!   E04JCF Example Program Text
!   Mark 27.3 Release. NAG Copyright 2021.
    Module e04jcfe_mod

!     E04JCF 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                           :: monfun, objfun
!     .. Parameters ..
      Integer, Parameter, Public       :: nout = 6
    Contains
      Subroutine objfun(n,x,f,iuser,ruser,inform)

!       .. Parameters ..
        Real (Kind=nag_wp), Parameter  :: five = 5.0_nag_wp
        Real (Kind=nag_wp), Parameter  :: ten = 1.0E1_nag_wp
        Real (Kind=nag_wp), Parameter  :: two = 2.0_nag_wp
!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: f
        Integer, Intent (Out)          :: inform
        Integer, Intent (In)           :: n
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
        Real (Kind=nag_wp), Intent (In) :: x(n)
        Integer, Intent (Inout)        :: iuser(*)
!       .. Executable Statements ..
        inform = 0

        f = (x(1)+ten*x(2))**2 + five*(x(3)-x(4))**2 + (x(2)-two*x(3))**4 +    &
          ten*(x(1)-x(4))**4

        Return

      End Subroutine objfun
      Subroutine monfun(n,nf,x,f,rho,iuser,ruser,inform)

!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (In) :: f, rho
        Integer, Intent (Out)          :: inform
        Integer, Intent (In)           :: n, nf
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
        Real (Kind=nag_wp), Intent (In) :: x(n)
        Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
        Logical                        :: verbose_output
!       .. Executable Statements ..
        inform = 0

        Write (nout,Fmt=99999) 'Monitoring: new trust region radius =', rho

!       Set this to .True. to get more detailed output
        verbose_output = .False.

        If (verbose_output) Then
          Write (nout,Fmt=99998) 'Number of function calls =', nf
          Write (nout,Fmt=99997) 'Current function value =', f
          Write (nout,Fmt=99996) 'The corresponding X is:', x(1:n)
        End If

        Return
99999   Format (/,4X,A,1P,E13.3)
99998   Format (4X,A,I16)
99997   Format (4X,A,1P,E12.4)
99996   Format (4X,A,/,(4X,5E12.4))
      End Subroutine monfun
    End Module e04jcfe_mod
    Program e04jcfe

!     Example problem for E04JCF.

!     .. Use Statements ..
      Use e04jcfe_mod, Only: monfun, nout, objfun
      Use nag_library, Only: e04jcf, nag_wp, x02alf
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: f, infbnd, rhobeg, rhoend
      Integer                          :: ifail, maxcal, n, nf, npt
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: bl(:), bu(:), x(:)
      Real (Kind=nag_wp)               :: ruser(1)
      Integer                          :: iuser(1)
!     .. Executable Statements ..
      Write (nout,*) 'E04JCF Example Program Results'

      maxcal = 500
      rhobeg = 1.0E-1_nag_wp
      rhoend = 1.0E-6_nag_wp
      n = 4
      npt = 2*n + 1

!     x(3) is unconstrained, so we're going to set bl(3) to a large
!     negative number and bu(3) to a large positive number.

      infbnd = x02alf()**0.25_nag_wp

      Allocate (bl(n),bu(n),x(n))

      bl(1:n) = (/1.0_nag_wp,-2.0_nag_wp,-infbnd,1.0_nag_wp/)
      bu(1:n) = (/3.0_nag_wp,0.0_nag_wp,infbnd,3.0_nag_wp/)
      x(1:n) = (/3.0_nag_wp,-1.0_nag_wp,0.0_nag_wp,1.0_nag_wp/)

      ifail = -1
      Call e04jcf(objfun,n,npt,x,bl,bu,rhobeg,rhoend,monfun,maxcal,f,nf,iuser, &
        ruser,ifail)

      Select Case (ifail)
      Case (0,2:5)

        If (ifail==0) Then
          Write (nout,Fmt=99999) 'Successful exit from E04JCF.',               &
            'Function value at lowest point found =', f
        Else
          Write (nout,Fmt=99998)                                               &
            'On exit from E04JCF, function value at lowest point found =', f
        End If

        Write (nout,Fmt=99997) 'The corresponding X is:', x(1:n)
      End Select

99999 Format (2(/,1X,A),1P,E13.3)
99998 Format (/,1X,A,1P,E13.3)
99997 Format (1X,A,/,(2X,5E13.3))
    End Program e04jcfe