NAG Library Manual, Mark 29.1
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description
!   E05JBF Example Program Text
!   Mark 29.1 Release. NAG Copyright 2023.

    Module e05jbfe_mod

!     E05JBF 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                           :: monit, objfun
!     .. Parameters ..
      Integer, Parameter, Public       :: lcomm = 100, nin = 5, nout = 6
!     .. Local Scalars ..
      Logical, Public, Save            :: plot
    Contains
      Subroutine outbox(boxl,boxu)

!       Displays edges of box with bounds BOXL and BOXU in format suitable
!       for plotting.

!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (In) :: boxl(2), boxu(2)
!       .. Executable Statements ..
        Write (nout,99999) boxl(1), boxl(2)
        Write (nout,99999) boxl(1), boxu(2)
        Write (nout,99998)
        Write (nout,99999) boxl(1), boxl(2)
        Write (nout,99999) boxu(1), boxl(2)
        Write (nout,99998)
        Write (nout,99999) boxl(1), boxu(2)
        Write (nout,99999) boxu(1), boxu(2)
        Write (nout,99998)
        Write (nout,99999) boxu(1), boxl(2)
        Write (nout,99999) boxu(1), boxu(2)
        Write (nout,99998)

        Return

99999   Format (F20.15,1X,F20.15)
99998   Format (A)
      End Subroutine outbox
      Subroutine objfun(n,x,f,nstate,iuser,ruser,inform)

!       Routine to evaluate E05JBF objective function.

!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: f
        Integer, Intent (Out)          :: inform
        Integer, Intent (In)           :: n, nstate
!       .. Array Arguments ..
        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)             :: x1, x2
!       .. Intrinsic Procedures ..
        Intrinsic                      :: exp
!       .. Executable Statements ..

!       This is a two-dimensional objective function.
!       As an example of using the inform mechanism,
!       terminate if any other problem size is supplied.

        If (n/=2) Then
          inform = -1
        Else
          inform = 0

          If (inform>=0) Then

!           If INFORM>=0 then we're prepared to evaluate OBJFUN
!           at the current X

            If (nstate==1) Then

!             This is the first call to OBJFUN

              Write (nout,*)
              Write (nout,99999)
            End If

            x1 = x(1)
            x2 = x(2)

            f = 3.0E0_nag_wp*(1.0E0_nag_wp-x1)**2*exp(-(x1**2)-(x2+            &
              1.0E0_nag_wp)**2) - 1.0E1_nag_wp*(x1/5.0E0_nag_wp-x1**3-x2**5)*  &
              exp(-x1**2-x2**2) - 1.0E0_nag_wp/3.0E0_nag_wp*exp(-(x1+          &
              1.0E0_nag_wp)**2-x2**2)
          End If

        End If

        Return

99999   Format (1X,'(OBJFUN was just called for the first time)')
      End Subroutine objfun
      Subroutine monit(n,ncall,xbest,icount,ninit,list,numpts,initpt,nbaskt,   &
        xbaskt,boxl,boxu,nstate,iuser,ruser,inform)

!       Monitoring routine for E05JBF.

!       .. Scalar Arguments ..
        Integer, Intent (Out)          :: inform
        Integer, Intent (In)           :: n, nbaskt, ncall, ninit, nstate
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (In) :: boxl(n), boxu(n), list(n,ninit),    &
                                          xbaskt(n,nbaskt), xbest(n)
        Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
        Integer, Intent (In)           :: icount(6), initpt(n), numpts(n)
        Integer, Intent (Inout)        :: iuser(*)
!       .. Local Scalars ..
        Integer                        :: i
!       .. Executable Statements ..
        inform = 0

        If (inform>=0) Then

!         We are going to allow the iterations to continue.

          If (nstate==0 .Or. nstate==1) Then

!           When NSTATE==1, MONIT is called for the first time. When
!           NSTATE==0, MONIT is called for the first AND last time.
!           Display a welcome message

            Write (nout,*)
            Write (nout,99999)
            Write (nout,*)

            Write (nout,99998)

            Do i = 1, n
              Write (nout,99997)
              Write (nout,99996) i
              Write (nout,99995) numpts(i)
              Write (nout,99994)
              Write (nout,99993) list(i,1:numpts(i))
              Write (nout,99992) initpt(i)
            End Do

            If (plot .And. (n==2)) Then
              Write (nout,99991)
              Write (nout,*)
            End If

          End If

          If (plot .And. (n==2)) Then

!           Display the coordinates of the edges of the current search
!           box

