def test_contract_with_sequence():
# 3 contract to complex number using a sequence
# ==========================
v = npc.Array.from_ndarray_trivial([[1. + .2j, .5], [0 + .1j, -1.6]], dtype=complex)
v.iset_leg_labels(['L1', 'L2'])
w = npc.Array.from_ndarray_trivial([[1.2 + .3j, .6], [0.1 + .2j, -1.2]], dtype=complex)
w.iset_leg_labels(['U1', 'U2'])
h2 = two_site_hamiltonian()
h = two_site_hamiltonian(coupling=.3)
S = Sy
S.iset_leg_labels(['U', 'L'])
# the supplied sequence should generate three suboptimal warnings
with warnings.catch_warnings(record=True) as cw:
# Cause all warnings to always be triggered.
warnings.simplefilter("always")
res = contract(tensor_list=[v, h2, S, h, w],
tensor_names=['v', 'h2', 'S', 'h', 'w'],
leg_contractions=[['v', 'L1', 'h2', 'p1*'], ['v', 'L2', 'h2', 'p2*'],
['h2', 'p1', 'h', 'p1*'], ['h2', 'p2', 'S', 'U'],
['S', 'L', 'h', 'p2*'], ['h', 'p1', 'w', 'U1'],
['h', 'p2', 'w', 'U2']],
sequence=[1, 3, 5, 6, 4, 2, 0])
assert len(cw) == 3
assert "Suboptimal contraction sequence" in str(cw[0].message)
assert "Suboptimal contraction sequence" in str(cw[1].message)
assert "Suboptimal contraction sequence" in str(cw[2].message)
expected_result = -0.1735 - 0.5015j # from MatLab
assert np.abs(res - expected_result) < 1.e-10
def test_contract_to_complex_number():
# 2 contract to complex number
# ==========================
v = npc.Array.from_ndarray_trivial([[1. + .2j, .5], [0 + .1j, -1.6]],
dtype=complex)
v.iset_leg_labels(['L1', 'L2'])
w = npc.Array.from_ndarray_trivial([[1.2 + .3j, .6], [0.1 + .2j, -1.2]],
dtype=complex)
w.iset_leg_labels(['U1', 'U2'])
h2 = two_site_hamiltonian()
h = two_site_hamiltonian(coupling=.3)
S = Sy
S.iset_leg_labels(['U', 'L'])
res = contract(tensor_list=[v, h2, S, h, w],
tensor_names=['v', 'h2', 'S', 'h', 'w'],
leg_contractions=[['v', 'L1', 'h2', 'p1*'],
['v', 'L2', 'h2', 'p2*'],
['h2', 'p1', 'h', 'p1*'],
['h2', 'p2', 'S', 'U'],
['S', 'L', 'h', 'p2*'],
['h', 'p1', 'w', 'U1'],
['h', 'p2', 'w', 'U2']])
expected_result = -0.1735 - 0.5015j # from MatLab
assert np.abs(res - expected_result) < 1.e-10
def test_contract_to_real_number():
# 1 contract to real number
# ==========================
v = npc.Array.from_ndarray_trivial([[1., .5], [0, -1.6]])
v.iset_leg_labels(['L1', 'L2'])
w = npc.Array.from_ndarray_trivial([[1.2, .6], [0.1, -1.2]])
w.iset_leg_labels(['U1', 'U2'])
h2 = two_site_hamiltonian()
h = two_site_hamiltonian(coupling=.3)
S = Sz
S.iset_leg_labels(['U', 'L'])
res = contract(tensor_list=[v, h2, S, h, w],
leg_contractions=[['v', 'L1', 'h2', 'p1*'],
['v', 'L2', 'h2', 'p2*'],
['h2', 'p1', 'h', 'p1*'],
['h2', 'p2', 'S', 'U'],
['S', 'L', 'h', 'p2*'],
['h', 'p1', 'w', 'U1'],
['h', 'p2', 'w', 'U2']],
open_legs=None,
tensor_names=['v', 'h2', 'S', 'h', 'w'])
expected_result = -0.2970000000000002 # from MatLab
assert np.abs(res - expected_result) < 1.e-10
def test_outer_product():
S = Sy
S.iset_leg_labels(['U', 'L'])
S2 = Sz
S2.iset_leg_labels(['U', 'L'])
res = contract(tensor_list=[S, S2],
tensor_names=['Sy', 'Sz'],
open_legs=[['Sy', 'U', 'U2'], ['Sy', 'L', 'L2'], ['Sz', 'U', 'U1'],
['Sz', 'L', 'L1']])
expected_result = np.kron(np.array([[1., 0.], [0., -1.]]), np.array([[0., -1.j], [1.j, 0.]]))
expected_result = expected_result.reshape([2, 2, 2, 2])
expected_result = expected_result.transpose([1, 3, 0, 2])
assert np.linalg.norm(res.to_ndarray() - expected_result) < 1.e-10
def test_contract_to_tensor():
h2 = two_site_hamiltonian()
h = two_site_hamiltonian(coupling=.3)
S = Sy
S.iset_leg_labels(['U', 'L'])
res = contract(tensor_list=[h2, S, h],
tensor_names=['h2', 'S', 'h'],
leg_contractions=[['h2', 'p1', 'h', 'p1*'], ['h2', 'p2', 'S', 'U'],
['S', 'L', 'h', 'p2*']],
open_legs=[['h2', 'p1*', 'U1'], ['h2', 'p2*', 'U2'], ['h', 'p1', 'L1'],
['h', 'p2', 'L2']])
expected_result = np.ones([2, 2, 2, 2], dtype=complex)
expected_result[:, :, 0, 0] = [[.35j, -1j], [0, .65j]]
expected_result[:, :, 1, 0] = [[0, -.65j], [-.35j, -1j]]
expected_result[:, :, 0, 1] = [[1j, +.35j], [.65j, 0]]
expected_result[:, :, 1, 1] = [[-.65j, 0], [1j, -.35j]]
assert np.linalg.norm(res.to_ndarray() - expected_result) < 1.e-10