!   D02NCF Example Program Text
!   Mark 26 Release. NAG Copyright 2016.

    Module d02ncfe_mod

!     D02NCF Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
      Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Accessibility Statements ..
      Private
      Public                           :: fcn, jac
!     .. Parameters ..
      Real (Kind=nag_wp), Parameter    :: alpha = 0.04_nag_wp
      Real (Kind=nag_wp), Parameter    :: beta = 1.0E4_nag_wp
      Real (Kind=nag_wp), Parameter    :: gamma = 3.0E7_nag_wp
      Real (Kind=nag_wp), Parameter    :: one = 1.0_nag_wp
      Real (Kind=nag_wp), Parameter    :: two = 2.0_nag_wp
      Integer, Parameter, Public       :: iset = 1, itrace = 0, ml = 1,        &
                                          mu = 2, neq = 3, nin = 5
      Integer, Parameter, Public       :: njcpvt = neq
      Integer, Parameter, Public       :: nout = 6
      Integer, Parameter, Public       :: nrw = 50 + 4*neq
      Integer, Parameter, Public       :: nwkjac = neq*(2*ml+mu+1)
      Integer, Parameter, Public       :: ldysav = neq
    Contains
      Subroutine fcn(neq,t,y,f,ires)

!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (In) :: t
        Integer, Intent (Inout)        :: ires
        Integer, Intent (In)           :: neq
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: f(neq)
        Real (Kind=nag_wp), Intent (In) :: y(neq)
!       .. Executable Statements ..
        f(1) = -alpha*y(1) + beta*y(2)*y(3)
        f(2) = alpha*y(1) - beta*y(2)*y(3) - gamma*y(2)*y(2)
        f(3) = gamma*y(2)*y(2)
        Return
      End Subroutine fcn

      Subroutine jac(neq,t,y,h,d,ml,mu,p)

!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (In) :: d, h, t
        Integer, Intent (In)           :: ml, mu, neq
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Inout) :: p(ml+mu+1,neq)
        Real (Kind=nag_wp), Intent (In) :: y(neq)
!       .. Local Scalars ..
        Real (Kind=nag_wp)             :: hxd
!       .. Executable Statements ..
        hxd = h*d

        p(1,1) = one - hxd*(-alpha)
        p(2,1) = -hxd*(beta*y(3))
        p(3,1) = -hxd*(beta*y(2))

        p(1,2) = -hxd*(alpha)
        p(2,2) = one - hxd*(-beta*y(3)-two*gamma*y(2))
        p(3,2) = -hxd*(-beta*y(2))

        p(1,3) = -hxd*(two*gamma*y(2))
        p(2,3) = one - hxd*(0.0_nag_wp)
        Return
      End Subroutine jac
    End Module d02ncfe_mod

    Program d02ncfe

!     D02NCF Example Main Program

!     .. Use Statements ..
      Use nag_library, Only: d02nby, d02ncf, d02ntf, d02nwf, d02nyf, d02nzf,   &
                             nag_wp, x04abf
      Use d02ncfe_mod, Only: fcn, iset, itrace, jac, ldysav, ml, mu, neq, nin, &
                             njcpvt, nout, nrw, nwkjac
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: h, h0, hmax, hmin, hu, t, tcrit,     &
                                          tcur, tolsf, tout
      Integer                          :: i, ifail, imxer, itask, itol,        &
                                          maxord, maxstp, mxhnil, niter, nje,  &
                                          nq, nqu, nre, nst, outchn, sdysav
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: atol(:), rtol(:), rwork(:),          &
                                          wkjac(:), y(:), ydot(:), ysav(:,:)
      Real (Kind=nag_wp)               :: con(6)
      Integer                          :: inform(23)
      Integer, Allocatable             :: jacpvt(:)
      Logical, Allocatable             :: algequ(:)
!     .. Executable Statements ..
      Write (nout,*) 'D02NCF Example Program Results'
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) maxord, maxstp, mxhnil
      sdysav = maxord + 3
      Allocate (atol(neq),rtol(neq),rwork(nrw),wkjac(nwkjac),y(neq),ydot(neq), &
        ysav(ldysav,sdysav),jacpvt(njcpvt),algequ(neq))
      outchn = nout
      Call x04abf(iset,outchn)

!     Integrate to tout (itask=1 i.e. overshooting and internal interpolation)
!     using the blend method. Default values for the array con are used.
!     Employ scalar relative tolerance and vector absolute tolerance.
!     The Jacobian is evaluated by jac.
!     monitr subroutine replaced by NAG dummy routine D02NBY.

      Read (nin,*) hmin, hmax, h0, tcrit
      Read (nin,*) t, tout
      Read (nin,*) itol
      Read (nin,*) y(1:neq)
      Read (nin,*) rtol(1)
      Read (nin,*) atol(1:neq)
      con(1:6) = 0.0_nag_wp
      itask = 1

!     ifail: behaviour on error exit
!             =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
      ifail = 0
      Call d02nwf(neq,sdysav,maxord,con,tcrit,hmin,hmax,h0,maxstp,mxhnil,      &
        'Average-L2',rwork,ifail)

      ifail = 0
      Call d02ntf(neq,neq,'Analytical',ml,mu,nwkjac,njcpvt,rwork,ifail)

      Write (nout,99993)(i,i=1,neq)
      Write (nout,99999) t, (y(i),i=1,neq)

!     Soft fail and error messages only

      ifail = -1
      Call d02ncf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform,fcn,    &
        ysav,sdysav,jac,wkjac,nwkjac,jacpvt,njcpvt,d02nby,itask,itrace,ifail)

      If (ifail==0) Then
        Write (nout,99999) t, (y(i),i=1,neq)
      Else
        Write (nout,*)
        Write (nout,99998) 'Exit D02NCF with IFAIL = ', ifail, '  and T = ', t
      End If
!     Reset tout and call D02NZF to override internal choice for step size.
!     No changes to other parameters.
      h = 0.7_nag_wp

      ifail = 0
      Call d02nzf(neq,tcrit,h,hmin,hmax,maxstp,mxhnil,rwork,ifail)

      tout = 10.0_nag_wp

      ifail = -1
      Call d02ncf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform,fcn,    &
        ysav,sdysav,jac,wkjac,nwkjac,jacpvt,njcpvt,d02nby,itask,itrace,ifail)

      If (ifail==0) Then
        Write (nout,99999) t, (y(i),i=1,neq)

        ifail = 0
        Call d02nyf(neq,neq,hu,h,tcur,tolsf,rwork,nst,nre,nje,nqu,nq,niter,    &
          imxer,algequ,inform,ifail)

        Write (nout,*)
        Write (nout,99997) hu, h, tcur
        Write (nout,99996) nst, nre, nje
        Write (nout,99995) nqu, nq, niter
        Write (nout,99994) ' Max Err Comp = ', imxer
        Write (nout,*)
      Else
        Write (nout,*)
        Write (nout,99998) 'Exit D02NCF with IFAIL = ', ifail, '  and T = ', t
      End If

99999 Format (1X,F8.3,3(F13.5,2X))
99998 Format (1X,A,I2,A,E12.5)
99997 Format (1X,' HUSED = ',E12.5,'  HNEXT = ',E12.5,'  TCUR = ',E12.5)
99996 Format (1X,' NST = ',I6,'    NRE = ',I6,'    NJE = ',I6)
99995 Format (1X,' NQU = ',I6,'    NQ  = ',I6,'  NITER = ',I6)
99994 Format (1X,A,I4)
99993 Format (/,1X,'    X ',3('         Y(',I1,')  '))
    End Program d02ncfe