            Call outbox(boxl,boxu)

          End If

          If (nstate<=0) Then

!           MONIT is called for the last time

            If (plot .And. (n==2)) Then
              Write (nout,99990)
              Write (nout,*)
            End If

            Write (nout,99989) icount(1)
            Write (nout,99988) 20*((ncall+10)/20)
            Write (nout,99987) 15*((icount(2)+7)/15)
            Write (nout,99986) icount(3)
            Write (nout,99985) icount(4)
            Write (nout,99984) icount(5)
            Write (nout,99983) icount(6)
            Write (nout,99982) nbaskt
            Write (nout,99981)

            Do i = 1, n
              Write (nout,99980) i, xbaskt(i,1:nbaskt)
            End Do

            Write (nout,99979)
            Write (nout,99978) xbest(1:n)

            Write (nout,*)
            Write (nout,99977)
            Write (nout,*)
          End If

        End If

        Return

99999   Format (1X,'*** Begin monitoring information ***')
99998   Format (1X,'Values controlling initial splitting of a box:')
99997   Format (1X,'**')
99996   Format (1X,'In dimension ',I5)
99995   Format (1X,'Extent of initialization list in this dimension =',I5)
99994   Format (1X,'Initialization points in this dimension:')
99993   Format (1X,'LIST(I,1:NUMPTS(I)) =',(6F9.5))
99992   Format (1X,'Initial point in this dimension: LIST(I,',I5,')')
99991   Format (1X,'<Begin displaying search boxes>')
99990   Format (1X,'<End displaying search boxes>')
99989   Format (1X,'Total sub-boxes =',I5)
99988   Format (1X,'Total function evaluations (rounded to nearest 20) =',I5)
99987   Format (1X,'Total function evaluations used in local search (rounded', &
          /,3X,'to nearest 15) =',I5)
99986   Format (1X,'Total points used in local search =',I5)
99985   Format (1X,'Total sweeps through levels =',I5)
99984   Format (1X,'Total splits by init. list =',I5)
99983   Format (1X,'Lowest level with nonsplit boxes =',I5)
99982   Format (1X,'Number of candidate minima in the "shopping basket','" =', &
          I5)
99981   Format (1X,'Shopping basket:')
99980   Format (1X,'XBASKT(',I3,',:) =',(6F9.5))
99979   Format (1X,'Best point:')
99978   Format (1X,'XBEST =',(6F9.5))
99977   Format (1X,'*** End monitoring information ***')
      End Subroutine monit
    End Module e05jbfe_mod
    Program e05jbfe

!     E05JBF Example Main Program

!     .. Use Statements ..
      Use e05jbfe_mod, Only: lcomm, monit, nin, nout, objfun, plot
      Use nag_library, Only: e05jaf, e05jbf, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: n = 2
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: obj
      Integer                          :: i, ibound, ifail, iinit, sdlist
!     .. Local Arrays ..
      Real (Kind=nag_wp)               :: bl(n), bu(n), comm(lcomm), ruser(1), &
                                          x(n)
      Real (Kind=nag_wp), Allocatable  :: list(:,:)
      Integer                          :: initpt(n), iuser(1), numpts(n)
!     .. Executable Statements ..
      Write (nout,*) 'E05JBF Example Program Results'

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

      Read (nin,*) sdlist
      Allocate (list(n,sdlist))

      Read (nin,*) ibound

      If (ibound==0) Then

!       Read in the whole of each bound

        Read (nin,*)(bl(i),i=1,n)
        Read (nin,*)(bu(i),i=1,n)
      Else If (ibound==3) Then

!       Bounds are uniform: read in only the first entry of each

        Read (nin,*) bl(1)
        Read (nin,*) bu(1)
      End If

      Read (nin,*) iinit

!     PLOT determines whether MONIT displays information on the
!     current search box:

      Read (nin,*) plot

!     The first argument to E05JAF is a legacy argument and has no
!     significance.

      ifail = 0
      Call e05jaf(0,comm,lcomm,ifail)

!     Solve the problem.

      ifail = 0
      Call e05jbf(n,objfun,ibound,iinit,bl,bu,sdlist,list,numpts,initpt,monit, &
        x,obj,comm,lcomm,iuser,ruser,ifail)

      Write (nout,*)
      Write (nout,99999) obj
      Write (nout,99998)(x(i),i=1,n)

99999 Format (1X,'Final objective value =',F11.5)
99998 Format (1X,'Global optimum X =',2F9.5)
    End Program e05jbfe