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)
