def test_projdiag(backend, dtype, chi): A = tn.randn((chi, chi), dtype=dtype, backend=backend, seed=10) B = tn.randn((chi, chi), dtype=dtype, backend=backend, seed=10) result = ct.projdiag(A, B) compare_val = tn.linalg.operations.ncon([A, B], [[1, 2], [1, 2]]) compare = compare_val * tn.eye(chi, dtype=dtype, backend=backend) rtol = (A.size + B.size) * np.finfo(dtype).eps np.testing.assert_allclose(result.array, compare.array, rtol=rtol)
def test_compute_hR_vs_expect(backend, dtype, chi, d): _, _, A_R, H = random_hermitian_system(backend, dtype, chi, d) I = tn.eye(chi, backend=backend, dtype=dtype) hR = ct.compute_hR(A_R, H) result = tn.abs(tn.trace(hR)) compare = ct.twositeexpect([A_R, I, A_R], H) rtol = (2*A_R.size + I.size + H.size) * np.finfo(dtype).eps np.testing.assert_allclose(result.array, compare.array, rtol=rtol)
def test_XopL_noX(backend, dtype, chi, d):
A = tn.randn((chi, d, chi), dtype=dtype, backend=backend, seed=10)
X = tn.eye(chi, dtype=dtype, backend=backend)
result = ct.XopL(A, X)
compare = tn.linalg.operations.ncon([A, A.conj()],
[[1, 3, -2],
[1, 3, -1]])
rtol = (2*A.size + X.size) * np.finfo(dtype).eps
np.testing.assert_allclose(result.array, compare.array, rtol=rtol)
def test_polar(backend, dtype, chi): A = tn.randn((chi, chi), backend=backend, dtype=dtype, seed=10) U = polar.polarU(A) UUdag = U @ U.H UdagU = U.H @ U eye = tn.eye(chi, dtype, backend=backend) atol = A.size * np.finfo(dtype).eps np.testing.assert_allclose(eye.array, UUdag.array, atol=atol) np.testing.assert_allclose(UUdag.array, eye.array, atol=atol)
def test_polar_mps(backend, dtype, chi, d): A = tn.randn((chi, d, chi), backend=backend, dtype=dtype, seed=10) UR = polar.polarU(A, pivot_axis=1) UL = polar.polarU(A, pivot_axis=2) eye = tn.eye(chi, dtype, backend=backend) testR = ct.XopR(UR, eye) testL = ct.XopL(UL, eye) atol = A.size * np.finfo(dtype).eps np.testing.assert_allclose(eye.array, testR.array, atol=atol) np.testing.assert_allclose(eye.array, testL.array, atol=atol)
def test_inv_vs_backend(backend, dtype):
shape = 6
dtype = testing_utils.np_dtype_to_backend(backend, dtype)
tensor = tensornetwork.eye(shape, backend=backend, dtype=dtype)
tn_result = linalg.inv(tensor)
if backend is None:
backend = backend_contextmanager.get_default_backend()
backend_obj = backends.backend_factory.get_backend(backend)
backend_result = backend_obj.inv(tensor.array)
np.testing.assert_allclose(tn_result.array, backend_result)
def test_eye(backend):
"""
Tests tensornetwork.eye against np.eye.
"""
N = 4
M = 6
backend_obj = backends.backend_factory.get_backend(backend)
for dtype in dtypes[backend]["all"]:
tnI = tensornetwork.eye(N, dtype=dtype, M=M, backend=backend)
npI = backend_obj.eye(N, dtype=dtype, M=M)
np.testing.assert_allclose(tnI.array, npI)
def test_gauge_match_right(backend, dtype, chi, d):
"""
Gauge matching is a null op on a system gauge matched on the RHS.
"""
_, C, A_R, _ = random_hermitian_system(backend, dtype, chi, d)
A_C = ct.leftmult(C, A_R)
_, A_R2 = vumps.gauge_match(A_C, C, True)
rtol = 2 * A_R.size * C.size * A_C.size * np.finfo(dtype).eps
np.testing.assert_allclose(A_R.array, A_R2.array, rtol=rtol)
I = tn.eye(chi, backend=backend, dtype=dtype)
XAR2 = ct.XopR(A_R2, I)
np.testing.assert_allclose(XAR2.array, I.array, atol=rtol)
def test_gauge_match_left(backend, dtype, chi, d):
"""
Gauge matching is a null op on a system gauge matched on the LHS.
"""
A_L, C, _, _ = random_hermitian_system(backend, dtype, chi, d)
A_C = ct.rightmult(A_L, C)
A_L2, _ = vumps.gauge_match(A_C, C, True)
rtol = 2 * A_L.size * C.size * A_C.size * np.finfo(dtype).eps
np.testing.assert_allclose(A_L.array, A_L2.array, rtol=rtol)
I = tn.eye(chi, backend=backend, dtype=dtype)
XAL2 = ct.XopL(A_L2, I)
np.testing.assert_allclose(XAL2.array, I.array, atol=rtol)
def test_expm_vs_backend(backend, dtype):
shape = 6
dtype = testing_utils.np_dtype_to_backend(backend, dtype)
tensor = tensornetwork.eye(shape, backend=backend, dtype=dtype)
if backend in ["pytorch"]:
with pytest.raises(NotImplementedError):
tn_result = linalg.expm(tensor)
else:
tn_result = linalg.expm(tensor)
backend_obj = backends.backend_factory.get_backend(backend)
if backend in ["pytorch"]:
with pytest.raises(NotImplementedError):
backend_result = backend_obj.expm(tensor.array)
else:
backend_result = backend_obj.expm(tensor.array)
np.testing.assert_allclose(tn_result.array, backend_result)
def H_ising(h: float,
J: float = 1.,
backend: Optional[BackendType] = None,
dtype: Optional[DtypeType] = None) -> tn.Tensor:
"""
The famous and beloved transverse-field Ising model,
H = J * XX + h * ZI
Args:
h : Transverse field.
J : Coupling strength, default 1.
backend: The backend.
dtype : dtype of data.
Returns:
H : The Hamiltonian, a tn.Tensor shape (2, 2, 2, 2).
"""
X = sigX(backend=backend, dtype=dtype)
Z = sigZ(backend=backend, dtype=dtype)
Id = tn.eye(2, backend=backend, dtype=dtype)
return J * tn.kron(X, X) + 0.5 * h * (tn.kron(Z, Id) + tn.kron(Id, Z))