! E04LBF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE e04lbfe_mod ! E04LBF 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. ! .. 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 .. 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 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 h(iflag,n,xc,fhesl,lh,fhesd,iw,liw,w,lw) ! Routine to evaluate 2nd derivatives ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (INOUT) :: iflag INTEGER, INTENT (IN) :: lh, liw, lw, n ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (INOUT) :: fhesd(n), w(lw) REAL (KIND=nag_wp), INTENT (OUT) :: fhesl(lh) REAL (KIND=nag_wp), INTENT (IN) :: xc(n) INTEGER, INTENT (INOUT) :: iw(liw) ! .. Executable Statements .. fhesd(1) = 2.0_nag_wp + 120.0_nag_wp*(xc(1)-xc(4))**2 fhesd(2) = 200.0_nag_wp + 12.0_nag_wp*(xc(2)-2.0_nag_wp*xc(3))**2 fhesd(3) = 10.0_nag_wp + 48.0_nag_wp*(xc(2)-2.0_nag_wp*xc(3))**2 fhesd(4) = 10.0_nag_wp + 120.0_nag_wp*(xc(1)-xc(4))**2 fhesl(1) = 20.0_nag_wp fhesl(2) = 0.0_nag_wp fhesl(3) = -24.0_nag_wp*(xc(2)-2.0_nag_wp*xc(3))**2 fhesl(4) = -120.0_nag_wp*(xc(1)-xc(4))**2 fhesl(5) = 0.0_nag_wp fhesl(6) = -10.0_nag_wp RETURN END SUBROUTINE h 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 e04lbfe_mod PROGRAM e04lbfe ! E04LBF Example Main Program ! .. Use Statements .. USE nag_library, ONLY : e04hcf, e04hdf, e04lbf USE e04lbfe_mod, ONLY : funct, h, lh, liw, lw, monit, n, nag_wp, nout ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. REAL (KIND=nag_wp) :: eta, f, stepmx, xtol INTEGER :: ibound, ifail, iprint, maxcal, nz ! .. 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) ! .. Intrinsic Functions .. INTRINSIC count ! .. Executable Statements .. WRITE (nout,*) 'E04LBF Example Program Results' FLUSH (nout) ! Set up an arbitrary point at which to check the derivatives x(1:n) = (/ 1.46_nag_wp, -0.82_nag_wp, 0.57_nag_wp, 1.21_nag_wp/) ! Check the 1st derivatives ifail = 0 CALL e04hcf(n,funct,x,f,g,iw,liw,w,lw,ifail) ! Check the 2nd derivatives ifail = 0 CALL e04hdf(n,funct,h,x,g,hesl,lh,hesd,iw,liw,w,lw,ifail) ! Continue setting parameters for E04LBF ! Set IPRINT to 1 to obtain output from MONIT at each iteration iprint = -1 maxcal = 50*n eta = 0.9_nag_wp ! Set XTOL to zero so that E04LBF will use the default tolerance xtol = 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 unconstrained, 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 e04lbf(n,funct,h,monit,iprint,maxcal,eta,xtol,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,99998) 'at the point', x(1:n) WRITE (nout,*) 'The corresponding (machine dependent) gradient is' WRITE (nout,99997) g(1:n) WRITE (nout,99996) 'ISTATE contains', istate(1:n) nz = count(istate(1:n)>0) WRITE (nout,99995) 'and HESD contains', hesd(1:nz) END SELECT 99999 FORMAT (1X,A,F9.4) 99998 FORMAT (1X,A,4F9.4) 99997 FORMAT (23X,1P,4E12.3) 99996 FORMAT (1X,A,4I5) 99995 FORMAT (1X,A,4E12.4) END PROGRAM e04lbfe