! E04YBF Example Program Text ! Mark 24 Release. NAG Copyright 2012. Module e04ybfe_mod ! E04YBF 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, mdec = 15, ndec = 3, & nin = 5, nout = 6 Integer, Parameter :: lb = ndec*(ndec+1)/2 Integer, Parameter :: ldfjac = mdec Integer, Parameter :: & lw = 5*ndec + mdec + mdec*ndec + ndec*(ndec-1)/2 ! .. Local Arrays .. Real (Kind=nag_wp) :: t(mdec,ndec), y(mdec) Contains Subroutine lsqfun(iflag,m,n,xc,fvec,fjac,ldfjac,iw,liw,w,lw) ! Routine to evaluate the residuals and their 1st derivatives ! .. 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) = 1.0E0_nag_wp dummy = -1.0E0_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) ! .. 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) = 0.0E0_nag_wp b(2) = 0.0E0_nag_wp sum22 = 0.0E0_nag_wp sum32 = 0.0E0_nag_wp sum33 = 0.0E0_nag_wp Do i = 1, m dummy = 2.0E0_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) = 0.0E0_nag_wp b(5) = sum32 b(6) = sum33 Return End Subroutine lsqhes End Module e04ybfe_mod Program e04ybfe ! E04YBF Example Main Program ! .. Use Statements .. Use nag_library, Only: e04yaf, e04ybf, nag_wp Use e04ybfe_mod, Only: lb, ldfjac, liw, lsqfun, lsqhes, lw, mdec, ndec, & nin, nout, t, y ! .. Implicit None Statement .. Implicit None ! .. Local Scalars .. Integer :: i, ifail, k, m, n ! .. Local Arrays .. Real (Kind=nag_wp) :: b(lb), fjac(ldfjac,ndec), & fvec(mdec), w(lw), x(ndec) Integer :: iw(liw) ! .. Executable Statements .. Write (nout,*) 'E04YBF Example Program Results' ! Skip heading in data file Read (nin,*) m = mdec n = ndec ! Observations of TJ (J = 1, 2, ..., n) are held in T(I, J) ! (I = 1, 2, ..., m) Do i = 1, m Read (nin,*) y(i), t(i,1:n) End Do ! Set up an arbitrary point at which to check the derivatives x(1:n) = (/0.19E0_nag_wp,-1.34E0_nag_wp,0.88E0_nag_wp/) ! Check the 1st derivatives ifail = 0 Call e04yaf(m,n,lsqfun,x,fvec,fjac,ldfjac,iw,liw,w,lw,ifail) Write (nout,*) Write (nout,*) 'The test point is' Write (nout,99999) x(1:n) ! Check the evaluation of B ifail = -1 Call e04ybf(m,n,lsqfun,lsqhes,x,fvec,fjac,ldfjac,b,lb,iw,liw,w,lw,ifail) If (ifail>=0 .And. ifail/=1) Then Select Case (ifail) Case (0) Write (nout,*) Write (nout,*) 'The matrix B is consistent with 1st derivatives' Case (2) Write (nout,*) Write (nout,*) 'Probable error in calculation of the matrix B' End Select Write (nout,*) Write (nout,*) 'At the test point, LSQFUN gives' Write (nout,*) Write (nout,*) ' Residuals 1st derivatives' Write (nout,99998)(fvec(i),fjac(i,1:n),i=1,m) Write (nout,*) Write (nout,*) 'and LSQHES gives the lower triangle of the matrix B' Write (nout,*) k = 1 Do i = 1, n Write (nout,99998) b(k:(k+i-1)) k = k + i End Do End If 99999 Format (1X,4F10.5) 99998 Format (1X,1P,4E15.3) End Program e04ybfe