!   E04NRF Example Program Text
!   Mark 26 Release. NAG Copyright 2016.

    Module e04nrfe_mod

!     E04NRF 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                           :: qphx
!     .. Parameters ..
      Integer, Parameter, Public       :: lencw = 600, leniw = 600,            &
                                          lenrw = 600, nin = 5, ninopt = 7,    &
                                          nout = 6
    Contains
      Subroutine qphx(ncolh,x,hx,nstate,cuser,iuser,ruser)
!       Routine to compute H*x. (In this version of QPHX, the Hessian
!       matrix H is not referenced explicitly.)

!       .. Scalar Arguments ..
        Integer, Intent (In)           :: ncolh, nstate
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: hx(ncolh)
        Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
        Real (Kind=nag_wp), Intent (In) :: x(ncolh)
        Integer, Intent (Inout)        :: iuser(*)
        Character (8), Intent (Inout)  :: cuser(*)
!       .. Executable Statements ..
        hx(1) = 2.0E0_nag_wp*x(1)
        hx(2) = 2.0E0_nag_wp*x(2)
        hx(3) = 2.0E0_nag_wp*(x(3)+x(4))
        hx(4) = hx(3)
        hx(5) = 2.0E0_nag_wp*x(5)
        hx(6) = 2.0E0_nag_wp*(x(6)+x(7))
        hx(7) = hx(6)

        Return

      End Subroutine qphx
    End Module e04nrfe_mod
    Program e04nrfe

!     E04NRF Example Main Program

!     .. Use Statements ..
      Use nag_library, Only: e04npf, e04nqf, e04nrf, e04nsf, e04ntf, e04nuf,   &
                             e04nxf, e04nyf, nag_wp, x04acf
      Use e04nrfe_mod, Only: lencw, leniw, lenrw, nin, ninopt, nout, qphx
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Character (*), Parameter         :: fname = 'e04nrfe.opt'
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: bndinf, featol, obj, objadd, sinf
      Integer                          :: elmode, i, icol, ifail, iobj, jcol,  &
                                          lenc, m, mode, n, ncolh, ne, ninf,   &
                                          nname, ns
      Logical                          :: verbose_output
      Character (8)                    :: prob
      Character (1)                    :: start
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: acol(:), bl(:), bu(:), c(:), pi(:),  &
                                          rc(:), x(:)
      Real (Kind=nag_wp)               :: ruser(1), rw(lenrw)
      Integer, Allocatable             :: helast(:), hs(:), inda(:), loca(:)
      Integer                          :: iuser(1), iw(leniw)
      Character (8)                    :: cuser(1), cw(lencw)
      Character (8), Allocatable       :: names(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max
!     .. Executable Statements ..
      Write (nout,*) 'E04NRF Example Program Results'

!     This program demonstrates the use of routines to set and
!     get values of optional parameters associated with E04NQF.

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

      Read (nin,*) n, m
      Read (nin,*) ne, iobj, ncolh, start, nname

      Allocate (inda(ne),loca(n+1),helast(n+m),hs(n+m),acol(ne),bl(n+m),       &
        bu(n+m),x(n+m),pi(m),rc(n+m),names(nname))

      Read (nin,*) names(1:nname)

!     Read the matrix ACOL from data file. Set up LOCA.

      jcol = 1
      loca(jcol) = 1

      Do i = 1, ne

!       Element ( INDA( I ), ICOL ) is stored in ACOL( I ).

        Read (nin,*) acol(i), inda(i), icol

        If (icol<jcol) Then

!         Elements not ordered by increasing column index.

          Write (nout,99999) 'Element in column', icol,                        &
            ' found after element in column', jcol, '. Problem', ' abandoned.'
          Go To 100
        Else If (icol==jcol+1) Then

!         Index in ACOL of the start of the ICOL-th column equals I.

          loca(icol) = i
          jcol = icol
        Else If (icol>jcol+1) Then

!         Index in ACOL of the start of the ICOL-th column equals I,
!         but columns JCOL+1,JCOL+2,...,ICOL-1 are empty. Set the
!         corresponding elements of LOCA to I.

          loca((jcol+1):icol) = i
          jcol = icol
        End If

      End Do

      loca(n+1) = ne + 1

      If (n>icol) Then

!       Columns N,N-1,...,ICOL+1 are empty. Set the corresponding
!       elements of LOCA accordingly.

        Do i = n, icol + 1, -1
          loca(i) = loca(i+1)
        End Do

      End If

      Read (nin,*) bl(1:(n+m))
      Read (nin,*) bu(1:(n+m))

      If (start=='C') Then
        Read (nin,*) hs(1:n)
      Else If (start=='W') Then
        Read (nin,*) hs(1:(n+m))
      End If

      Read (nin,*) x(1:n)

!     We have no explicit objective vector so set LENC = 0; the
!     objective vector is stored in row IOBJ of ACOL.

      lenc = 0
      Allocate (c(max(1,lenc)))

      objadd = 0.0E0_nag_wp
      prob = ' '

      Write (nout,99998) n, m

!     Call E04NPF to initialize E04NQF.

      ifail = 0
      Call e04npf(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 E04NQF does not print monitoring information.
!       Use E04NTF to set the integer-valued option 'Print file'
!       unit number to get information.
        ifail = 0
        Call e04ntf('Print file',nout,cw,iw,rw,ifail)
      End If

!     Open the options file for reading

      mode = 0

      ifail = 0
      Call x04acf(ninopt,fname,mode,ifail)

!     Use E04NRF to read the options file for the remaining
!     options

      ifail = 0
      Call e04nrf(ninopt,cw,iw,rw,ifail)

      Write (nout,*)

!     Use E04NXF to find the value of integer-valued option
!     'Elastic mode'.

      ifail = 0
      Call e04nxf('Elastic mode',elmode,cw,iw,rw,ifail)

      Write (nout,99997) elmode

!     If Elastic Mode is nonzero, set HELAST.

      If (elmode/=0) Then
        helast(1:(n+m)) = 0
      End If

!     Use E04NUF to set the value of real-valued option
!     'Infinite bound size'.

      bndinf = 1.0E10_nag_wp

      ifail = 0
      Call e04nuf('Infinite bound size',bndinf,cw,iw,rw,ifail)

!     Use E04NYF to find the value of real-valued option
!     'Feasibility tolerance'.

      ifail = 0
      Call e04nyf('Feasibility tolerance',featol,cw,iw,rw,ifail)

      Write (nout,99996) featol

!     Use E04NSF to set the option 'Iterations limit'.

      ifail = 0
      Call e04nsf('Iterations limit 50',cw,iw,rw,ifail)

!     Solve the QP problem.

      ifail = 0
      Call e04nqf(start,qphx,m,n,ne,nname,lenc,ncolh,iobj,objadd,prob,acol,    &
        inda,loca,bl,bu,c,names,helast,hs,x,pi,rc,ns,ninf,sinf,obj,cw,lencw,   &
        iw,leniw,rw,lenrw,cuser,iuser,ruser,ifail)

      Write (nout,*)
      Write (nout,99995) obj
      Write (nout,99994) x(1:n)

100   Continue

99999 Format (1X,A,I5,A,I5,A,A)
99998 Format (1X,/,1X,'QP problem contains ',I3,' variables and ',I3,          &
        ' linear constraints')
99997 Format (1X,'Option ''Elastic mode'' has the value ',I3,'.')
99996 Format (1X,'Option ''Feasibility tolerance'' has the value ',1P,E11.3,   &
        '.')
99995 Format (1X,'Final objective value = ',1P,E11.3)
99994 Format (1X,'Optimal X = ',7F9.2)
    End Program e04nrfe