class TestPSDMatricesRankK(geomstats.tests.TestCase): r"""Test of PSD Matrices Rank k methods.""" def setUp(self): r"""Set up the test.""" warnings.simplefilter("ignore", category=ImportWarning) gs.random.seed(1234) self.n = 3 self.k = 2 self.space = PSDMatrices(self.n, self.k) self.sym = SymmetricMatrices(self.n) def test_belongs(self): r"""Test of belongs method.""" psd_n_k = self.space mat_not_psd_n_k = gs.array([[0.8369314, -0.7342977, 1.0402943], [0.04035992, -0.7218659, 1.0794858], [0.9032698, -0.73601735, -0.36105633]]) mat_psd_n_k = gs.array([[1.0, 1.0, 0], [1.0, 4.0, 0], [0, 0, 0]]) result = psd_n_k.belongs(mat_not_psd_n_k) self.assertFalse(result) result = psd_n_k.belongs(mat_psd_n_k) self.assertTrue(result) def test_projection_and_belongs(self): r"""Test the projection and the belongs methods.""" points = self.sym.random_point(3) proj_points = self.space.projection(points) result = self.space.belongs(proj_points) self.assertTrue(gs.all(result)) def test_random_and_belongs(self): r"""Test the random and the belongs methods.""" mat = self.space.random_point(4) result = self.space.belongs(mat) self.assertTrue(gs.all(result)) def test_is_tangent_and_to_tangent(self): r"""Test the tangent functions.""" base_point = self.space.random_point(3) vectors = self.sym.random_point(3) vectors_t = self.space.to_tangent(base_point=base_point, vector=vectors) vectors_t_bp0 = self.space.to_tangent(base_point=base_point[0], vector=vectors) result = self.space.is_tangent(base_point=base_point, vector=vectors) self.assertFalse(gs.all(result)) result = self.space.is_tangent(base_point=base_point, vector=vectors_t) self.assertTrue(gs.all(result)) result = self.space.is_tangent(base_point=base_point[0], vector=vectors) self.assertFalse(gs.all(result)) result = self.space.is_tangent(base_point=base_point[0], vector=vectors_t_bp0) self.assertTrue(gs.all(result)) result = self.space.is_tangent(base_point=base_point[0], vector=vectors[0]) self.assertFalse(gs.all(result)) result = self.space.is_tangent(base_point=base_point[0], vector=vectors_t_bp0[0]) self.assertTrue(gs.all(result))
class TestSymmetricMatrices(geomstats.tests.TestCase): """Test of SymmetricMatrices methods.""" def setUp(self): """Set up the test.""" warnings.simplefilter("ignore", category=ImportWarning) gs.random.seed(1234) self.n = 3 self.space = SymmetricMatrices(self.n) def test_belongs(self): """Test of belongs method.""" sym_n = self.space mat_sym = gs.array([[1.0, 2.0, 3.0], [2.0, 4.0, 5.0], [3.0, 5.0, 6.0]]) mat_not_sym = gs.array([[1.0, 0.0, 3.0], [2.0, 4.0, 5.0], [3.0, 5.0, 6.0]]) result = sym_n.belongs(mat_sym) expected = True self.assertAllClose(result, expected) result = sym_n.belongs(mat_not_sym) expected = False self.assertAllClose(result, expected) def test_basis(self): """Test of belongs method.""" sym_n = SymmetricMatrices(2) mat_sym_1 = gs.array([[1.0, 0.0], [0, 0]]) mat_sym_2 = gs.array([[0, 1.0], [1.0, 0]]) mat_sym_3 = gs.array([[0, 0.0], [0, 1.0]]) expected = gs.stack([mat_sym_1, mat_sym_2, mat_sym_3]) result = sym_n.basis self.assertAllClose(result, expected) def test_expm(self): """Test of expm method.""" sym_n = SymmetricMatrices(self.n) v = gs.array([[0.0, 1.0, 0.0], [1.0, 0.0, 0.0], [0.0, 0.0, 1.0]]) result = sym_n.expm(v) c = math.cosh(1) s = math.sinh(1) e = math.exp(1) expected = gs.array([[c, s, 0.0], [s, c, 0.0], [0.0, 0.0, e]]) four_dim_v = gs.broadcast_to(v, (2, 2) + v.shape) four_dim_expected = gs.broadcast_to(expected, (2, 2) + expected.shape) four_dim_result = sym_n.expm(four_dim_v) self.assertAllClose(result, expected) self.assertAllClose(four_dim_result, four_dim_expected) def test_powerm(self): """Test of powerm method.""" sym_n = SymmetricMatrices(self.n) expected = gs.array( [[[1, 1.0 / 4.0, 0.0], [1.0 / 4, 2.0, 0.0], [0.0, 0.0, 1.0]]] ) power = gs.array(1.0 / 2.0) result = sym_n.powerm(expected, power) result = gs.matmul(result, gs.transpose(result, (0, 2, 1))) self.assertAllClose(result, expected) def test_vector_from_symmetric_matrix_and_symmetric_matrix_from_vector(self): """Test for matrix to vector and vector to matrix conversions.""" sym_mat_1 = gs.array([[1.0, 0.6, -3.0], [0.6, 7.0, 0.0], [-3.0, 0.0, 8.0]]) vector_1 = self.space.to_vector(sym_mat_1) result_1 = self.space.from_vector(vector_1) expected_1 = sym_mat_1 self.assertTrue(gs.allclose(result_1, expected_1)) vector_2 = gs.array([1, 2, 3, 4, 5, 6]) sym_mat_2 = self.space.from_vector(vector_2) result_2 = self.space.to_vector(sym_mat_2) expected_2 = vector_2 self.assertTrue(gs.allclose(result_2, expected_2)) def test_vector_and_symmetric_matrix_vectorization(self): """Test of vectorization.""" n_samples = 5 vector = gs.random.rand(n_samples, 6) sym_mat = self.space.from_vector(vector) result = self.space.to_vector(sym_mat) expected = vector self.assertTrue(gs.allclose(result, expected)) vector = self.space.to_vector(sym_mat) result = self.space.from_vector(vector) expected = sym_mat self.assertTrue(gs.allclose(result, expected)) def test_symmetric_matrix_from_vector(self): vector_2 = gs.array([1, 2, 3, 4, 5, 6]) result = self.space.from_vector(vector_2) expected = gs.array([[1.0, 2.0, 3.0], [2.0, 4.0, 5.0], [3.0, 5.0, 6.0]]) self.assertAllClose(result, expected) def test_projection_and_belongs(self): shape = (2, self.n, self.n) result = helper.test_projection_and_belongs(self.space, shape) for res in result: self.assertTrue(res) def test_random_and_belongs(self): mat = self.space.random_point() result = self.space.belongs(mat) self.assertTrue(result) def test_dim(self): result = self.space.dim n = self.space.n expected = int(n * (n + 1) / 2) self.assertAllClose(result, expected)
class TestSymmetricMatrices(geomstats.tests.TestCase): """Test of SymmetricMatrices methods.""" def setUp(self): """Set up the test.""" warnings.simplefilter('ignore', category=ImportWarning) gs.random.seed(1234) self.n = 3 self.space = SymmetricMatrices(self.n) def test_belongs(self): """Test of belongs method.""" sym_n = self.space mat_sym = gs.array([[1., 2., 3.], [2., 4., 5.], [3., 5., 6.]]) mat_not_sym = gs.array([[1., 0., 3.], [2., 4., 5.], [3., 5., 6.]]) result = sym_n.belongs(mat_sym) expected = True self.assertAllClose(result, expected) result = sym_n.belongs(mat_not_sym) expected = False self.assertAllClose(result, expected) def test_basis(self): """Test of belongs method.""" sym_n = SymmetricMatrices(2) mat_sym_1 = gs.array([[1., 0.], [0, 0]]) mat_sym_2 = gs.array([[0, 1.], [1., 0]]) mat_sym_3 = gs.array([[0, 0.], [0, 1.]]) expected = gs.stack([mat_sym_1, mat_sym_2, mat_sym_3]) result = sym_n.basis self.assertAllClose(result, expected) def test_expm(self): """Test of expm method.""" sym_n = SymmetricMatrices(self.n) v = gs.array([[0., 1., 0.], [1., 0., 0.], [0., 0., 1.]]) result = sym_n.expm(v) c = math.cosh(1) s = math.sinh(1) e = math.exp(1) expected = gs.array([[c, s, 0.], [s, c, 0.], [0., 0., e]]) self.assertAllClose(result, expected) def test_powerm(self): """Test of powerm method.""" sym_n = SymmetricMatrices(self.n) expected = gs.array( [[[1, 1. / 4., 0.], [1. / 4, 2., 0.], [0., 0., 1.]]]) expected = gs.cast(expected, gs.float64) power = gs.array(1. / 2) power = gs.cast(power, gs.float64) result = sym_n.powerm(expected, power) result = gs.matmul(result, gs.transpose(result, (0, 2, 1))) self.assertAllClose(result, expected) def test_vector_from_symmetric_matrix_and_symmetric_matrix_from_vector( self): """Test for matrix to vector and vector to matrix conversions.""" sym_mat_1 = gs.array([[1., 0.6, -3.], [0.6, 7., 0.], [-3., 0., 8.]]) vector_1 = self.space.to_vector(sym_mat_1) result_1 = self.space.from_vector(vector_1) expected_1 = sym_mat_1 self.assertTrue(gs.allclose(result_1, expected_1)) vector_2 = gs.array([1, 2, 3, 4, 5, 6]) sym_mat_2 = self.space.from_vector(vector_2) result_2 = self.space.to_vector(sym_mat_2) expected_2 = vector_2 self.assertTrue(gs.allclose(result_2, expected_2)) def test_vector_and_symmetric_matrix_vectorization(self): """Test of vectorization.""" n_samples = 5 vector = gs.random.rand(n_samples, 6) sym_mat = self.space.from_vector(vector) result = self.space.to_vector(sym_mat) expected = vector self.assertTrue(gs.allclose(result, expected)) vector = self.space.to_vector(sym_mat) result = self.space.from_vector(vector) expected = sym_mat self.assertTrue(gs.allclose(result, expected)) def test_symmetric_matrix_from_vector(self): vector_2 = gs.array([1, 2, 3, 4, 5, 6]) result = self.space.from_vector(vector_2) expected = gs.array([[1., 2., 3.], [2., 4., 5.], [3., 5., 6.]]) self.assertAllClose(result, expected) def test_projection_and_belongs(self): mat = gs.random.rand(3, 3) projection = self.space.projection(mat) result = self.space.belongs(projection) self.assertTrue(result) def test_random_and_belongs(self): mat = self.space.random_point() result = self.space.belongs(mat) self.assertTrue(result)