrinsic_manifold = Hyperboloid(dim=dim, coords_type="intrinsic") extrinsic_manifold = Hyperbolic(dim=dim, coords_type="extrinsic") ball_manifold = PoincareBall(dim) x_extr = intrinsic_manifold.to_coordinates( x_intrinsic, to_coords_type="extrinsic" ) y_extr = intrinsic_manifold.to_coordinates( y_intrinsic, to_coords_type="extrinsic" ) x_ball = extrinsic_manifold.to_coordinates(x_extr, to_coords_type="ball") y_ball = extrinsic_manifold.to_coordinates(y_extr, to_coords_type="ball") x_ball_exp_after_log = ball_manifold.metric.exp( ball_manifold.metric.log(y_ball, x_ball), x_ball ) x_extr_a = extrinsic_manifold.metric.exp( extrinsic_manifold.metric.log(y_extr, x_extr), x_extr ) x_extr_b = extrinsic_manifold.from_coordinates( x_ball_exp_after_log, from_coords_type="ball" ) self.assertAllClose(x_extr_a, x_extr_b, atol=3e-4)
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)
def test_product_distance_extrinsic_representation(self): """Test the distance using the extrinsic representation.""" coords_type = 'extrinsic' point_a_intrinsic = gs.array([[0.01, 0.0]]) point_b_intrinsic = gs.array([[0.0, 0.0]]) hyperbolic_space = Hyperbolic(dimension=2, coords_type=coords_type) point_a = hyperbolic_space.from_coordinates(point_a_intrinsic, "intrinsic") point_b = hyperbolic_space.from_coordinates(point_b_intrinsic, "intrinsic") duplicate_point_a = gs.vstack([point_a, point_a]) duplicate_point_b = gs.vstack([point_b, point_b]) single_disk = PoincarePolydisk(n_disks=1, coords_type=coords_type) two_disks = PoincarePolydisk(n_disks=2, coords_type=coords_type) distance_single_disk = single_disk.metric.dist(point_a, point_b) distance_two_disks = two_disks.metric.dist(duplicate_point_a, duplicate_point_b) result = distance_two_disks expected = 3**0.5 * distance_single_disk self.assertAllClose(result, expected)
def intrinsic_to_extrinsic_coords(self, point_intrinsic): """Convert point from intrinsic to extrensic coordinates. Convert the parameterization of a point in the hyperbolic space from its intrinsic coordinates, to its extrinsic coordinates in Minkowski space. Parameters ---------- point_intrinsic : array-like, shape=[n_samples, n_disk, dimension] Returns ------- point_extrinsic : array-like, shape=[n_samples, n_disks, dimension + 1] """ n_disks = point_intrinsic.shape[1] hyperbolic_space = Hyperbolic(dimension=2) point_extrinsic = gs.stack( [hyperbolic_space.from_coordinates( point_intrinsic[:, i_disk, ...], 'intrinsic') for i_disk in range(n_disks)], axis=1) return point_extrinsic
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 = 3 self.space = Hyperbolic(dimension=self.dimension) self.metric = self.space.metric self.ball_manifold = Hyperbolic(dimension=2, coords_type='ball') self.n_samples = 10 def test_random_uniform_and_belongs(self): point = self.space.random_uniform() result = self.space.belongs(point) expected = gs.array([[True]]) self.assertAllClose(result, expected) def test_random_uniform(self): result = self.space.random_uniform() self.assertAllClose(gs.shape(result), (1, self.dimension + 1)) def test_intrinsic_and_extrinsic_coords(self): """ Test that the composition of intrinsic_to_extrinsic_coords and extrinsic_to_intrinsic_coords gives the identity. """ point_int = gs.ones(self.dimension) point_ext = self.space.from_coordinates(point_int, 'intrinsic') result = self.space.to_coordinates(point_ext, 'intrinsic') expected = point_int expected = helper.to_vector(expected) self.assertAllClose(result, expected) point_ext = gs.array([2.0, 1.0, 1.0, 1.0]) point_int = self.space.to_coordinates(point_ext, 'intrinsic') result = self.space.from_coordinates(point_int, 'intrinsic') expected = point_ext expected = helper.to_vector(expected) self.assertAllClose(result, expected) def test_intrinsic_and_extrinsic_coords_vectorization(self): """ Test that the composition of intrinsic_to_extrinsic_coords and extrinsic_to_intrinsic_coords gives the identity. """ point_int = gs.array([[.1, 0., 0., .1, 0., 0.], [.1, .1, .1, .4, .1, 0.], [.1, .3, 0., .1, 0., 0.], [-0.1, .1, -.4, .1, -.01, 0.], [0., 0., .1, .1, -0.08, -0.1], [.1, .1, .1, .1, 0., -0.5]]) point_ext = self.space.from_coordinates(point_int, 'intrinsic') result = self.space.to_coordinates(point_ext, 