UMatInd_base Function

    elemental FUNCTION UMatInd_base(I, J, K, L, nBI) result(UMatInd)
        ! Get the index of physical order UMAT element <IJ|KL>.
        ! Indices are internally reordered such that I>K, J>L,(I,K)>(J,L)
        ! Note: (i,k)>(j,l) := (k>l) || ((k==l)&&(i>j))
        ! In:
        !    I,J,K,L: orbital indices. These refer to spin orbitals in
        !      unrestricted calculations and spatial orbitals in restricted
        !      calculations.
        !    nBasis: size of basis. If =0, use nStates instead.
        !    nOccupied: # of occupied orbitals.  If =0, then nOcc is used.
        !    Should only be passed as non-zero during the freezing process.
        INTEGER, intent(in) :: I, J, K, L, nBI
        integer(int64) :: UMatInd
        integer :: A, B

        if (t_non_hermitian_2_body) then
            A = (I - 1) * nBi + K
            B = (J - 1) * nBi + L
        else
            !Combine indices I and K, ensuring I>K
            IF (I > K) THEN
                A = (I * (I - 1)) / 2 + K
            ELSE
                A = (K * (K - 1)) / 2 + I
            END IF

            !Combine indices J and L, ensuring J>L
            IF (J > L) THEN
                B = (J * (J - 1)) / 2 + L
            ELSE
                B = (L * (L - 1)) / 2 + J
            END IF
        end if

        !Combine (IK) and (JL) in a unique way  (k > l or if k = l then i > j)
        IF (A > B) THEN
            UMatInd = (int(A, int64) * int(A - 1, int64)) / 2 + int(B, int64)
        ELSE
            UMatInd = (int(B, int64) * int(B - 1, int64)) / 2 + int(A, int64)
        END IF
#ifdef CMPLX_
        if (.not. tComplexWalkers_RealInts) then
            UMatInd = (UmatInd - 1) * 2 + 1
            !We need to test whether we have swapped i and k or j and l independantly of each other
            !If we have done this, it is one of the 'other' integrals - add one.
            if (((I > K) .and. (J < L)) .or. ((I < K) .and. (J > L))) then
                UMatInd = UMatInd + 1
            end if
        end if
#endif
    END FUNCTION UMatInd_Base