diagonalise_tridiagonal Subroutine

    subroutine diagonalise_tridiagonal(this, N, t_calc_eigenvectors)
        type(LanczosCalcType), intent(inout) :: this
        integer, intent(in) :: N
        logical, intent(in) :: t_calc_eigenvectors
        integer :: lwork, info
        real(dp), allocatable :: rwork(:)
        character :: jobz

        lwork = max(1, 3 * N + 1)
        safe_malloc(rwork, (lwork))
        if (t_calc_eigenvectors) then
            jobz = 'V'
        else
            jobz = 'N'
        end if

        if (.not. t_calc_eigenvectors) then
            this%ritz_values_old(1:this%n_states) = this%ritz_values(1:this%n_states)
            this%super%projected_hamil_work(1:N, 1:N) = this%super%projected_hamil(1:N, 1:N)
        end if

        call dsyev( &
            jobz, &
            'U', &
            N, &
            this%super%projected_hamil_work(1:N, 1:N), &
            N, &
            this%ritz_values(1:N), &
            rwork, &
            lwork, &
            info &
            )
        safe_free(rwork)

        if (t_calc_eigenvectors) then
            ! move the eigenvectors out of the working array
#ifdef CMPLX_
            this%T_eigenvectors(1:N, 1:this%n_states) = &
                cmplx(this%super%projected_hamil_work(1:N, 1:this%n_states), kind=dp)
#else
            this%T_eigenvectors(1:N, 1:this%n_states) = &
                this%super%projected_hamil_work(1:N, 1:this%n_states)
#endif
        end if
    end subroutine diagonalise_tridiagonal