dfnrmd Subroutine

subroutine dfnrmd( &
   neq, y, t, ydot, r, cj, tscale, wt, &
   res, ires, rnorm, rwm, iwm, rpar, ipar)
!! This routine calculates the scaled preconditioned norm of the nonlinear function used
!! in the nonlinear iteration for obtaining consistent initial conditions. Specifically,
!! it calculates the weighted root-mean-square norm of the vector:
!!
!! $$  r = J^{-1} G(t,y,\dot{y}) $$
!!
!! where \(J\) is the Jacobian matrix and \(G\) is the DAE equation vector.

   use daskr_kinds, only: rk, zero
   use daskr
   implicit none

   integer, intent(in) :: neq
      !! Problem size.
   real(rk), intent(in) :: y(neq)
      !! Solution vector.
   real(rk), intent(in) :: t
      !! Independent variable.
   real(rk), intent(in) :: ydot(neq)
      !! Derivative of solution vector.
   real(rk), intent(out) :: r(neq)
      !! Result vector.
   real(rk), intent(in) :: cj
      !! Scalar used in forming the system Jacobian.
   real(rk), intent(in) :: tscale ! @todo: what is "t?
      !! Scale factor in `t`; used for stopping tests if nonzero.
   real(rk), intent(inout) :: wt(neq)
      !! Scaling factors.
   procedure(res_t) :: res
      !! User-defined residuals routine.
   integer, intent(out) :: ires
      !! Error flag from `res`.
   real(rk), intent(out) :: rnorm
      !! Weighted root-mean-square norm of `r`.
   real(rk), intent(inout) :: rwm(*)
      !! Real workspace for the linear system solver.
   integer, intent(inout) :: iwm(*)
      !! Integer workspace for the linear system solver.
   real(rk), intent(inout) :: rpar(*)
      !! User real workspace.
   integer, intent(inout) :: ipar(*)
      !! User integer workspace.

   real(rk), external :: ddwnrm ! @todo: remove this once inside module

   ! Call RES routine.
   ires = 0
   call res(t, y, ydot, cj, r, ires, rpar, ipar)
   if (ires .lt. 0) return

   ! Apply inverse of Jacobian to vector R.
   call dslvd(neq, r, rwm, iwm)

   ! Calculate norm of R.
   rnorm = ddwnrm(neq, r, wt, rpar, ipar)
   if (tscale .gt. zero) rnorm = rnorm*tscale*abs(cj)

end subroutine dfnrmd