! E04HEF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE e04hefe_mod ! E04HEF 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 = 1, m = 15, n = 3, nin = 5, & nout = 6, nt = 3 INTEGER, PARAMETER :: lb = n*(n+1)/2 INTEGER, PARAMETER :: ldfjac = m INTEGER, PARAMETER :: ldv = n INTEGER, PARAMETER :: lw = 7*n + m*n + 2*m + n*n ! .. Local Arrays .. REAL (KIND=nag_wp) :: t(m,nt), y(m) CONTAINS SUBROUTINE lsqgrd(m,n,fvec,fjac,ldfjac,g) ! Routine to evaluate gradient of the sum of squares ! .. Use Statements .. USE nag_library, ONLY : dgemv ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: ldfjac, m, n ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: fjac(ldfjac,n), fvec(m) REAL (KIND=nag_wp), INTENT (OUT) :: g(n) ! .. Executable Statements .. ! The NAG name equivalent of dgemv is f06paf CALL dgemv('T',m,n,1.0_nag_wp,fjac,ldfjac,fvec,1,0.0_nag_wp,g,1) g(1:n) = 2.0_nag_wp*g(1:n) RETURN END SUBROUTINE lsqgrd SUBROUTINE lsqfun(iflag,m,n,xc,fvec,fjac,ldfjac,iw,liw,w,lw) ! Routine to evaluate the residuals and their 1st derivatives ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (INOUT) :: iflag INTEGER, INTENT (IN) :: ldfjac, liw, lw, m, n ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (INOUT) :: fjac(ldfjac,n), w(lw) REAL (KIND=nag_wp), INTENT (OUT) :: fvec(m) REAL (KIND=nag_wp), INTENT (IN) :: xc(n) INTEGER, INTENT (INOUT) :: iw(liw) ! .. Local Scalars .. REAL (KIND=nag_wp) :: denom, dummy INTEGER :: i ! .. Executable Statements .. DO i = 1, m denom = xc(2)*t(i,2) + xc(3)*t(i,3) fvec(i) = xc(1) + t(i,1)/denom - y(i) fjac(i,1) = 1.0_nag_wp dummy = -1.0_nag_wp/(denom*denom) fjac(i,2) = t(i,1)*t(i,2)*dummy fjac(i,3) = t(i,1)*t(i,3)*dummy END DO RETURN END SUBROUTINE lsqfun SUBROUTINE lsqhes(iflag,m,n,fvec,xc,b,lb,iw,liw,w,lw) ! Routine to compute the lower triangle of the matrix B ! (stored by rows in the array B) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (INOUT) :: iflag INTEGER, INTENT (IN) :: lb, liw, lw, m, n ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: b(lb) REAL (KIND=nag_wp), INTENT (IN) :: fvec(m), xc(n) REAL (KIND=nag_wp), INTENT (INOUT) :: w(lw) INTEGER, INTENT (INOUT) :: iw(liw) ! .. Local Scalars .. REAL (KIND=nag_wp) :: dummy, sum22, sum32, sum33 INTEGER :: i ! .. Executable Statements .. b(1) = 0.0_nag_wp b(2) = 0.0_nag_wp sum22 = 0.0_nag_wp sum32 = 0.0_nag_wp sum33 = 0.0_nag_wp DO i = 1, m dummy = 2.0_nag_wp*t(i,1)/(xc(2)*t(i,2)+xc(3)*t(i,3))**3 sum22 = sum22 + fvec(i)*dummy*t(i,2)**2 sum32 = sum32 + fvec(i)*dummy*t(i,2)*t(i,3) sum33 = sum33 + fvec(i)*dummy*t(i,3)**2 END DO b(3) = sum22 b(4) = 0.0_nag_wp b(5) = sum32 b(6) = sum33 RETURN END SUBROUTINE lsqhes SUBROUTINE lsqmon(m,n,xc,fvec,fjac,ldfjac,s,igrade,niter,nf,iw,liw,w, & lw) ! Monitoring routine ! .. Use Statements .. USE nag_library, ONLY : f06eaf ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. INTEGER, PARAMETER :: ndec = 3 ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: