! E04KDF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE e04kdfe_mod ! E04KDF Example Program Module: ! Parameters and User-defined Routines ! .. Use Statements .. USE nag_library, ONLY : nag_wp ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. INTEGER, PARAMETER :: liw = 2, n = 4, nout = 6 INTEGER, PARAMETER :: lh = n*(n-1)/2 INTEGER, PARAMETER :: lw = 7*n + n*(n-1)/2 CONTAINS SUBROUTINE funct(iflag,n,xc,fc,gc,iw,liw,w,lw) ! Routine to evaluate objective function and its 1st derivatives. ! A global variable could be updated here to count the number of ! calls of FUNCT with IFLAG = 1 (since NF in MONIT only counts ! calls with IFLAG = 2) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: fc INTEGER, INTENT (INOUT) :: iflag INTEGER, INTENT (IN) :: liw, lw, n ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: gc(n) REAL (KIND=nag_wp), INTENT (INOUT) :: w(lw) REAL (KIND=nag_wp), INTENT (IN) :: xc(n) INTEGER, INTENT (INOUT) :: iw(liw) ! .. Executable Statements .. IF (iflag/=1) THEN fc = (xc(1)+10.0_nag_wp*xc(2))**2 + 5.0_nag_wp*(xc(3)-xc(4))**2 + & (xc(2)-2.0_nag_wp*xc(3))**4 + 10.0_nag_wp*(xc(1)-xc(4))**4 END IF gc(1) = 2.0_nag_wp*(xc(1)+10.0_nag_wp*xc(2)) + & 40.0_nag_wp*(xc(1)-xc(4))**3 gc(2) = 20.0_nag_wp*(xc(1)+10.0_nag_wp*xc(2)) + & 4.0_nag_wp*(xc(2)-2.0_nag_wp*xc(3))**3 gc(3) = 10.0_nag_wp*(xc(3)-xc(4)) - 8.0_nag_wp*(xc(2)-2.0_nag_wp*xc( & 3))**3 gc(4) = 10.0_nag_wp*(xc(4)-xc(3)) - 40.0_nag_wp*(xc(1)-xc(4))**3 RETURN END SUBROUTINE funct SUBROUTINE monit(n,xc,fc,gc,istate,gpjnrm,cond,posdef,niter,nf,iw,liw, & w,lw) ! Monitoring routine ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: cond, fc, gpjnrm INTEGER, INTENT (IN) :: liw, lw, n, nf, niter LOGICAL, INTENT (IN) :: posdef ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: gc(n), xc(n) REAL (KIND=nag_wp), INTENT (INOUT) :: w(lw) INTEGER, INTENT (IN) :: istate(n) INTEGER, INTENT (INOUT) :: iw(liw) ! .. Local Scalars .. INTEGER :: isj, j ! .. Executable Statements .. WRITE (nout,*) WRITE (nout,*) ' Itn Fn evals Fn value' // & ' Norm of proj gradient' WRITE (nout,99999) niter, nf, fc, gpjnrm WRITE (nout,*) WRITE (nout,*) & ' J X(J) G(J) Status' DO j = 1, n isj = istate(j) SELECT CASE (isj) CASE (1:) WRITE (nout,99998) j, xc(j), gc(j), ' Free' CASE (-1) WRITE (nout,99998) j, xc(j), gc(j), ' Upper Bound' CASE (-2) WRITE (nout,99998) j, xc(j), gc(j), ' Lower Bound' CASE (-3) WRITE (nout,99998) j, xc(j), gc(j), ' Constant' END SELECT END DO IF (cond/=0.0_nag_wp) THEN IF (cond>1.0E6_nag_wp) THEN WRITE (nout,*) WRITE (nout,*) 'Estimated condition number of projected & &Hessian is more than 1.0E+6' ELSE WRITE (nout,*) WRITE (nout,99997) & 'Estimated condition number of projected Hessian = ', cond END IF IF ( .NOT. posdef) THEN WRITE (nout,*) WRITE (nout,*) & 'Projected Hessian matrix is not positive definite' END IF END IF RETURN 99999 FORMAT (1X,I3,6X,I5,2(6X,1P,E20.4)) 99998 FORMAT (1X,I2,1X,1P,2E20.4,A) 99997 FORMAT (1X,A,1P,E10.2) END SUBROUTINE monit END MODULE e04kdfe_mod PROGRAM e04kdfe ! E04KDF Example Main Program ! .. Use Statements .. USE nag_library, ONLY : e04hcf, e04kdf USE e04kdfe_mod, ONLY : funct, lh, liw, lw, monit, n, nag_wp, nout ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. REAL (KIND=nag_wp) :: delta, eta, f, stepmx, xtol INTEGER :: ibound, ifail, iprint, maxcal ! .. Local Arrays .. REAL (KIND=nag_wp) :: bl(n), bu(n), g(n), hesd(n), & hesl(lh), w(lw), x(n) INTEGER :: istate(n), iw(liw) ! .. Executable Statements .. WRITE (nout,*) 'E04KDF Example Program Results' FLUSH (nout) ! Check FUNCT by calling E04HCF at an arbitrary point. Since E04HCF ! only checks the derivatives calculated when IFLAG = 2, a separate ! program should be run before using E04HCF or E04KDF to check that ! FUNCT gives the same values for the GC(J) when IFLAG is set to 1 ! as when IFLAG is set to 2. x(1:n) = (/ 1.46_nag_wp, -0.82_nag_wp, 0.57_nag_wp, 1.21_nag_wp/) ifail = 0 CALL e04hcf(n,funct,x,f,g,iw,liw,w,lw,ifail) ! Continue setting parameters for E04KDF ! Set IPRINT to 1 to obtain output from MONIT at each iteration iprint = -1 maxcal = 50*n eta = 0.5_nag_wp ! Set XTOL and DELTA to zero so that E04KDF will use the default ! values xtol = 0.0_nag_wp delta = 0.0_nag_wp ! We estimate that the minimum will be within 4 units of the ! starting point stepmx = 4.0_nag_wp ibound = 0 ! X(3) is not bounded, so we set BL(3) to a large negative ! number and BU(3) to a large positive number bl(1:n) = (/ 1.0_nag_wp, -2.0_nag_wp, -1.0E6_nag_wp, 1.0_nag_wp/) bu(1:n) = (/ 3.0_nag_wp, 0.0_nag_wp, 1.0E6_nag_wp, 3.0_nag_wp/) ! Set up starting point x(1:n) = (/ 3.0_nag_wp, -1.0_nag_wp, 0.0_nag_wp, 1.0_nag_wp/) ifail = -1 CALL e04kdf(n,funct,monit,iprint,maxcal,eta,xtol,delta,stepmx,ibound, & bl,bu,x,hesl,lh,hesd,istate,f,g,iw,liw,w,lw,ifail) SELECT CASE (ifail) CASE (0,2:) WRITE (nout,*) WRITE (nout,99999) 'Function value on exit is ', f WRITE (nout,99999) 'at the point', x(1:n) WRITE (nout,*) 'The corresponding (machine dependent) gradient is' WRITE (nout,99998) g(1:n) WRITE (nout,99997) 'ISTATE contains', istate(1:n) WRITE (nout,99996) 'and HESD contains', hesd(1:n) END SELECT 99999 FORMAT (1X,A,4F12.4) 99998 FORMAT (24X,1P,4E12.3) 99997 FORMAT (1X,A,4I5) 99996 FORMAT (1X,A,4E12.4) END PROGRAM e04kdfe