!   E04CBF Example Program Text
!   Mark 28.4 Release. NAG Copyright 2022.
    Module e04cbfe_mod

!     E04CBF 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                           :: funct, monit
!     .. Parameters ..
      Integer, Parameter, Public       :: nout = 6
    Contains
      Subroutine funct(n,xc,fc,iuser,ruser)

!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: fc
        Integer, Intent (In)           :: n
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
        Real (Kind=nag_wp), Intent (In) :: xc(n)
        Integer, Intent (Inout)        :: iuser(*)
!       .. Intrinsic Procedures ..
        Intrinsic                      :: exp
!       .. Executable Statements ..
        fc = exp(xc(1))*(4.0_nag_wp*xc(1)*(xc(1)+xc(2))+2.0_nag_wp*xc(2)*(xc(2 &
          )+1.0_nag_wp)+1.0_nag_wp)

        Return

      End Subroutine funct
      Subroutine monit(fmin,fmax,sim,n,ncall,serror,vratio,iuser,ruser)

!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (In) :: fmax, fmin, serror, vratio
        Integer, Intent (In)           :: n, ncall
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
        Real (Kind=nag_wp), Intent (In) :: sim(n+1,n)
        Integer, Intent (Inout)        :: iuser(*)
!       .. Executable Statements ..
        Write (nout,*)
        Write (nout,99999) ncall
        Write (nout,99998) fmin
        Write (nout,99997)
        Write (nout,99996) sim(1:(n+1),1:n)
        Write (nout,99995) serror
        Write (nout,99994) vratio

        Return

99999   Format (1X,'There have been',I5,' function calls')
99998   Format (1X,'The smallest function value is',F10.4)
99997   Format (1X,'The simplex is')
99996   Format (1X,2F10.4)
99995   Format (1X,'The standard deviation in function values at the ',        &
          'vertices of the simplex is',F10.4)
99994   Format (1X,'The linearized volume ratio of the current simplex',       &
          ' to the starting one is',F10.4)
      End Subroutine monit
    End Module e04cbfe_mod
    Program e04cbfe

!     E04CBF Example Main Program

!     .. Use Statements ..
      Use e04cbfe_mod, Only: funct, monit, nout
      Use nag_library, Only: e04cbf, e04cbk, nag_wp, x02ajf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: n = 2
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: f, tolf, tolx
      Integer                          :: ifail, maxcal
      Logical                          :: monitoring
!     .. Local Arrays ..
      Real (Kind=nag_wp)               :: ruser(1), x(n)
      Integer                          :: iuser(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: sqrt
!     .. Executable Statements ..
      Write (nout,*) 'E04CBF Example Program Results'

!     Set MONITORING to .TRUE. to obtain monitoring information

      monitoring = .False.

      x(1:n) = (/-1.0_nag_wp,1.0_nag_wp/)
      tolf = sqrt(x02ajf())
      tolx = sqrt(tolf)
      maxcal = 100

      ifail = 0

      If (.Not. monitoring) Then

        Call e04cbf(n,x,f,tolf,tolx,funct,e04cbk,maxcal,iuser,ruser,ifail)

      Else

        Call e04cbf(n,x,f,tolf,tolx,funct,monit,maxcal,iuser,ruser,ifail)

      End If

      Write (nout,*)
      Write (nout,99999) f
      Write (nout,99998) x(1:n)

99999 Format (1X,'The final function value is',F12.4)
99998 Format (1X,'at the point',2F12.4)
    End Program e04cbfe