pytc.ansatz.det.update_inverse_sherman_morrison

pytc.ansatz.det.update_inverse_sherman_morrison(inv, new_row, old_row, row_idx, ratio)

Update the inverse matrix via Sherman-Morrison after a rank-1 row update.

Using S @ inv = I, we have old_row @ inv = e_k^T, so:

inv’ = inv - outer(inv[:, k], new_row @ inv - e_k^T) / ratio

Parameters:

• inv – (n_occ, n_occ) — current S^{-1}

• new_row – (n_occ,)

• old_row – (n_occ,) — unused, kept for API clarity

• row_idx – int

• ratio – scalar — det(S’)/det(S)

Returns:

(n_occ, n_occ)

Return type:

inv’