def test_max_truncation_error_relative(self): absolute = np.diag([2.0, 1.0, 0.2, 0.1]) relative = np.diag([2.0, 1.0, 0.2, 0.1]) max_truncation_err = 0.2 _, _, _, trunc_sv_absolute = decompositions.svd_decomposition( np, absolute, 1, max_truncation_error=max_truncation_err, relative=False) _, _, _, trunc_sv_relative = decompositions.svd_decomposition( np, relative, 1, max_truncation_error=max_truncation_err, relative=True) np.testing.assert_almost_equal(trunc_sv_absolute, [0.1]) np.testing.assert_almost_equal(trunc_sv_relative, [0.2, 0.1])
def test_expected_shapes(self): val = np.zeros((2, 3, 4, 5)) u, s, vh, _ = decompositions.svd_decomposition(np, val, 2) self.assertEqual(u.shape_tensor, (2, 3, 6)) self.assertEqual(s.shape_tensor, (6, )) self.assertAllClose(s, np.zeros(6)) self.assertEqual(vh.shape_tensor, (6, 4, 5))
def svd_decomposition(self, tensor: Tensor, split_axis: int, max_singular_values: Optional[int] = None, max_truncation_error: Optional[float] = None ) -> Tuple[Tensor, Tensor, Tensor, Tensor]: return decompositions.svd_decomposition( self.np, tensor, split_axis, max_singular_values, max_truncation_error)
def test_max_singular_values_larger_than_bond_dimension(self): random_matrix = np.random.rand(10, 6) unitary1, _, unitary2 = np.linalg.svd(random_matrix, full_matrices=False) singular_values = np.array(range(6)) val = unitary1.dot(np.diag(singular_values).dot(unitary2.T)) u, s, vh, _ = decompositions.svd_decomposition( np, val, 1, max_singular_values=30) self.assertEqual(u.shape, (10, 6)) self.assertEqual(s.shape, (6,)) self.assertEqual(vh.shape, (6, 6))
def test_max_truncation_error(self): random_matrix = np.random.rand(10, 10) unitary1, _, unitary2 = np.linalg.svd(random_matrix) singular_values = np.array(range(10)) val = unitary1.dot(np.diag(singular_values).dot(unitary2.T)) u, s, vh, trun = decompositions.svd_decomposition( np, val, 1, max_truncation_error=math.sqrt(5.1)) self.assertEqual(u.shape_tensor, (10, 7)) self.assertEqual(s.shape_tensor, (7, )) self.assertAllClose(s, np.arange(9, 2, -1)) self.assertEqual(vh.shape_tensor, (7, 10)) self.assertAllClose(trun, np.arange(2, -1, -1))
def test_singular_values(dtype, R, R1, num_charges): np.random.seed(10) D = 30 charges = [ BaseCharge(np.random.randint(-5, 6, (num_charges, D)), charge_types=[U1Charge] * num_charges) for n in range(R) ] flows = [True] * R A = BlockSparseTensor.random( [Index(charges[n], flows[n]) for n in range(R)], dtype=dtype) _, s, _, _ = decompositions.svd_decomposition(bs, A, R1) _, s_dense, _, _ = np_decompositions.svd_decomposition(np, A.todense(), R1) np.testing.assert_almost_equal(np.sort(s.todense()), np.sort(s_dense[s_dense > 1E-13]))
def test_svd_decompositions(dtype, R, R1, num_charges): np.random.seed(10) D = 30 charges = [ BaseCharge(np.random.randint(-5, 6, (num_charges, D)), charge_types=[U1Charge] * num_charges) for n in range(R) ] flows = [True] * R A = BlockSparseTensor.random( [Index(charges[n], flows[n]) for n in range(R)], dtype=dtype) u, s, v, _ = decompositions.svd_decomposition(bs, A, R1) u_dense, s_dense, v_dense, _ = np_decompositions.svd_decomposition( np, A.todense(), R1) res1 = bs.tensordot(bs.tensordot(u, bs.diag(s), 1), v, 1) res2 = np.tensordot(np.tensordot(u_dense, np.diag(s_dense), 1), v_dense, 1) np.testing.assert_almost_equal(res1.todense(), res2)