!   E04UQA Example Program Text
!   Mark 26 Release. NAG Copyright 2016.

    Module e04uqae_mod

!     E04UQA 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                           :: confun, objfun
!     .. Parameters ..
      Real (Kind=nag_wp), Parameter, Public :: one = 1.0_nag_wp
      Real (Kind=nag_wp), Parameter, Public :: zero = 0.0_nag_wp
      Integer, Parameter, Public       :: inc1 = 1, iset = 1, lcwsav = 1,      &
                                          liwsav = 610, llwsav = 120,          &
                                          lrwsav = 475, nin = 5, ninopt = 7,   &
                                          nout = 6
    Contains
      Subroutine objfun(mode,m,n,ldfj,needfi,x,f,fjac,nstate,iuser,ruser)
!       Routine to evaluate the subfunctions and their 1st derivatives.

!       .. Parameters ..
        Real (Kind=nag_wp), Parameter  :: a(44) = (/8.0_nag_wp,8.0_nag_wp,     &
                                          10.0_nag_wp,10.0_nag_wp,10.0_nag_wp, &
                                          10.0_nag_wp,12.0_nag_wp,12.0_nag_wp, &
                                          12.0_nag_wp,12.0_nag_wp,14.0_nag_wp, &
                                          14.0_nag_wp,14.0_nag_wp,16.0_nag_wp, &
                                          16.0_nag_wp,16.0_nag_wp,18.0_nag_wp, &
                                          18.0_nag_wp,20.0_nag_wp,20.0_nag_wp, &
                                          20.0_nag_wp,22.0_nag_wp,22.0_nag_wp, &
                                          22.0_nag_wp,24.0_nag_wp,24.0_nag_wp, &
                                          24.0_nag_wp,26.0_nag_wp,26.0_nag_wp, &
                                          26.0_nag_wp,28.0_nag_wp,28.0_nag_wp, &
                                          30.0_nag_wp,30.0_nag_wp,30.0_nag_wp, &
                                          32.0_nag_wp,32.0_nag_wp,34.0_nag_wp, &
                                          36.0_nag_wp,36.0_nag_wp,38.0_nag_wp, &
                                          38.0_nag_wp,40.0_nag_wp,             &
                                          42.0_nag_wp/)
!       .. Scalar Arguments ..
        Integer, Intent (In)           :: ldfj, m, n, needfi, nstate
        Integer, Intent (Inout)        :: mode
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: f(m)
        Real (Kind=nag_wp), Intent (Inout) :: fjac(ldfj,n), ruser(*)
        Real (Kind=nag_wp), Intent (In) :: x(n)
        Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
        Real (Kind=nag_wp)             :: ai, temp, x1, x2
        Integer                        :: i
        Logical                        :: mode02, mode12
!       .. Intrinsic Procedures ..
        Intrinsic                      :: exp
!       .. Executable Statements ..
        x1 = x(1)
        x2 = x(2)

        mode02 = (mode==0 .Or. mode==2)
        mode12 = (mode==1 .Or. mode==2)

loop:   Do i = 1, m

          If (needfi==i) Then
            f(i) = x1 + (0.49_nag_wp-x1)*exp(-x2*(a(i)-8.0_nag_wp))
            Exit loop
          End If

          ai = a(i)
          temp = exp(-x2*(ai-8.0_nag_wp))

          If (mode02) Then
            f(i) = x1 + (0.49_nag_wp-x1)*temp
          End If

          If (mode12) Then
            fjac(i,1) = one - temp
            fjac(i,2) = -(0.49_nag_wp-x1)*(ai-8.0_nag_wp)*temp
          End If

        End Do loop

        Return

      End Subroutine objfun
      Subroutine confun(mode,ncnln,n,ldcj,needc,x,c,cjac,nstate,iuser,ruser)
!       Routine to evaluate the nonlinear constraint and its 1st
!       derivatives.

