banps Subroutine

   subroutine banps(neq, t, y, yprime, savr, wk, cj, wght, wp, iwp, b, eplin, ier, rpar, ipar)
   !! This subroutine uses the factors produced by [[banja]] to solve linear systems \(P x = b\)
   !! for the banded preconditioner \(P\), given a vector \(b\). It calls the LINPACK routine
   !! [[DGBSL]] for this.
      integer, intent(in) :: neq
        !! Problem size.
      real(rk), intent(in) :: t
        !! Independent variable (not used).
      real(rk), intent(in) :: y(*)
        !! Current dependent variables (not used).
      real(rk), intent(in) :: yprime(*)
        !! Current derivatives of dependent variables (not used).
      real(rk), intent(in) :: savr(*)
        !! Current residual evaluated at `(t, y, yprime)` (not used).
      real(rk), intent(in) :: wk(*)
        !! Real work space of length `neq` (not used).
      real(rk), intent(in) :: cj
        !! Scalar proportional to `1/h` (not used).
      real(rk), intent(in) :: wght(*)
        !! Error weights for computing norms (not used).
      real(rk), intent(inout) :: wp(*)
        !! Real work array containing the LU decomposition of P.
      integer, intent(inout) :: iwp(*)
        !! Integer array containing matrix pivot information.
      real(rk), intent(inout) :: b(*)
        !! Right-hand side vector on input; solution on output.
      real(rk), intent(in) :: eplin
        !! Tolerance for linear system (not used).
      integer, intent(inout) :: ier
        !! Output error flag (not used; assumed 0 on input).
      real(rk), intent(inout) :: rpar(*)
        !! Real array used for communication between the calling program and external user
        !! routines (not used).
      integer, intent(inout) :: ipar(*)
        !! Integer array used for communication between the calling program and external user
        !! routines (not used). `ipar(1)` and `ipar(2)` must contain `ml` and `mu`, respectively.

      external :: dgbsl
      integer :: meband, ml, mu

      ml = ipar(1)
      mu = ipar(2)
      meband = 2*ml + mu + 1
      call dgbsl(wp, meband, neq, ml, mu, iwp, b, 0)

   end subroutine banps