def svd(
self,
tensor: Tensor,
pivot_axis: int = -1,
max_singular_values: Optional[int] = None,
max_truncation_error: Optional[float] = None,
relative: Optional[bool] = False
) -> Tuple[Tensor, Tensor, Tensor, Tensor]:
return decompositions.svd(self.bs, tensor, pivot_axis, max_singular_values,
max_truncation_error, relative)
def test_singular_values(dtype, R, R1, num_charges):
np.random.seed(10)
D = 30
charges = [
BaseCharge(np.random.randint(-5, 6, (D, num_charges)),
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)
_, s, _, _ = decompositions.svd(bs, A, R1)
_, s_dense, _, _ = np_decompositions.svd(np, A.todense(), R1)
np.testing.assert_almost_equal(np.sort(s.todense()),
np.sort(s_dense[s_dense > 1E-13]))
def test_max_singular_values(dtype, R, R1, num_charges):
np.random.seed(10)
D = 30
max_singular_values = 12
charges = [
BaseCharge(np.random.randint(-5, 6, (D, num_charges)),
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)
_, s, _, _ = decompositions.svd(bs,
A,
R1,
max_singular_values=max_singular_values)
assert len(s.data) <= max_singular_values
def test_svds(dtype, R, R1, num_charges):
np.random.seed(10)
D = 30
charges = [
BaseCharge(np.random.randint(-5, 6, (D, num_charges)),
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)
u, s, v, _ = decompositions.svd(bs, A, R1)
u_dense, s_dense, v_dense, _ = np_decompositions.svd(np, A.todense(), R1)
res1 = bs.tensordot(bs.tensordot(u, bs.diag(s), 1), v, 1)
res2 = np.tensordot(np.tensordot(u_dense, np.diag(s_dense), 1), v_dense, 1)
np.testing.assert_almost_equal(res1.todense(), res2)
def test_max_singular_values_larger_than_bond_dimension(dtype, num_charges):
np.random.seed(10)
R = 2
D = 30
charges = [
BaseCharge(np.random.randint(-5, 6, (D, num_charges)),
charge_types=[U1Charge] * num_charges) for n in range(R)
]
flows = [True] * R
random_matrix = BlockSparseTensor.random(
[Index(charges[n], flows[n]) for n in range(R)], dtype=dtype)
U, S, V = bs.svd(random_matrix, full_matrices=False)
S.data = np.array(range(len(S.data)))
val = U @ bs.diag(S) @ V
_, S2, _, _ = decompositions.svd(bs, val, 1, max_singular_values=40)
assert S2.shape == S.shape
def test_max_truncation_error(dtype, num_charges):
np.random.seed(10)
R = 2
D = 30
charges = [
BaseCharge(np.random.randint(-5, 6, (D, num_charges)),
charge_types=[U1Charge] * num_charges) for n in range(R)
]
flows = [True] * R
random_matrix = BlockSparseTensor.random(
[Index(charges[n], flows[n]) for n in range(R)], dtype=dtype)
U, S, V = bs.svd(random_matrix, full_matrices=False)
svals = np.array(range(1, len(S.data) + 1)).astype(np.float64)
S.data = svals[::-1]
val = U @ bs.diag(S) @ V
trunc = 8
mask = np.sqrt(np.cumsum(np.square(svals))) >= trunc
_, S2, _, _ = decompositions.svd(bs, val, 1, max_truncation_error=trunc)
np.testing.assert_allclose(S2.data, svals[mask][::-1])
