def tpdm_to_opdm_mapping(dim: int, normalization: Union[float,
int]) -> DualBasis:
"""
Construct the DualBasis for mapping of the tpdm to the opdm
Args:
dim: dimension of the spin-orbital basis.
normalization: Scalar for mapping tpdm to opdm. Generally, this is
1 / (N - 1) where N is the number of electrons.
Returns:
DualBasis for all dim^2
"""
db_basis = DualBasis()
for i in range(dim):
for j in range(i, dim):
dbe = DualBasisElement()
# contract over tpdm terms
for r in range(dim):
# duplicate entries get summed in DualBasisElement
dbe.add_element('cckk', (i, r, j, r), 0.5)
dbe.add_element('cckk', (j, r, i, r), 0.5)
# opdm terms
dbe.add_element('ck', (i, j), -0.5 * normalization)
dbe.add_element('ck', (j, i), -0.5 * normalization)
dbe.simplify()
db_basis += dbe
return db_basis
def test_simplify():
i, j, k, l = 0, 1, 2, 3
names = ['opdm'] * 3 + ['oqdm']
elements = [(i, j), (i, j), (i, l), (l, k)]
coeffs = [1, 1, 0.25, 0.3]
dbe = DualBasisElement(tensor_names=names,
tensor_elements=elements,
tensor_coeffs=coeffs)
dbe.simplify()
assert len(dbe.primal_tensors_names) == 3
assert set(dbe.primal_coeffs) == {2, 0.25, 0.3}
assert set(dbe.primal_tensors_names) == {'opdm', 'oqdm'}
assert set(dbe.primal_elements) == {(0, 1), (0, 3), (3, 2)}