igrade, ldfjac, liw, lw, m, & n, nf, niter ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: fjac(ldfjac,n), fvec(m), & s(n), xc(n) REAL (KIND=nag_wp), INTENT (INOUT) :: w(lw) INTEGER, INTENT (INOUT) :: iw(liw) ! .. Local Scalars .. REAL (KIND=nag_wp) :: fsumsq, gtg INTEGER :: j ! .. Local Arrays .. REAL (KIND=nag_wp) :: g(ndec) ! .. Executable Statements .. fsumsq = f06eaf(m,fvec,1,fvec,1) CALL lsqgrd(m,n,fvec,fjac,ldfjac,g) gtg = f06eaf(n,g,1,g,1) WRITE (nout,*) WRITE (nout,*) & ' Itns F evals SUMSQ GTG grade' WRITE (nout,99999) niter, nf, fsumsq, gtg, igrade WRITE (nout,*) WRITE (nout,*) & ' X G Singular values' DO j = 1, n WRITE (nout,99998) xc(j), g(j), s(j) END DO RETURN 99999 FORMAT (1X,I4,6X,I5,6X,1P,E13.5,6X,1P,E9.1,6X,I3) 99998 FORMAT (1X,1P,E13.5,10X,1P,E9.1,10X,1P,E9.1) END SUBROUTINE lsqmon END MODULE e04hefe_mod PROGRAM e04hefe ! E04HEF Example Main Program ! .. Use Statements .. USE nag_library, ONLY : e04hef, e04yaf, e04ybf, x02ajf USE e04hefe_mod, ONLY : lb, ldfjac, ldv, liw, lsqfun, lsqgrd, lsqhes, & lsqmon, lw, m, n, nag_wp, nin, nout, nt, t, y ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. REAL (KIND=nag_wp) :: eta, fsumsq, stepmx, xtol INTEGER :: i, ifail, iprint, maxcal, nf, & niter ! .. Local Arrays .. REAL (KIND=nag_wp) :: b(lb), fjac(ldfjac,n), fvec(m), & g(n), s(n), v(ldv,n), w(lw), x(n) INTEGER :: iw(liw) ! .. Intrinsic Functions .. INTRINSIC sqrt ! .. Executable Statements .. WRITE (nout,*) 'E04HEF Example Program Results' ! Skip heading in data file READ (nin,*) ! Observations of TJ (J = 1, 2, ..., nt) are held in T(I, J) ! (I = 1, 2, ..., m) DO i = 1, m READ (nin,*) y(i), t(i,1:nt) END DO ! Set up an arbitrary point at which to check the derivatives x(1:nt) = (/ 0.19_nag_wp, -1.34_nag_wp, 0.88_nag_wp/) ! Check the 1st derivatives ifail = 0 CALL e04yaf(m,n,lsqfun,x,fvec,fjac,ldfjac,iw,liw,w,lw,ifail) ! Check the evaluation of B ifail = 0 CALL e04ybf(m,n,lsqfun,lsqhes,x,fvec,fjac,ldfjac,b,lb,iw,liw,w,lw, & ifail) ! Continue setting parameters for E04HEF ! Set IPRINT to 1 to obtain output from LSQMON at each iteration iprint = -1 maxcal = 50*n eta = 0.9_nag_wp xtol = 10.0_nag_wp*sqrt(x02ajf()) ! We estimate that the minimum will be within 10 units of the ! starting point stepmx = 10.0_nag_wp ! Set up the starting point x(1:nt) = (/ 0.5_nag_wp, 1.0_nag_wp, 1.5_nag_wp/) ifail = -1 CALL e04hef(m,n,lsqfun,lsqhes,lsqmon,iprint,maxcal,eta,xtol,stepmx,x, & fsumsq,fvec,fjac,ldfjac,s,v,ldv,niter,nf,iw,liw,w,lw,ifail) SELECT CASE (ifail) CASE (0,2:) WRITE (nout,*) WRITE (nout,99999) 'On exit, the sum of squares is', fsumsq WRITE (nout,99999) 'at the point', x(1:n) CALL lsqgrd(m,n,fvec,fjac,ldfjac,g) WRITE (nout,99998) 'The corresponding gradient is', g(1:n) WRITE (nout,*) ' (machine dependent)' WRITE (nout,*) 'and the residuals are' WRITE (nout,99997) fvec(1:m) END SELECT 99999 FORMAT (1X,A,3F12.4) 99998 FORMAT (1X,A,1P,3E12.3) 99997 FORMAT (1X,1P,E9.1) END PROGRAM e04hefe