def test_product_distance_extrinsic_representation(self): """Test the distance using the extrinsic representation.""" point_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, point_type=point_type) point_a = hyperbolic_space.intrinsic_to_extrinsic_coords( point_a_intrinsic) point_b = hyperbolic_space.intrinsic_to_extrinsic_coords( point_b_intrinsic) duplicate_point_a = gs.stack([point_a, point_a], axis=1) duplicate_point_b = gs.stack([point_b, point_b], axis=1) single_disk = PoincarePolydisk(n_disks=1, point_type=point_type) two_disks = PoincarePolydisk(n_disks=2, point_type=point_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 test_product_distance_extrinsic_representation(self): point_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, point_type=point_type) point_a = hyperbolic_space.intrinsic_to_extrinsic_coords( point_a_intrinsic) point_b = hyperbolic_space.intrinsic_to_extrinsic_coords( point_b_intrinsic) duplicate_point_a = gs.zeros((2, ) + point_a.shape) duplicate_point_a[0] = point_a duplicate_point_a[1] = point_a duplicate_point_b = gs.zeros((2, ) + point_b.shape) duplicate_point_b[0] = point_b duplicate_point_b[1] = point_b single_disk = PoincarePolydisk(n_disks=1, point_type=point_type) two_disks = PoincarePolydisk(n_disks=2, point_type=point_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.intrinsic_to_extrinsic_coords( point_intrinsic=point_intrinsic[:, i_disk, ...]) 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 = 3 self.space = Hyperbolic(dimension=self.dimension) self.metric = self.space.metric 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.intrinsic_to_extrinsic_coords(point_int) result = self.space.extrinsic_to_intrinsic_coords(point_ext) 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.extrinsic_to_intrinsic_coords(point_ext) result = self.space.intrinsic_to_extrinsic_coords(point_int) 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.intrinsic_to_extrinsic_coords(point_int) result = self.space.extrinsic_to_intrinsic_coords(point_ext) 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.extrinsic_to_intrinsic_coords(point_ext) result = self.space.intrinsic_to_extrinsic_coords(point_int) 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.intrinsic_to_extrinsic_coords( base_point_intrinsic) point_intrinsic = (base_point_intrinsic + 1e-12 * gs.array([-1., -2., 1.])) point = self.space.intrinsic_to_extrinsic_coords( point_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.point_type = 'ball' dist_a_b = self.metric.dist(point_a, point_b) self.space.metric.point_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.point_type = 'ball' result = 0 expected = 0 self.space.metric.point_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.point_type = 'ball' result = self.space.metric.log(point, base_point) expected = gs.array([-0.01733576, 0.21958634]) self.space.metric.point_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_and_tf_only def test_variance(self): point = gs.array([2., 1., 1., 1.]) points = gs.array([point, point]) result = self.metric.variance(points) expected = helper.to_scalar(0.) self.assertAllClose(result, expected) @geomstats.tests.np_and_tf_only def test_mean(self): point = gs.array([2., 1., 1., 1.]) points = gs.array([point, point]) result = self.metric.mean(points) expected = helper.to_vector(point) self.assertAllClose(result, expected) @geomstats.tests.np_and_tf_only def test_mean_and_belongs(self): point_a = self.space.random_uniform() point_b = self.space.random_uniform() point_c = self.space.random_uniform() points = gs.concatenate([point_a, point_b, point_c], axis=0) mean = self.metric.mean(points) result = self.space.belongs(mean) expected = gs.array([[True]]) self.assertAllClose(result, expected) @geomstats.tests.np_only def test_scaled_inner_product(self): base_point_intrinsic = gs.array([1, 1, 1]) base_point = self.space.intrinsic_to_extrinsic_coords( base_point_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.intrinsic_to_extrinsic_coords( base_point_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.intrinsic_to_extrinsic_coords(point_a_intrinsic) point_b = self.space.intrinsic_to_extrinsic_coords(point_b_intrinsic) scale = 2 default_space = Hyperbolic(dimension=self.dimension) scaled_space = Hyperbolic(dimension=self.dimension, scale=2) distance_default_metric = default_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)