apply_transformation Subroutine

    subroutine apply_transformation(nI, orig_orbs, trans_orbs, nJ, n_phase)
        ! apply the transformation encoded in the orig_orbs and trans_orbs
        ! to nI to obtain nJ. nJ will not be sorted except
        ! the phase is present, where the fermionic phase from reshuffling the
        ! orbitals into natural order is also outputted.
        integer, intent(in) :: nI(nel), orig_orbs(nBasis / 2), trans_orbs(nBasis / 2)
        integer, intent(out) :: nJ(nel)
        integer, intent(out), optional :: n_phase
#ifdef DEBUG_
        character(*), parameter :: this_routine = "apply_transformation"
#endif
        integer :: i, pos

        nJ = 0

        do i = 1, nel

            ! i cant use binary search, since orig orbs is not sorted!
!             pos = binary_search_int(orig_orbs, get_spatial(nI(i)))
            pos = stupid_search(orig_orbs, get_spatial(nI(i)))

            ! it has to be found!
            if (pos <= 0) then
                print *, "orig_orbs: ", orig_orbs
                print *, "nI: ", nI
                print *, "spatial: ", get_spatial(nI)
            end if
            ASSERT(pos > 0)

            if (is_beta(nI(i))) then
                nJ(i) = 2 * trans_orbs(pos) - 1
            else
                nJ(i) = 2 * trans_orbs(pos)
            end if

        end do

        if (present(n_phase)) then
            call sort_orbitals(nJ, n_phase)
!             call sort(nJ, par = n_phase)
        end if

    end subroutine apply_transformation