!   E04VHF Example Program Text
!   Mark 26 Release. NAG Copyright 2016.

    Module e04vhfe_mod

!     E04VHF 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                           :: usrfun
!     .. Parameters ..
      Integer, Parameter, Public       :: lencw = 600, leniw = 600,            &
                                          lenrw = 600, nin = 5, nout = 6
    Contains
      Subroutine usrfun(status,n,x,needf,nf,f,needg,leng,g,cuser,iuser,ruser)

!       .. Scalar Arguments ..
        Integer, Intent (In)           :: leng, n, needf, needg, nf
        Integer, Intent (Inout)        :: status
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Inout) :: f(nf), g(leng), ruser(*)
        Real (Kind=nag_wp), Intent (In) :: x(n)
        Integer, Intent (Inout)        :: iuser(*)
        Character (8), Intent (Inout)  :: cuser(*)
!       .. Intrinsic Procedures ..
        Intrinsic                      :: cos, sin
!       .. Executable Statements ..
        If (needf>0) Then

!         The nonlinear components of f_i(x) need to be assigned,
!         for i = 1 to NF

          f(1) = 1000.0E+0_nag_wp*sin(-x(1)-0.25E+0_nag_wp) +                  &
            1000.0E+0_nag_wp*sin(-x(2)-0.25E+0_nag_wp)
          f(2) = 1000.0E+0_nag_wp*sin(x(1)-0.25E+0_nag_wp) +                   &
            1000.0E+0_nag_wp*sin(x(1)-x(2)-0.25E+0_nag_wp)
          f(3) = 1000.0E+0_nag_wp*sin(x(2)-x(1)-0.25E+0_nag_wp) +              &
            1000.0E+0_nag_wp*sin(x(2)-0.25E+0_nag_wp)

!         N.B. in this example there is no need to assign for the wholly
!         linear components f_4(x) and f_5(x).

          f(6) = 1.0E-6_nag_wp*x(3)**3 + 2.0E-6_nag_wp*x(4)**3/3.0E+0_nag_wp
        End If

        If (needg>0) Then

!         The derivatives of the function f_i(x) need to be assigned.
!         G(k) should be set to partial derivative df_i(x)/dx_j where
!         i = IGFUN(k) and j = IGVAR(k), for k = 1 to LENG.

          g(1) = -1000.0E+0_nag_wp*cos(-x(1)-0.25E+0_nag_wp)
          g(2) = -1000.0E+0_nag_wp*cos(-x(2)-0.25E+0_nag_wp)
          g(3) = 1000.0E+0_nag_wp*cos(x(1)-0.25E+0_nag_wp) +                   &
            1000.0E+0_nag_wp*cos(x(1)-x(2)-0.25E+0_nag_wp)
          g(4) = -1000.0E+0_nag_wp*cos(x(1)-x(2)-0.25E+0_nag_wp)
          g(5) = -1000.0E+0_nag_wp*cos(x(2)-x(1)-0.25E+0_nag_wp)
          g(6) = 1000.0E+0_nag_wp*cos(x(2)-x(1)-0.25E+0_nag_wp) +              &
            1000.0E+0_nag_wp*cos(x(2)-0.25E+0_nag_wp)
          g(7) = 3.0E-6_nag_wp*x(3)**2
          g(8) = 2.0E-6_nag_wp*x(4)**2
        End If

        Return

      End Subroutine usrfun
    End Module e04vhfe_mod
    Program e04vhfe

!     E04VHF Example Main Program

!     .. Use Statements ..
      Use nag_library, Only: e04vgf, e04vhf, e04vmf, nag_wp
      Use e04vhfe_mod, Only: lencw, leniw, lenrw, nin, nout, usrfun
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: objadd, sinf
      Integer                          :: i, ifail, lena, leng, n, nea, neg,   &
                                          nf, nfname, ninf, ns, nxname,        &
                                          objrow, start
      Logical                          :: verbose_output
      Character (8)                    :: prob
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:), f(:), flow(:), fmul(:),        &
                                          fupp(:), x(:), xlow(:), xmul(:),     &
                                          xupp(:)
      Real (Kind=nag_wp)               :: ruser(1), rw(lenrw)
      Integer, Allocatable             :: fstate(:), iafun(:), igfun(:),       &
                                          javar(:), jgvar(:), xstate(:)
      Integer                          :: iuser(1), iw(leniw)
      Character (8)                    :: cuser(1), cw(lencw)
      Character (8), Allocatable       :: fnames(:), xnames(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max
!     .. Executable Statements ..
      Write (nout,*) 'E04VHF Example Program Results'

!     Skip heading in data file
      Read (nin,*)

      Read (nin,*) n, nf
      Read (nin,*) nea, neg, objrow, start
      lena = max(1,nea)
      leng = max(1,neg)
      nxname = n
      nfname = nf
      Allocate (iafun(lena),javar(lena),igfun(leng),jgvar(leng),xstate(n),     &
        fstate(nf),a(lena),xlow(n),xupp(n),flow(nf),fupp(nf),x(n),xmul(n),     &
        f(nf),fmul(nf),xnames(nxname),fnames(nfname))

!     Read the variable names

      Read (nin,*) xnames(1:nxname)

!     Read the function names

      Read (nin,*) fnames(1:nfname)

!     Read the sparse matrix A, the linear part of F

      Do i = 1, nea

!       For each element read row, column, A(row,column)

        Read (nin,*) iafun(i), javar(i), a(i)
      End Do

!     Read the structure of sparse matrix G, the nonlinear part of F

      Do i = 1, neg

!       For each element read row, column

        Read (nin,*) igfun(i), jgvar(i)
      End Do

!     Read the lower and upper bounds on the variables

      Do i = 1, n
        Read (nin,*) xlow(i), xupp(i)
      End Do

!     Read the lower and upper bounds on the functions

      Do i = 1, nf
        Read (nin,*) flow(i), fupp(i)
      End Do

!     Initialize X, XSTATE, XMUL, F, FSTATE, FMUL

      Read (nin,*) x(1:n)
      Read (nin,*) xstate(1:n)
      Read (nin,*) xmul(1:n)
      Read (nin,*) f(1:nf)
      Read (nin,*) fstate(1:nf)
      Read (nin,*) fmul(1:nf)

      objadd = 0.0E0_nag_wp
      prob = ' '

      Write (nout,99999) n

!     Call E04VGF to initialize E04VHF.

      ifail = 0
      Call e04vgf(cw,lencw,iw,leniw,rw,lenrw,ifail)

!     Set this to .True. to cause e04nqf to produce intermediate
!     progress output
      verbose_output = .False.

      If (verbose_output) Then
!       By default e04vhf does not print monitoring
!       information. Set the print file unit or the summary
!       file unit to get information.
        ifail = 0
        Call e04vmf('Print file',nout,cw,iw,rw,ifail)
      End If

!     Solve the problem.

      ifail = 0
      Call e04vhf(start,nf,n,nxname,nfname,objadd,objrow,prob,usrfun,iafun,    &
        javar,a,lena,nea,igfun,jgvar,leng,neg,xlow,xupp,xnames,flow,fupp,      &
        fnames,x,xstate,xmul,f,fstate,fmul,ns,ninf,sinf,cw,lencw,iw,leniw,rw,  &
        lenrw,cuser,iuser,ruser,ifail)

      Write (nout,*)
      Write (nout,99998) f(objrow)
      Write (nout,99997) x(1:n)

99999 Format (1X,/,1X,'NLP problem contains ',I3,' variables')
99998 Format (1X,'Final objective value = ',F11.1)
99997 Format (1X,'Optimal X = ',7F10.3)
    End Program e04vhfe