def test_random_operators_are_reproducible(self):
op1 = random_diagonal_coulomb_hamiltonian(5, seed=5947)
op2 = random_diagonal_coulomb_hamiltonian(5, seed=5947)
numpy.testing.assert_allclose(op1.one_body, op2.one_body)
numpy.testing.assert_allclose(op1.two_body, op2.two_body)
op1 = random_interaction_operator(5, seed=8911)
op2 = random_interaction_operator(5, seed=8911)
numpy.testing.assert_allclose(op1.one_body_tensor, op2.one_body_tensor)
numpy.testing.assert_allclose(op1.two_body_tensor, op2.two_body_tensor)
op1 = random_quadratic_hamiltonian(5, seed=17711)
op2 = random_quadratic_hamiltonian(5, seed=17711)
numpy.testing.assert_allclose(op1.combined_hermitian_part,
op2.combined_hermitian_part)
numpy.testing.assert_allclose(op1.antisymmetric_part,
op2.antisymmetric_part)
op1 = random_antisymmetric_matrix(5, seed=24074)
op2 = random_antisymmetric_matrix(5, seed=24074)
numpy.testing.assert_allclose(op1, op2)
op1 = random_hermitian_matrix(5, seed=56753)
op2 = random_hermitian_matrix(5, seed=56753)
numpy.testing.assert_allclose(op1, op2)
op1 = random_unitary_matrix(5, seed=56486)
op2 = random_unitary_matrix(5, seed=56486)
numpy.testing.assert_allclose(op1, op2)
def test_square(self):
m, n = (3, 3)
# Obtain a random matrix of orthonormal rows
Q = random_unitary_matrix(n)
Q = Q[:m, :]
Q = Q[:m, :]
# Get Givens decomposition of Q
givens_rotations, V, diagonal = givens_decomposition(Q)
# There should be no Givens rotations
self.assertEqual(givens_rotations, list())
# Compute V * Q * U^\dagger
W = V.dot(Q)
# Construct the diagonal matrix
D = numpy.zeros((m, n), dtype=complex)
D[numpy.diag_indices(m)] = diagonal
# Assert that W and D are the same
for i in range(m):
for j in range(n):
self.assertAlmostEqual(D[i, j], W[i, j])
def test_real_numbers(self):
for m, n in self.test_dimensions:
# Obtain a random real matrix of orthonormal rows
Q = random_unitary_matrix(n, real=True)
Q = Q[:m, :]
# Get Givens decomposition of Q
givens_rotations, V, diagonal = givens_decomposition(Q)
# Compute U
U = numpy.eye(n, dtype=complex)
for parallel_set in givens_rotations:
combined_givens = numpy.eye(n, dtype=complex)
for i, j, theta, phi in reversed(parallel_set):
c = numpy.cos(theta)
s = numpy.sin(theta)
phase = numpy.exp(1.j * phi)
G = numpy.array([[c, -phase * s],
[s, phase * c]], dtype=complex)
givens_rotate(combined_givens, G, i, j)
U = combined_givens.dot(U)
# Compute V * Q * U^\dagger
W = V.dot(Q.dot(U.T.conj()))
# Construct the diagonal matrix
D = numpy.zeros((m, n), dtype=complex)
D[numpy.diag_indices(m)] = diagonal
# Assert that W and D are the same
for i in range(m):
for j in range(n):
self.assertAlmostEqual(D[i, j], W[i, j])
def test_bad_dimensions(self):
m, n = (3, 2)
# Obtain a random matrix of orthonormal rows
Q = random_unitary_matrix(m)
Q = Q[:m, :]
Q = Q[:m, :n]
with self.assertRaises(ValueError):
_ = givens_decomposition(Q)
