def test_inv_raises():
num_charges = 1
np.random.seed(10)
R = 3
D = 10
charge = BaseCharge(
np.random.randint(-5, 6, (num_charges, D), dtype=np.int16),
charge_types=[U1Charge] * num_charges)
A = BlockSparseTensor.random([Index(charge, False) for n in range(R)],
(-0.5, 0.5))
with pytest.raises(ValueError):
inv(A)
def test_inv(dtype, num_charges):
np.random.seed(10)
R = 2
D = 10
charge = BaseCharge(np.random.randint(-5,
6, (num_charges, D),
dtype=np.int16),
charge_types=[U1Charge] * num_charges)
flows = [True, False]
A = BlockSparseTensor.random([Index(charge, flows[n]) for n in range(R)],
(-0.5, 0.5),
dtype=dtype)
invA = inv(A)
left_eye = invA @ A
blocks, _, shapes = _find_diagonal_sparse_blocks(left_eye.flat_charges,
left_eye.flat_flows, 1)
for n, block in enumerate(blocks):
t = np.reshape(left_eye.data[block], shapes[:, n])
assert np.linalg.norm(t - np.eye(t.shape[0], t.shape[1])) < 1E-12
right_eye = A @ invA
blocks, _, shapes = _find_diagonal_sparse_blocks(right_eye.flat_charges,
right_eye.flat_flows, 1)
for n, block in enumerate(blocks):
t = np.reshape(right_eye.data[block], shapes[:, n])
assert np.linalg.norm(t - np.eye(t.shape[0], t.shape[1])) < 1E-12
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)