!       .. Scalar Arguments ..
        Integer, Intent (In)           :: ldcj, n, ncnln, nstate
        Integer, Intent (Inout)        :: mode
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: c(ncnln)
        Real (Kind=nag_wp), Intent (Inout) :: cjac(ldcj,n), ruser(*)
        Real (Kind=nag_wp), Intent (In) :: x(n)
        Integer, Intent (Inout)        :: iuser(*)
        Integer, Intent (In)           :: needc(ncnln)
!       .. Executable Statements ..
        If (nstate==1) Then

!         First call to CONFUN.  Set all Jacobian elements to zero.
!         Note that this will only work when 'Derivative Level = 3'
!         (the default; see Section 11.2).

          cjac(1:ncnln,1:n) = zero
        End If

        If (needc(1)>0) Then

          If (mode==0 .Or. mode==2) Then
            c(1) = -0.09_nag_wp - x(1)*x(2) + 0.49_nag_wp*x(2)
          End If

          If (mode==1 .Or. mode==2) Then
            cjac(1,1) = -x(2)
            cjac(1,2) = -x(1) + 0.49_nag_wp
          End If

        End If

        Return

      End Subroutine confun
    End Module e04uqae_mod
    Program e04uqae

!     E04UQA Example Main Program

!     .. Use Statements ..
      Use nag_library, Only: dgemv, e04uqa, e04ura, e04usa, e04wbf, nag_wp,    &
                             x04abf, x04acf, x04baf
      Use e04uqae_mod, Only: confun, inc1, iset, lcwsav, liwsav, llwsav,       &
                             lrwsav, nin, ninopt, nout, objfun, one, zero
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Character (*), Parameter         :: fname = 'e04uqae.opt'
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: objf
      Integer                          :: i, ifail, inform, iter, j, lda,      &
                                          ldcj, ldfj, ldr, liwork, lwork, m,   &
                                          mode, n, nclin, ncnln, outchn, sda,  &
                                          sdcjac
      Character (80)                   :: rec
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), bl(:), bu(:), c(:),          &
                                          cjac(:,:), clamda(:), f(:),          &
                                          fjac(:,:), r(:,:), work(:), x(:),    &
                                          y(:)
      Real (Kind=nag_wp)               :: rwsav(lrwsav), user(1)
      Integer, Allocatable             :: istate(:), iwork(:)
      Integer                          :: iuser(1), iwsav(liwsav)
      Logical                          :: lwsav(llwsav)
      Character (80)                   :: cwsav(lcwsav)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max
!     .. Executable Statements ..
      Write (rec,99991) 'E04UQA Example Program Results'
      Call x04baf(nout,rec)

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

      Read (nin,*) m, n
      Read (nin,*) nclin, ncnln
      liwork = 3*n + nclin + 2*ncnln
      lda = max(1,nclin)

      If (nclin>0) Then
        sda = n
      Else
        sda = 1
      End If

      ldcj = max(1,ncnln)

      If (ncnln>0) Then
        sdcjac = n
      Else
        sdcjac = 1
      End If

      ldfj = m
      ldr = n

      If (ncnln==0 .And. nclin>0) Then
        lwork = 20*n + m*(n+3) + 2*n**2 + 11*nclin
      Else If (ncnln>0 .And. nclin>=0) Then
        lwork = 20*n + m*(n+3) + 2*n**2 + 11*nclin + n*nclin + 2*n*ncnln +     &
          21*ncnln
      Else
        lwork = 20*n + m*(n+3)
      End If

      Allocate (istate(n+nclin+ncnln),iwork(liwork),a(lda,sda),                &
        bl(n+nclin+ncnln),bu(n+nclin+ncnln),y(m),c(max(1,                      &
        ncnln)),cjac(ldcj,sdcjac),f(m),fjac(ldfj,n),clamda(n+nclin+ncnln),     &
        r(ldr,n),x(n),work(lwork))

      If (nclin>0) Then
        Read (nin,*)(a(i,1:sda),i=1,nclin)
      End If

      Read (nin,*) y(1:m)
      Read (nin,*) bl(1:(n+nclin+ncnln))
      Read (nin,*) bu(1:(n+nclin+ncnln))
      Read (nin,*) x(1:n)

