def test_exp_small_vec(self): H2 = Hyperboloid(dim=2) METRIC = H2.metric base_point = H2.regularize(gs.array([1., 0., 0.])) self.assertTrue(H2.belongs(base_point)) tangent_vec = 1e-9 * H2.to_tangent(vector=gs.array([1., 2., 1.]), base_point=base_point) exp = METRIC.exp(tangent_vec=tangent_vec, base_point=base_point) self.assertTrue(H2.belongs(exp))
class TestHyperbolic(geomstats.tests.TestCase): def setup_method(self): gs.random.seed(1234) self.dimension = 3 self.space = Hyperboloid(dim=self.dimension) self.metric = self.space.metric self.ball_manifold = PoincareBall(dim=2) self.n_samples = 10 def test_belongs_intrinsic(self): self.space.coords_type = "intrinsic" point = gs.random.rand(self.n_samples, self.dimension) result = self.space.belongs(point) self.assertTrue(gs.all(result)) def test_regularize_intrinsic(self): self.space.coords_type = "intrinsic" point = gs.random.rand(self.n_samples, self.dimension) regularized = self.space.regularize(point) self.space.coords_type = "extrinsic" result = self.space.belongs(regularized) self.assertTrue(gs.all(result)) def test_regularize_zero_norm(self): point = gs.array([-1.0, 1.0, 0.0, 0.0]) with pytest.raises(ValueError): self.space.regularize(point) with pytest.raises(NameError): self.space.extrinsic_to_intrinsic_coords(point) def test_random_uniform_and_belongs(self): point = self.space.random_point() result = self.space.belongs(point) expected = True self.assertAllClose(result, expected) def test_random_uniform(self): result = self.space.random_point() self.assertAllClose(gs.shape(result), (self.dimension + 1,)) def test_projection_to_tangent_space(self): base_point = gs.array([1.0, 0.0, 0.0, 0.0]) belongs = self.space.belongs(base_point) self.assertTrue(belongs) tangent_vec = self.space.to_tangent( vector=gs.array([1.0, 2.0, 1.0, 3.0]), base_point=base_point ) result = self.metric.inner_product(tangent_vec, base_point) expected = 0.0 self.assertAllClose(result, expected) result = self.space.to_tangent( vector=gs.array([1.0, 2.0, 1.0, 3.0]), base_point=base_point ) expected = tangent_vec self.assertAllClose(result, expected) 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.intrinsic_to_extrinsic_coords(point_int) result = self.space.extrinsic_to_intrinsic_coords(point_ext) expected = point_int 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 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( [ [0.1, 0.0, 0.0, 0.1, 0.0, 0.0], [0.1, 0.1, 0.1, 0.4, 0.1, 0.0], [0.1, 0.3, 0.0, 0.1, 0.0, 0.0], [-0.1, 0.1, -0.4, 0.1, -0.01, 0.0], [0.0, 0.0, 0.1, 0.1, -0.08, -0.1], [0.1, 0.1, 0.1, 0.1, 0.0, -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( [ [2.0, 1.0, 1.0, 1.0], [4.0, 1.0, 3.0, math.sqrt(5.0)], [3.0, 2.0, 0.0, 2.0], ] ) 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_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, 1.0, 3.0, math.sqrt(5.0)]) 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 = point self.assertAllClose(result, expected) def test_log_and_exp_general_case_general_dim(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 dim = 5 n_samples = self.n_samples h5 = Hyperboloid(dim=dim) h5_metric = h5.metric base_point = h5.random_point() point = h5.random_point() point = gs.cast(point, gs.float64) base_point = gs.cast(base_point, gs.float64) one_log = h5_metric.log(point=point, base_point=base_point) result = h5_metric.exp(tangent_vec=one_log, base_point=base_point) expected = point self.assertAllClose(result, expected) # Test vectorization of log base_point = gs.stack([base_point] * n_samples, axis=0) point = gs.stack([point] * n_samples, axis=0) expected = gs.stack([one_log] * n_samples, axis=0) log = h5_metric.log(point=point, base_point=base_point) result = log self.assertAllClose(gs.shape(result), (n_samples, dim + 1)) self.assertAllClose(result, expected) result = h5_metric.exp(tangent_vec=log, base_point=base_point) expected = point self.assertAllClose(gs.shape(result), (n_samples, dim + 1)) self.assertAllClose(result, expected) # Test vectorization of exp tangent_vec = gs.stack([one_log] * n_samples, axis=0) exp = h5_metric.exp(tangent_vec=tangent_vec, base_point=base_point) result = exp expected = point self.assertAllClose(gs.shape(result), (n_samples, dim + 1)) self.assertAllClose(result, expected) def test_exp_and_belongs(self): H2 = Hyperboloid(dim=2) METRIC = H2.metric base_point = gs.array([1.0, 0.0, 0.0]) self.assertTrue(H2.belongs(base_point)) tangent_vec = H2.to_tangent( vector=gs.array([1.0, 2.0, 1.0]), base_point=base_point ) exp = METRIC.exp(tangent_vec=tangent_vec, base_point=base_point) self.assertTrue(H2.belongs(exp)) def test_exp_small_vec(self): H2 = Hyperboloid(dim=2) METRIC = H2.metric base_point = H2.regularize(gs.array([1.0, 0.0, 0.0])) self.assertTrue(H2.belongs(base_point)) tangent_vec = 1e-9 * H2.to_tangent( vector=gs.array([1.0, 2.0, 1.0]), base_point=base_point ) exp = METRIC.exp(tangent_vec=tangent_vec, base_point=base_point) self.assertTrue(H2.belongs(exp)) 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, 3.0, 1.0, math.sqrt(5)]) n_vecs = gs.array( [ [2.0, 1.0, 1.0, 1.0], [4.0, 1.0, 3.0, math.sqrt(5.0)], [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], ] ) one_tangent_vec = self.space.to_tangent(one_vec, base_point=one_base_point) result = self.metric.exp(one_tangent_vec, one_base_point) self.assertAllClose(gs.shape(result), (dim,)) n_tangent_vecs = self.space.to_tangent(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 = [] for i in range(n_samples): expected.append(self.metric.exp(n_tangent_vecs[i], one_base_point)) expected = gs.stack(expected, axis=0) expected = helper.to_vector(gs.array(expected)) self.assertAllClose(result, expected, atol=1e-2) one_tangent_vec = self.space.to_tangent(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 = [] for i in range(n_samples): expected.append(self.metric.exp(one_tangent_vec[i], n_base_points[i])) expected = gs.stack(expected, axis=0) expected = helper.to_vector(gs.array(expected)) self.assertAllClose(result, expected) n_tangent_vecs = self.space.to_tangent(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 = [] for i in range(n_samples): expected.append(self.metric.exp(n_tangent_vecs[i], n_base_points[i])) expected = gs.stack(expected, axis=0) 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, 3.0, 1.0, math.sqrt(5)]) n_points = gs.array( [[2.0, 1.0, 1.0, 1.0], [4.0, 1.0, 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), (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.to_tangent( vector=gs.array([10.0, 200.0, 1.0, 1.0]), base_point=base_point ) tangent_vec_b = self.space.to_tangent( vector=gs.array([11.0, 20.0, -21.0, 0.0]), 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 ) 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, 1.0, 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) 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, 1.0, 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) 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([1.0, 2.0, 3.0]) base_point = self.space.from_coordinates(base_point_intrinsic, "intrinsic") point_intrinsic = base_point_intrinsic + 1e-12 * gs.array([-1.0, -2.0, 1.0]) 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 self.assertAllClose(result, expected) 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, 1.0, 3.0, math.sqrt(5)]) vector = gs.array([2.0, 1.0, 1.0, 1.0]) vector = self.space.to_tangent(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 self.assertAllClose(result, expected) def test_dist(self): # Distance between a point and itself is 0. point_a = gs.array([4.0, 1.0, 3.0, math.sqrt(5)]) point_b = point_a result = self.metric.dist(point_a, point_b) expected = 0 self.assertAllClose(result, expected) def