class TestVisualizationMethods(geomstats.tests.TestCase): def setUp(self): self.n_samples = 10 self.SO3_GROUP = SpecialOrthogonalGroup(n=3) self.SE3_GROUP = SpecialEuclideanGroup(n=3) self.S1 = Hypersphere(dimension=1) self.S2 = Hypersphere(dimension=2) self.H2 = HyperbolicSpace(dimension=2) plt.figure() @geomstats.tests.np_only def test_plot_points_so3(self): points = self.SO3_GROUP.random_uniform(self.n_samples) visualization.plot(points, space='SO3_GROUP') @geomstats.tests.np_only def test_plot_points_se3(self): points = self.SE3_GROUP.random_uniform(self.n_samples) visualization.plot(points, space='SE3_GROUP') @geomstats.tests.np_only def test_plot_points_s1(self): points = self.S1.random_uniform(self.n_samples) visualization.plot(points, space='S1') @geomstats.tests.np_only def test_plot_points_s2(self): points = self.S2.random_uniform(self.n_samples) visualization.plot(points, space='S2') @geomstats.tests.np_only def test_plot_points_h2_poincare_disk(self): points = self.H2.random_uniform(self.n_samples) visualization.plot(points, space='H2_poincare_disk') @geomstats.tests.np_only def test_plot_points_h2_poincare_half_plane(self): points = self.H2.random_uniform(self.n_samples) visualization.plot(points, space='H2_poincare_half_plane') @geomstats.tests.np_only def test_plot_points_h2_klein_disk(self): points = self.H2.random_uniform(self.n_samples) visualization.plot(points, space='H2_klein_disk')
def main(): fig = plt.figure(figsize=(15, 5)) hyperbolic_plane = HyperbolicSpace(dimension=2) data = hyperbolic_plane.random_uniform(n_samples=140) mean = hyperbolic_plane.metric.mean(data) tpca = TangentPCA(metric=hyperbolic_plane.metric, n_components=2) tpca = tpca.fit(data, base_point=mean) tangent_projected_data = tpca.transform(data) geodesic_0 = hyperbolic_plane.metric.geodesic( initial_point=mean, initial_tangent_vec=tpca.components_[0]) geodesic_1 = hyperbolic_plane.metric.geodesic( initial_point=mean, initial_tangent_vec=tpca.components_[1]) n_steps = 100 t = np.linspace(-1, 1, n_steps) geodesic_points_0 = geodesic_0(t) geodesic_points_1 = geodesic_1(t) print('Coordinates of the Log of the first 5 data points at the mean, ' 'projected on the principal components:') print(tangent_projected_data[:5]) ax_var = fig.add_subplot(121) xticks = np.arange(1, 2 + 1, 1) ax_var.xaxis.set_ticks(xticks) ax_var.set_title('Explained variance') ax_var.set_xlabel('Number of Principal Components') ax_var.set_ylim((0, 1)) ax_var.plot(xticks, tpca.explained_variance_ratio_) ax = fig.add_subplot(122) visualization.plot(mean, ax, space='H2_poincare_disk', color='darkgreen', s=10) visualization.plot(geodesic_points_0, ax, space='H2_poincare_disk', linewidth=2) visualization.plot(geodesic_points_1, ax, space='H2_poincare_disk', linewidth=2) visualization.plot(data, ax, space='H2_poincare_disk', color='black', alpha=0.7) plt.show()
class TestHyperbolicSpaceMethods(geomstats.tests.TestCase): _multiprocess_can_split_ = True def setUp(self): gs.random.seed(1234) self.dimension = 3 self.space = HyperbolicSpace(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 = HyperbolicSpace(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))) 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 = np.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 = np.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 = np.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 = MinkowskiSpace(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) 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)