def test_diag_raises():
np.random.seed(10)
Ds = [8, 9, 10]
rank = len(Ds)
indices = [
Index(
BaseCharge(np.random.randint(-2, 3, (1, Ds[n])),
charge_types=[U1Charge]), False) for n in range(rank)
]
arr = BlockSparseTensor.random(indices)
chargearr = ChargeArray.random([indices[0], indices[1]])
with pytest.raises(ValueError):
diag(arr)
with pytest.raises(ValueError):
diag(chargearr)
def test_get_diag(dtype, num_charges, Ds, flow):
np.random.seed(10)
np_flow = -np.int((np.int(flow) - 0.5) * 2)
indices = [
Index(
BaseCharge(
np.random.randint(-2, 3, (num_charges, Ds[n])),
charge_types=[U1Charge] * num_charges), flow) for n in range(2)
]
arr = BlockSparseTensor.random(indices, dtype=dtype)
fused = fuse_charges(arr.flat_charges, arr.flat_flows)
inds = np.nonzero(fused == np.zeros((num_charges, 1), dtype=np.int16))[0]
# pylint: disable=no-member
left, _ = np.divmod(inds, Ds[1])
unique = np.unique(
np_flow * (indices[0]._charges[0].charges[:, left]), axis=1)
diagonal = diag(arr)
sparse_blocks, _, block_shapes = _find_diagonal_sparse_blocks(
arr.flat_charges, arr.flat_flows, 1)
data = np.concatenate([
np.diag(np.reshape(arr.data[sparse_blocks[n]], block_shapes[:, n]))
for n in range(len(sparse_blocks))
])
np.testing.assert_allclose(data, diagonal.data)
np.testing.assert_allclose(unique, diagonal.flat_charges[0].unique_charges)
def test_get_empty_diag(dtype, num_charges, Ds):
np.random.seed(10)
indices = [
Index(
BaseCharge(np.random.randint(-2, 3, (num_charges, Ds[n])),
charge_types=[U1Charge] * num_charges), False)
for n in range(2)
]
arr = BlockSparseTensor.random(indices, dtype=dtype)
diagonal = diag(arr)
np.testing.assert_allclose([], diagonal.data)
for c in diagonal.flat_charges:
assert len(c) == 0
def test_eig_prod(dtype, Ds, num_charges):
np.random.seed(10)
R = len(Ds)
charges = [
BaseCharge(
np.random.randint(-5, 6, (num_charges, Ds[n]), dtype=np.int16),
charge_types=[U1Charge] * num_charges) for n in range(R)
]
flows = [False] * R
inds = [Index(charges[n], flows[n]) for n in range(R)]
A = BlockSparseTensor.random(
inds + [i.copy().flip_flow() for i in inds], dtype=dtype)
dims = np.prod(Ds)
A = A.reshape([dims, dims])
E, V = eig(A)
A_ = V @ diag(E) @ inv(V)
np.testing.assert_allclose(A.data, A_.data)
def test_svd_prod(dtype, Ds, R1, num_charges):
np.random.seed(10)
R = len(Ds)
charges = [
BaseCharge(np.random.randint(-5, 6, (num_charges, Ds[n])),
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)
d1 = np.prod(Ds[:R1])
d2 = np.prod(Ds[R1:])
A = A.reshape([d1, d2])
U, S, V = svd(A, full_matrices=False)
A_ = U @ diag(S) @ V
assert A_.dtype == A.dtype
np.testing.assert_allclose(A.data, A_.data)
for n in range(len(A._charges)):
assert charge_equal(A_._charges[n], A._charges[n])
def test_eigh_prod(dtype, Ds, num_charges):
np.random.seed(10)
R = len(Ds)
charges = [
BaseCharge(
np.random.randint(-5, 6, (num_charges, Ds[n]), dtype=np.int16),
charge_types=[U1Charge] * num_charges) for n in range(R)
]
flows = [False] * R
inds = [Index(charges[n], flows[n]) for n in range(R)]
A = BlockSparseTensor.random(
inds + [i.copy().flip_flow() for i in inds], dtype=dtype)
dims = np.prod(Ds)
A = A.reshape([dims, dims])
B = A + A.T.conj()
E, V = eigh(B)
B_ = V @ diag(E) @ V.conj().T
np.testing.assert_allclose(B.data, B_.data)
for n in range(len(B._charges)):
assert charge_equal(B_._charges[n], B._charges[n])
def test_create_diag(dtype, num_charges):
np.random.seed(10)
D = 200
index = Index(
BaseCharge(np.random.randint(-2, 3, (num_charges, D)),
charge_types=[U1Charge] * num_charges), False)
arr = ChargeArray.random([index], dtype=dtype)
diagarr = diag(arr)
dense = np.ravel(diagarr.todense())
np.testing.assert_allclose(np.sort(dense[dense != 0.0]),
np.sort(diagarr.data[diagarr.data != 0.0]))
sparse_blocks, charges, block_shapes = _find_diagonal_sparse_blocks(
diagarr.flat_charges, diagarr.flat_flows, 1)
#in range(index._charges[0].unique_charges.shape[1]):
for n, block in enumerate(sparse_blocks):
shape = block_shapes[:, n]
block_diag = np.diag(np.reshape(diagarr.data[block], shape))
np.testing.assert_allclose(
arr.data[np.squeeze(index._charges[0] == charges[n])], block_diag)
assert np.allclose(en_even0, en_even1)
assert np.allclose(en_odd0, en_odd1)
"""
Example 2: compute truncated eigendecomposition of a reduced density matrix,
keeping only the eigenvalues above some cut-off threshold
"""
rho_temp = BT.fromdense([ind_chib1] + [ind_chib0],
np.array([[1, 0], [0, 0]], dtype=float))
V = V.reshape([2**(n_sites // 2), 2**(n_sites // 2), 2])
rho_half = tn.ncon([V, rho_temp, V.conj()], [[-1, 1, 2], [2, 3], [-2, 1, 3]])
# decomp with evalues sorted by magnitude
E2, V2 = eigh(rho_half,
which='LM',
full_sort=False,
threshold=1e-10,
max_kept=15)
rho_recover = V2 @ BLA.diag(E2) @ V2.T.conj()
assert np.allclose(rho_half.todense(), rho_recover.todense())
# decomp with evalues sorted by magnitude within each charge block
E2, V2 = eigh(rho_half, which='LM', threshold=1e-10, full_sort=False)
rho_recover = V2 @ BLA.diag(E2) @ V2.T.conj()
assert np.allclose(rho_half.todense(), rho_recover.todense())
# decomp with no truncation
E2, V2 = eigh(rho_half, which='LM')
rho_recover = V2 @ BLA.diag(E2) @ V2.T.conj()
assert np.allclose(rho_half.todense(), rho_recover.todense())
