construct_matrix_representation Function

    function construct_matrix_representation(states, orig_orbs, trans_orbs) &
        result(matrix)
        ! construct the matrix representation of the symmetry operation
        ! for a given basis. the symmetry operation is encoded in
        ! orig orbs and trans orbs
        integer, intent(in) :: states(:, :), orig_orbs(nBasis / 2), trans_orbs(nBasis / 2)
        integer :: matrix(size(states, 2), size(states, 2))
        integer :: i, j, nJ(nel), phase

        matrix = 0

        do i = 1, size(states, 2)
            do j = 1, size(states, 2)
                call apply_transformation(states(:, j), orig_orbs, trans_orbs, &
                                          nJ, phase)

                if (all(nJ == states(:, i))) then
                    matrix(i, j) = phase
!                     matrix(j,i) = phase
                end if
            end do
        end do

    end function construct_matrix_representation