def test_mps_qrpos():
tensor = np.random.randn(2, 3, 2) + 1j * np.random.randn(2, 3, 2)
mps = MPS(tensor)
el = np.random.randn(2, 2) + 1j * np.random.randn(2, 2)
q, r = mps._QRPos(el)
expected = np.reshape(np.einsum('ijk,ai->ajk', tensor, el), (6, 2))
np.testing.assert_allclose(expected, np.dot(q, r))
np.testing.assert_allclose(np.diag(r), np.real(np.diag(r)))
def test_mps_left_orthonormalize_gives_correct_lambda():
tensor = np.random.randn(2, 3, 2)
mps = MPS(tensor)
transfer_matrix = np.reshape(mps.transfer_matrix.tensor, (4, 4))
L0 = np.random.randn(2, 2)
_, _, lamb = mps.left_orthonormalize(L0, 10**(-10))
val = np.max(eigvals(transfer_matrix))
np.testing.assert_almost_equal(np.sqrt(val), lamb)
def test_mps_apply_transfer_matrix():
tensor = np.random.randn(2, 3, 2) + 1j * np.random.randn(2, 3, 2)
mps = MPS(tensor)
v = np.random.randn(2, 2)
actual = mps.apply_transfer_matrix(v)
transfer_matrix = np.einsum('ijk,ajb->iakb', tensor, np.conj(tensor))
expected = np.einsum('ijkl,ji->lk', transfer_matrix, v)
np.testing.assert_allclose(actual, expected)
def test_mps_left_orthonormalize_gives_same_uniform_mps():
tensor = np.random.randn(2, 3, 2)
mps = MPS(tensor)
L0 = np.random.randn(2, 2)
AL, _, lamb = mps.left_orthonormalize(L0, 10**(-10))
ALt = np.conj(np.reshape(AL, (2, 3, 2)))
mixed = np.reshape(np.einsum('ijk,ajb->iakb', tensor, ALt), (4, 4))
val = np.max(eigvals(mixed))
np.testing.assert_almost_equal(val, lamb, decimal=8)
def test_mps_left_orthonormalize_gives_fixed_point_qrpos():
tensor = np.random.randn(2, 3, 2)
mps = MPS(tensor)
L0 = np.random.randn(2, 2)
_, L, _ = mps.left_orthonormalize(L0, 10**(-6))
_, L2 = mps._QRPos(L)
np.testing.assert_array_almost_equal(L / np.linalg.norm(L),
L2 / np.linalg.norm(L2))
def test_mps_apply_mixed_transfer_matrix():
tensor = np.random.randn(2, 3, 2)
mps = MPS(tensor)
B = np.random.randn(4, 3, 4)
v = np.random.randn(4, 2)
actual = mps.apply_mixed_transfer_matrix(B, v)
transfer_matrix = np.einsum('ijk,ajb->iakb', tensor, B)
expected = np.einsum('ijkl,ji->lk', transfer_matrix, v)
np.testing.assert_allclose(actual, expected)
def test_mps_left_orthonormalize_gives_fixed_point_mixed_transfer_matrix():
tensor = np.random.randn(2, 3, 2)
mps = MPS(tensor)
L0 = np.random.randn(2, 2)
AL, L, _ = mps.left_orthonormalize(L0, 10**(-6))
actual = mps.apply_mixed_transfer_matrix(
np.reshape(np.conj(AL), (2, 3, 2)), L)
expected = L
np.testing.assert_array_almost_equal(actual / norm(actual),
expected / norm(expected))
def test_mps_left_orthonormalize_gives_fixed_point_single_layer():
tensor = np.random.randn(2, 3, 2)
mps = MPS(tensor)
L0 = np.random.randn(2, 2)
AL, L, lamb = mps.left_orthonormalize(L0, 10**(-10))
expected = np.einsum('ijk,ai->ajk', tensor, L)
actual = np.einsum('ijk,ka->ija', np.reshape(AL, (2, 3, 2)), L)
np.testing.assert_almost_equal(norm(expected) / norm(actual),
lamb,
decimal=8)
np.testing.assert_array_almost_equal(actual / np.linalg.norm(actual),
expected / np.linalg.norm(expected))
def test_mps_init():
tensor = np.random.randn(3, 2, 3)
mps = MPS(tensor)
assert mps.axis_order == ["left_virtual", "physical", "right_virtual"]
assert mps.virtual_dimension == 3
assert mps.physical_dimension == 2
np.testing.assert_allclose(mps.tensor, tensor)
def test_mps_init_different_axis_order():
tensor = np.random.randn(3, 3, 2)
mps = MPS(tensor, left_virtual=1, physical=2, right_virtual=0)
assert mps.axis_order == ["left_virtual", "physical", "right_virtual"]
assert mps.virtual_dimension == 3
assert mps.physical_dimension == 2
np.testing.assert_allclose(mps.tensor, np.transpose(tensor, (1, 2, 0)))
def test_mps_to_matrix_error():
tensor = np.random.randn(2, 3, 2)
mps = MPS(tensor)
with pytest.raises(ValueError):
mps.to_matrix(left_indices=["left_virtual", "physical"],
right_indices=[])
with pytest.raises(ValueError):
mps.to_matrix(left_indices=["left_virtual", "physical"],
right_indices=["left_virtual"])
with pytest.raises(ValueError):
mps.to_matrix(left_indices=["left_virtual", "physical"],
right_indices=["left_virtual", "right_virtual"])
with pytest.raises(ValueError):
mps.to_matrix(left_indices=["left_virtual", "physical"],
right_indices=["a"])
def test_mps_to_matrix():
tensor = np.random.randn(3, 2, 3)
mps = MPS(tensor, left_virtual=0, physical=1, right_virtual=2)
expected = np.reshape(tensor, (6, 3))
actual = mps.to_matrix(left_indices=["left_virtual", "physical"],
right_indices=["right_virtual"])
np.testing.assert_allclose(actual, expected)
expected = np.reshape(np.transpose(tensor, (1, 0, 2)), (6, 3))
actual = mps.to_matrix(left_indices=["physical", "left_virtual"],
right_indices=["right_virtual"])
np.testing.assert_allclose(actual, expected)
expected = np.reshape(np.transpose(tensor, (0, 2, 1)), (3, 6))
actual = mps.to_matrix(left_indices=["left_virtual"],
right_indices=["right_virtual", "physical"])
np.testing.assert_allclose(actual, expected)
expected = np.reshape(tensor, (3, 6))
actual = mps.to_matrix(left_indices=["left_virtual"],
right_indices=["physical", "right_virtual"])
np.testing.assert_allclose(actual, expected)
def test_mps_init_wrong_dimensions():
tensor = np.random.randn(3, 2, 2)
with pytest.raises(ValueError):
MPS(tensor)
def test_mps_transfer_matrix():
tensor = np.random.randn(2, 3, 2) + 1j * np.random.randn(2, 3, 2)
mps = MPS(tensor)
actual = mps.transfer_matrix
expected = np.einsum('ijk,ajb->iakb', tensor, np.conj(tensor))
np.testing.assert_allclose(actual.tensor, expected)