'intrinsic') expected = point_int expected = helper.to_vector(expected) self.assertAllClose(result, expected) point_ext = gs.array([[2., 1., 1., 1.], [4., 1., 3., math.sqrt(5.)], [3., 2., 0., 2.]]) point_int = self.space.to_coordinates(point_ext, 'intrinsic') result = self.space.from_coordinates(point_int, 'intrinsic') expected = point_ext expected = helper.to_vector(expected) self.assertAllClose(result, expected) def test_log_and_exp_general_case(self): """ Test that the Riemannian exponential and the Riemannian logarithm are inverse. Expect their composition to give the identity function. """ # Riemannian Log then Riemannian Exp # General case base_point = gs.array([4.0, 1., 3.0, math.sqrt(5.)]) point = gs.array([2.0, 1.0, 1.0, 1.0]) log = self.metric.log(point=point, base_point=base_point) result = self.metric.exp(tangent_vec=log, base_point=base_point) expected = helper.to_vector(point) self.assertAllClose(result, expected) def test_exp_and_belongs(self): H2 = Hyperbolic(dimension=2) METRIC = H2.metric base_point = gs.array([1., 0., 0.]) with self.session(): self.assertTrue(gs.eval(H2.belongs(base_point))) tangent_vec = H2.projection_to_tangent_space(vector=gs.array( [1., 2., 1.]), base_point=base_point) exp = METRIC.exp(tangent_vec=tangent_vec, base_point=base_point) with self.session(): self.assertTrue(gs.eval(H2.belongs(exp))) @geomstats.tests.np_and_pytorch_only def test_exp_vectorization(self): n_samples = 3 dim = self.dimension + 1 one_vec = gs.array([2.0, 1.0, 1.0, 1.0]) one_base_point = gs.array([4.0, 3., 1.0, math.sqrt(5)]) n_vecs = gs.array([[2., 1., 1., 1.], [4., 1., 3., math.sqrt(5.)], [3., 2., 0., 2.]]) n_base_points = gs.array( [[2.0, 0.0, 1.0, math.sqrt(2)], [5.0, math.sqrt(8), math.sqrt(8), math.sqrt(8)], [1.0, 0.0, 0.0, 0.0]]) one_tangent_vec = self.space.projection_to_tangent_space( one_vec, base_point=one_base_point) result = self.metric.exp(one_tangent_vec, one_base_point) self.assertAllClose(gs.shape(result), (1, dim)) n_tangent_vecs = self.space.projection_to_tangent_space( n_vecs, base_point=one_base_point) result = self.metric.exp(n_tangent_vecs, one_base_point) self.assertAllClose(gs.shape(result), (n_samples, dim)) expected = gs.zeros((n_samples, dim)) with self.session(): for i in range(n_samples): expected[i] = gs.eval( self.metric.exp(n_tangent_vecs[i], one_base_point)) expected = helper.to_vector(gs.array(expected)) self.assertAllClose(result, expected) one_tangent_vec = self.space.projection_to_tangent_space( one_vec, base_point=n_base_points) result = self.metric.exp(one_tangent_vec, n_base_points) self.assertAllClose(gs.shape(result), (n_samples, dim)) expected = gs.zeros((n_samples, dim)) with self.session(): for i in range(n_samples): expected[i] = gs.eval( self.metric.exp(one_tangent_vec[i], n_base_points[i])) expected = helper.to_vector(gs.array(expected)) self.assertAllClose(result, expected) n_tangent_vecs = self.space.projection_to_tangent_space( n_vecs, base_point=n_base_points) result = self.metric.exp(n_tangent_vecs, n_base_points) self.assertAllClose(gs.shape(result), (n_samples, dim)) expected = gs.zeros((n_samples, dim)) with self.session(): for i in range(n_samples): expected[i] = gs.eval( self.metric.exp(n_tangent_vecs[i], n_base_points[i])) expected = helper.to_vector(gs.array(expected)) self.assertAllClose(result, expected) def test_log_vectorization(self): n_samples = 3 dim = self.dimension + 1 one_point = gs.array([2.0, 1.0, 1.0, 1.0]) one_base_point = gs.array([4.0, 3., 1.0, math.sqrt(5)]) n_points = gs.array([[2.0, 1.0, 1.0, 1.0], [4.0, 1., 3.0, math.sqrt(5)], [3.0, 2.0, 0.0, 2.0]]) n_base_points = gs.array( [[2.0, 0.0, 1.0, math.sqrt(2)], [5.0, math.sqrt(8), math.sqrt(8), math.sqrt(8)], [1.0, 0.0, 0.0, 0.0]]) result = self.metric.log(one_point, one_base_point) self.assertAllClose(gs.shape(result), (1, dim)) result = self.metric.log(n_points, one_base_point) self.assertAllClose(gs.shape(result), (n_samples, dim)) result = self.metric.log(one_point, n_base_points) self.assertAllClose(gs.shape(result), (n_samples, dim)) result = self.metric.log(n_points, n_base_points) self.assertAllClose(gs.shape(result), (n_samples, dim)) def test_inner_product(self): """ Test that the inner product between two tangent vectors is the Minkowski inner product. """ minkowski_space = Minkowski(self.dimension + 1) base_point = gs.array( [1.16563816, 0.36381045, -0.47000603, 0.07381469]) tangent_vec_a = self.space.projection_to_tangent_space( vector=gs.array([10., 200., 1., 1.]), base_point=base_point) tangent_vec_b = self.space.projection_to_tangent_space( vector=gs.array([11., 20., -21., 0.]), base_point=base_point) result = self.metric.inner_product(tangent_vec_a, tangent_vec_b, base_point) expected = minkowski_space.metric.inner_product( tangent_vec_a, tangent_vec_b, base_point) with self.session(): self.assertAllClose(result, expected) def test_squared_norm_and_squared_dist(self): """ Test that the squared distance between two points is the squared norm of their logarithm. """ point_a = gs.array([2.0, 1.0, 1.0, 1.0]) point_b = gs.array([4.0, 1., 3.0, math.sqrt(5)]) log = self.metric.log(point=point_a, base_point=point_b) result = self.metric.squared_norm(vector=log) expected = self.metric.squared_dist(point_a, point_b) with self.session(): self.assertAllClose(result, expected) def test_norm_and_dist(self): """ Test that the distance between two points is the norm of their logarithm. """ point_a = gs.array([2.0, 1.0, 1.0, 1.0]) point_b = gs.array([4.0, 1., 3.0, math.sqrt(5)]) log = self.metric.log(point=point_a, base_point=point_b) result = self.metric.norm(vector=log) expected = self.metric.dist(point_a, point_b) with self.session(): self.assertAllClose(result, expected) def test_log_and_exp_edge_case(self): """ Test that the Riemannian exponential and the Riemannian logarithm are inverse. Expect their composition to give the identity function. """ # Riemannian Log then Riemannian Exp # Edge case: two very close points, base_point_2 and point_2, # form an angle < epsilon base_point_intrinsic = gs.array([1., 2., 3.]) base_point =\ self.space.from_coordinates(base_point_intrinsic, 'intrinsic') point_intrinsic = (base_point_intrinsic + 1e-12 * gs.array([-1., -2., 1.])) point =\ self.space.from_coordinates(point_intrinsic, 'intrinsic') log = self.metric.log(point=point, base_point=base_point) result = self.metric.exp(tangent_vec=log, base_point=base_point) expected = point with self.session(): self.assertAllClose(result, expected) @geomstats.tests.np_and_tf_only def test_exp_and_log_and_projection_to_tangent_space_general_case(self): """ Test that the Riemannian exponential and the Riemannian logarithm are inverse. Expect their composition to give the identity function. """ # Riemannian Exp then Riemannian Log # General case base_point = gs.array([4.0, 1., 3.0, math.sqrt(5)]) vector = gs.array([2.0, 1.0, 1.0, 1.0]) vector = self.space.projection_to_tangent_space(vector=vector, base_point=base_point) exp = self.metric.exp(tangent_vec=vector, base_point=base_point) result = self.metric.log(point=exp, base_point=base_point) expected = vector with self.session(): self.assertAllClose(result, expected) def test_dist(self): # Distance between a point and itself is 0. point_a = gs.array([4.0, 1., 3.0, math.sqrt(5)]) point_b = point_a result = self.metric.dist(point_a, point_b) expected = gs.array([[0]]) with self.session(): self.assertAllClose(result, expected) @geomstats.tests.np_and_pytorch_only def test_dist_poincare(self): point_a = gs.array([0.5, 0.5]) point_b = gs.array([0.5, -0.5]) self.space.metric.coords_type = 'ball' dist_a_b = self.metric.dist(point_a, point_b) self.space.metric.coords_type = 'extrinsic' result = dist_a_b expected = gs.array([[2.887270927429199]]) with self.session(): self.assertAllClose(result, expected) def test_exp_poincare(self): self.space.metric.coords_type = 'ball' result = 0 expected = 0 self.space.metric.coords_type = 'extrinsic' with self.session(): self.assertAllClose(result, expected) @geomstats.tests.np_only def test_log_poincare(self): point = gs.array([[0.3, 0.5]]) base_point = gs.array([[0.3, 0.3]]) self.space.metric.coords_type = 'ball' result = self.space.metric.log(point, base_point) expected = gs.array([[-0.01733576, 0.21958634]]) self.space.metric.coords_type = 'extrinsic' with self.session(): self.assertAllClose(result, expected) def