double_factorized_2body

double_factorized_2body(two_body_tensor, tol, max_vecs=None, cholesky=True)

Double-factorized decomposition of a real two-body tensor.

Represents \(h_{pqrs} = \sum_t \sum_{kl} Z^{(t)}_{kl} U^{(t)}_{pk} U^{(t)}_{qk} U^{(t)}_{rl} U^{(t)}_{sl}\), returning a list of \((Z, U)\) terms where each \(Z\) is a real symmetric diagonal Coulomb matrix and each \(U\) is a unitary orbital rotation.

When cholesky is True (the default behavior) the outer factorization uses a modified Cholesky decomposition; otherwise it uses a truncated eigendecomposition.

Parameters:

  • two_body_tensor – the real two-body tensor of shape (norb, norb, norb, norb).

  • tol – the tolerance controlling the truncation error of the decomposition.

  • max_vecs – the maximum number of terms to retain. Defaults to norb * (norb + 1) / 2.

  • cholesky – whether to use the modified Cholesky decomposition (True) or a truncated eigendecomposition (False) for the outer factorization.

Returns:

A list of \((Z, U)\) 2-tuples, where Z is the diagonal Coulomb matrix and U is the orbital rotation.