!     Set the unit number for advisory messages to OUTCHN

      outchn = nout
      Call x04abf(iset,outchn)

!     Initialise E04USA

      ifail = 0
      Call e04wbf('E04USA',cwsav,lcwsav,lwsav,llwsav,iwsav,liwsav,rwsav,       &
        lrwsav,ifail)

!     Set two options using E04URF

      Call e04ura(' Infinite Bound Size = 1.0D+25 ',lwsav,iwsav,rwsav,inform)

      If (inform==0) Then

        Call e04ura(' Verify Level = -1 ',lwsav,iwsav,rwsav,inform)

      End If

      If (inform/=0) Then
        Write (rec,99992) 'E04URA terminated with INFORM = ', inform
        Call x04baf(nout,rec)
        Go To 100
      End If

!     Open the options file for reading

      mode = 0

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

!     Read the options file for the remaining options

      Call e04uqa(ninopt,lwsav,iwsav,rwsav,inform)

      If (inform/=0) Then
        Write (rec,99992) 'E04UQA terminated with INFORM = ', inform
        Call x04baf(nout,rec)
        Go To 100
      End If

!     Solve the problem

      ifail = -1
      Call e04usa(m,n,nclin,ncnln,lda,ldcj,ldfj,ldr,a,bl,bu,y,confun,objfun,   &
        iter,istate,c,cjac,f,fjac,clamda,objf,r,x,iwork,liwork,work,lwork,     &
        iuser,user,lwsav,iwsav,rwsav,ifail)

      Select Case (ifail)
      Case (0:8)
        Write (rec,'()')
        Call x04baf(nout,rec)
        Write (rec,99999)
        Call x04baf(nout,rec)
        Write (rec,'()')
        Call x04baf(nout,rec)

        Do i = 1, n
          Write (rec,99998) i, istate(i), x(i), clamda(i)
          Call x04baf(nout,rec)
        End Do

        If (nclin>0) Then

!         A*x --> work
!         The NAG name equivalent of dgemv is f06paf
          Call dgemv('N',nclin,n,one,a,lda,x,inc1,zero,work,inc1)

          Write (rec,'()')
          Call x04baf(nout,rec)
          Write (rec,'()')
          Call x04baf(nout,rec)
          Write (rec,99997)
          Call x04baf(nout,rec)
          Write (rec,'()')
          Call x04baf(nout,rec)

          Do i = n + 1, n + nclin
            j = i - n
            Write (rec,99996) j, istate(i), work(j), clamda(i)
            Call x04baf(nout,rec)
          End Do

        End If

        If (ncnln>0) Then
          Write (rec,'()')
          Call x04baf(nout,rec)
          Write (rec,'()')
          Call x04baf(nout,rec)
          Write (rec,99995)
          Call x04baf(nout,rec)
          Write (rec,'()')
          Call x04baf(nout,rec)

          Do i = n + nclin + 1, n + nclin + ncnln
            j = i - n - nclin
            Write (rec,99994) j, istate(i), c(j), clamda(i)
            Call x04baf(nout,rec)
          End Do

        End If

        Write (rec,'()')
        Call x04baf(nout,rec)
        Write (rec,'()')
        Call x04baf(nout,rec)
        Write (rec,99993) objf
        Call x04baf(nout,rec)
      End Select

100   Continue

99999 Format (1X,'Varbl',2X,'Istate',3X,'Value',9X,'Lagr Mult')
99998 Format (1X,'V',2(1X,I3),4X,1P,G14.6,2X,1P,G12.4)
99997 Format (1X,'L Con',2X,'Istate',3X,'Value',9X,'Lagr Mult')
99996 Format (1X,'L',2(1X,I3),4X,1P,G14.6,2X,1P,G12.4)
99995 Format (1X,'N Con',2X,'Istate',3X,'Value',9X,'Lagr Mult')
99994 Format (1X,'N',2(1X,I3),4X,1P,G14.6,2X,1P,G12.4)
99993 Format (1X,'Final objective value = ',G15.7)
99992 Format (1X,A,I5)
99991 Format (1X,A)
    End Program e04uqae