test_exp_and_dist_and_projection_to_tangent_space(self): base_point = gs.array([4.0, 1., 3.0, math.sqrt(5)]) vector = gs.array([0.001, 0., -.00001, -.00003]) tangent_vec = self.space.projection_to_tangent_space( vector=vector, base_point=base_point) exp = self.metric.exp(tangent_vec=tangent_vec, base_point=base_point) result = self.metric.dist(base_point, exp) sq_norm = self.metric.embedding_metric.squared_norm(tangent_vec) expected = sq_norm with self.session(): self.assertAllClose(result, expected, atol=1e-2) def test_geodesic_and_belongs(self): # TODO(nina): Fix this tests, as it fails when geodesic goes "too far" initial_point = gs.array([4.0, 1., 3.0, math.sqrt(5)]) n_geodesic_points = 100 vector = gs.array([1., 0., 0., 0.]) initial_tangent_vec = self.space.projection_to_tangent_space( vector=vector, base_point=initial_point) geodesic = self.metric.geodesic( initial_point=initial_point, initial_tangent_vec=initial_tangent_vec) t = gs.linspace(start=0., stop=1., num=n_geodesic_points) points = geodesic(t) result = self.space.belongs(points) expected = gs.array(n_geodesic_points * [[True]]) with self.session(): self.assertAllClose(expected, result) def test_exp_and_log_and_projection_to_tangent_space_edge_case(self): """ Test that the Riemannian exponential and the Riemannian logarithm are inverse. Expect their composition to give the identity function. """ # Riemannian Exp then Riemannian Log # Edge case: tangent vector has norm < epsilon base_point = gs.array([2., 1., 1., 1.]) vector = 1e-10 * gs.array([.06, -51., 6., 5.]) exp = self.metric.exp(tangent_vec=vector, base_point=base_point) result = self.metric.log(point=exp, base_point=base_point) expected = self.space.projection_to_tangent_space( vector=vector, base_point=base_point) self.assertAllClose(result, expected, atol=1e-8) @geomstats.tests.np_only def test_scaled_inner_product(self): base_point_intrinsic = gs.array([1, 1, 1]) base_point = self.space.from_coordinates(base_point_intrinsic, "intrinsic") tangent_vec_a = gs.array([1, 2, 3, 4]) tangent_vec_b = gs.array([5, 6, 7, 8]) tangent_vec_a = self.space.projection_to_tangent_space( tangent_vec_a, base_point) tangent_vec_b = self.space.projection_to_tangent_space( tangent_vec_b, base_point) scale = 2 default_space = Hyperbolic(dimension=self.dimension) scaled_space = Hyperbolic(dimension=self.dimension, scale=2) inner_product_default_metric = \ default_space.metric.inner_product( tangent_vec_a, tangent_vec_b, base_point) inner_product_scaled_metric = \ scaled_space.metric.inner_product( tangent_vec_a, tangent_vec_b, base_point) result = inner_product_scaled_metric expected = scale**2 * inner_product_default_metric self.assertAllClose(result, expected) @geomstats.tests.np_only def test_scaled_squared_norm(self): base_point_intrinsic = gs.array([1, 1, 1]) base_point = self.space.from_coordinates(base_point_intrinsic, 'intrinsic') tangent_vec = gs.array([1, 2, 3, 4]) tangent_vec = self.space.projection_to_tangent_space( tangent_vec, base_point) scale = 2 default_space = Hyperbolic(dimension=self.dimension) scaled_space = Hyperbolic(dimension=self.dimension, scale=2) squared_norm_default_metric = default_space.metric.squared_norm( tangent_vec, base_point) squared_norm_scaled_metric = scaled_space.metric.squared_norm( tangent_vec, base_point) result = squared_norm_scaled_metric expected = scale**2 * squared_norm_default_metric self.assertAllClose(result, expected) @geomstats.tests.np_only def test_scaled_distance(self): point_a_intrinsic = gs.array([1, 2, 3]) point_b_intrinsic = gs.array([4, 5, 6]) point_a = self.space.from_coordinates(point_a_intrinsic, "intrinsic") point_b = self.space.from_coordinates(point_b_intrinsic, "intrinsic") scale = 2 scaled_space = Hyperbolic(dimension=self.dimension, scale=2) distance_default_metric = self.space.metric.dist(point_a, point_b) distance_scaled_metric = scaled_space.metric.dist(point_a, point_b) result = distance_scaled_metric expected = scale * distance_default_metric self.assertAllClose(result, expected) @geomstats.tests.np_and_pytorch_only 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.ball_manifold.metric tangent_vec = ball_metric.log(y, x) ball_metric.retraction(tangent_vec, x)