test_exp_and_dist_and_projection_to_tangent_space(self): base_point = gs.array([4.0, 1.0, 3.0, math.sqrt(5)]) vector = gs.array([0.001, 0.0, -0.00001, -0.00003]) tangent_vec = self.space.to_tangent(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 self.assertAllClose(result, expected, atol=1e-2) def test_geodesic_and_belongs(self): initial_point = gs.array([4.0, 1.0, 3.0, math.sqrt(5)]) n_geodesic_points = 100 vector = gs.array([1.0, 0.0, 0.0, 0.0]) initial_tangent_vec = self.space.to_tangent( vector=vector, base_point=initial_point ) geodesic = self.metric.geodesic( initial_point=initial_point, initial_tangent_vec=initial_tangent_vec ) t = gs.linspace(start=0.0, stop=1.0, num=n_geodesic_points) points = geodesic(t) result = gs.all(self.space.belongs(points)) self.assertTrue(result) def test_geodesic_and_belongs_large_initial_velocity(self): initial_point = gs.array([4.0, 1.0, 3.0, math.sqrt(5)]) n_geodesic_points = 100 vector = gs.array([2.0, 0.0, 0.0, 0.0]) initial_tangent_vec = self.space.to_tangent( vector=vector, base_point=initial_point ) geodesic = self.metric.geodesic( initial_point=initial_point, initial_tangent_vec=initial_tangent_vec ) t = gs.linspace(start=0.0, stop=1.0, num=n_geodesic_points) points = geodesic(t) result = gs.all(self.space.belongs(points, atol=gs.atol * 1e4)) self.assertTrue(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([2.0, 1.0, 1.0, 1.0]) vector = 1e-10 * gs.array([0.06, -51.0, 6.0, 5.0]) exp = self.metric.exp(tangent_vec=vector, base_point=base_point) result = self.metric.log(point=exp, base_point=base_point) expected = self.space.to_tangent(vector=vector, base_point=base_point) self.assertAllClose(result, expected) def test_scaled_inner_product(self): base_point_intrinsic = gs.array([1.0, 1.0, 1.0]) base_point = self.space.from_coordinates(base_point_intrinsic, "intrinsic") tangent_vec_a = gs.array([1.0, 2.0, 3.0, 4.0]) tangent_vec_b = gs.array([5.0, 6.0, 7.0, 8.0]) tangent_vec_a = self.space.to_tangent(tangent_vec_a, base_point) tangent_vec_b = self.space.to_tangent(tangent_vec_b, base_point) scale = 2 default_space = Hyperboloid(dim=self.dimension) scaled_space = Hyperboloid(dim=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) def test_scaled_squared_norm(self): base_point_intrinsic = gs.array([1.0, 1.0, 1.0]) base_point = self.space.from_coordinates(base_point_intrinsic, "intrinsic") tangent_vec = gs.array([1.0, 2.0, 3.0, 4.0]) tangent_vec = self.space.to_tangent(tangent_vec, base_point) scale = 2 default_space = Hyperboloid(dim=self.dimension) scaled_space = Hyperboloid(dim=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) def test_scaled_distance(self): point_a_intrinsic = gs.array([1.0, 2.0, 3.0]) point_b_intrinsic = gs.array([4.0, 5.0, 6.0]) point_a = self.space.from_coordinates(point_a_intrinsic, "intrinsic") point_b = self.space.from_coordinates(point_b_intrinsic, "intrinsic") scale = 2 scaled_space = Hyperboloid(dim=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) def test_is_tangent(self): base_point = gs.array([4.0, 1.0, 3.0, math.sqrt(5.0)]) point = gs.array([2.0, 1.0, 1.0, 1.0]) log = self.metric.log(point=point, base_point=base_point) result = self.space.is_tangent(log, base_point) self.assertTrue(result) @geomstats.tests.np_autograd_and_tf_only def test_parallel_transport_vectorization(self): space = self.space shape = (4, space.dim + 1) metric = space.metric results = helper.test_parallel_transport(space, metric, shape) for res in results: self.assertTrue(res) def test_projection_and_belongs(self): shape = (self.n_samples, self.dimension + 1) result = helper.test_projection_and_belongs( self.space, shape, atol=gs.atol * 100 ) for res in result: self.assertTrue(res) point = gs.array([0.0, 1.0, 0.0, 0.0]) projected = self.space.projection(point) result = self.space.belongs(projected) self.assertTrue(result)