!   E04DGA Example Program Text
!   Mark 27.3 Release. NAG Copyright 2021.
    Module e04dgae_mod

!     E04DGA 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                           :: objfun
!     .. Parameters ..
      Integer, Parameter, Public       :: lcwsav = 1, liwsav = 610,            &
                                          llwsav = 120, lrwsav = 475, nin = 5, &
                                          nout = 6
    Contains
      Subroutine objfun(mode,n,x,objf,objgrd,nstate,iuser,ruser)
!       Routine to evaluate F(x) and its 1st derivatives.

!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: objf
        Integer, Intent (Inout)        :: mode
        Integer, Intent (In)           :: n, nstate
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: objgrd(n)
        Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
        Real (Kind=nag_wp), Intent (In) :: x(n)
        Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
        Real (Kind=nag_wp)             :: expx1, x1, x2
!       .. Intrinsic Procedures ..
        Intrinsic                      :: exp
!       .. Executable Statements ..
        x1 = x(1)
        x2 = x(2)
        expx1 = exp(x1)
        objf = expx1*(4.0_nag_wp*x1**2+2.0_nag_wp*x2**2+4.0_nag_wp*x1*x2+      &
          2.0_nag_wp*x2+1.0_nag_wp)

        If (mode==2) Then
          objgrd(1:n) = (/4.0_nag_wp*expx1*(2.0_nag_wp*x1+x2)+objf,            &
            2.0_nag_wp*expx1*(2.0_nag_wp*x2+2.0_nag_wp*x1+1.0_nag_wp)/)
        End If

        Return

      End Subroutine objfun
    End Module e04dgae_mod
    Program e04dgae

!     E04DGA Example Main Program

!     .. Use Statements ..
      Use e04dgae_mod, Only: lcwsav, liwsav, llwsav, lrwsav, nin, nout, objfun
      Use nag_library, Only: e04dga, e04wbf, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: objf
      Integer                          :: i, ifail, iter, n
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: objgrd(:), work(:), x(:)
      Real (Kind=nag_wp)               :: rwsav(lrwsav), user(1)
      Integer                          :: iuser(1), iwsav(liwsav)
      Integer, Allocatable             :: iwork(:)
      Logical                          :: lwsav(llwsav)
      Character (80)                   :: cwsav(lcwsav)
!     .. Executable Statements ..
      Write (nout,*) 'E04DGA Example Program Results'

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

      Read (nin,*) n
      Allocate (iwork(n+1),objgrd(n),x(n),work(13*n))

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

!     Initialise E04DGA

      ifail = 0
      Call e04wbf('E04DGA',cwsav,lcwsav,lwsav,llwsav,iwsav,liwsav,rwsav,       &
        lrwsav,ifail)

!     Solve the problem

      ifail = -1
      Call e04dga(n,objfun,iter,objf,objgrd,x,iwork,work,iuser,user,lwsav,     &
        iwsav,rwsav,ifail)

      Select Case (ifail)
      Case (0:8)
        Write (nout,*)
        Write (nout,99999)
        Write (nout,*)

        Do i = 1, n
          Write (nout,99998) i, x(i), objgrd(i)
        End Do

        Write (nout,*)
        Write (nout,*)
        Write (nout,99997) objf
      End Select

99999 Format (1X,'Variable',10X,'Value',8X,'Gradient value')
99998 Format (1X,'Varbl',1X,I3,4X,1P,G15.7,4X,1P,G9.1)
99997 Format (1X,'Final objective value = ',G15.7)
    End Program e04dgae