! D02TZF Example Program Text ! Mark 24 Release. NAG Copyright 2012. Module d02tzfe_mod ! D02TZF Example Program Module: ! Parameters and User-defined Routines ! .. Use Statements .. Use nag_library, Only: nag_wp ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: mmax = 2, neq = 1, nin = 5, & nlbc = 1, nout = 6, nrbc = 1 ! .. Local Scalars .. Real (Kind=nag_wp) :: alpha, beta, eps ! .. Local Arrays .. Integer :: m(1) = (/2/) Contains Subroutine ffun(x,y,neq,m,f) ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: x Integer, Intent (In) :: neq ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Out) :: f(neq) Real (Kind=nag_wp), Intent (In) :: y(neq,0:*) Integer, Intent (In) :: m(neq) ! .. Executable Statements .. f(1) = (y(1,0)-y(1,0)*y(1,1))/eps Return End Subroutine ffun Subroutine fjac(x,y,neq,m,dfdy) ! .. Use Statements .. Use nag_library, Only: x02ajf ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: x Integer, Intent (In) :: neq ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Inout) :: dfdy(neq,neq,0:*) Real (Kind=nag_wp), Intent (In) :: y(neq,0:*) Integer, Intent (In) :: m(neq) ! .. Local Scalars .. Real (Kind=nag_wp) :: epsh, fac, ptrb Integer :: i, j, k ! .. Local Arrays .. Real (Kind=nag_wp) :: f1(1), f2(1), yp(1,0:3) ! .. Intrinsic Procedures .. Intrinsic :: abs, max, sqrt ! .. Executable Statements .. epsh = 100.0_nag_wp*x02ajf() fac = sqrt(x02ajf()) Do i = 1, neq Do j = 0, m(i) - 1 yp(i,j) = y(i,j) End Do End Do Do i = 1, neq Do j = 0, m(i) - 1 ptrb = max(epsh,fac*abs(y(i,j))) yp(i,j) = y(i,j) + ptrb Call ffun(x,yp,neq,m,f1) yp(i,j) = y(i,j) - ptrb Call ffun(x,yp,neq,m,f2) Do k = 1, neq dfdy(k,i,j) = 0.5_nag_wp*(f1(k)-f2(k))/ptrb End Do yp(i,j) = y(i,j) End Do End Do Return End Subroutine fjac Subroutine gafun(ya,neq,m,nlbc,ga) ! .. Scalar Arguments .. Integer, Intent (In) :: neq, nlbc ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Out) :: ga(nlbc) Real (Kind=nag_wp), Intent (In) :: ya(neq,0:*) Integer, Intent (In) :: m(neq) ! .. Executable Statements .. ga(1) = ya(1,0) - alpha Return End Subroutine gafun Subroutine gbfun(yb,neq,m,nrbc,gb) ! .. Scalar Arguments .. Integer, Intent (In) :: neq, nrbc ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Out) :: gb(nrbc) Real (Kind=nag_wp), Intent (In) :: yb(neq,0:*) Integer, Intent (In) :: m(neq) ! .. Executable Statements .. gb(1) = yb(1,0) - beta Return End Subroutine gbfun Subroutine gajac(ya,neq,m,nlbc,dgady) ! .. Parameters .. Real (Kind=nag_wp), Parameter :: one = 1.0_nag_wp ! .. Scalar Arguments .. Integer, Intent (In) :: neq, nlbc ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Inout) :: dgady(nlbc,neq,0:*) Real (Kind=nag_wp), Intent (In) :: ya(neq,0:*) Integer, Intent (In) :: m(neq) ! .. Executable Statements .. dgady(1,1,0) = one Return End Subroutine gajac Subroutine gbjac(yb,neq,m,nrbc,dgbdy) ! .. Parameters .. Real (Kind=nag_wp), Parameter :: one = 1.0_nag_wp ! .. Scalar Arguments .. Integer, Intent (In) :: neq, nrbc ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Inout) :: dgbdy(nrbc,neq,0:*) Real (Kind=nag_wp), Intent (In) :: yb(neq,0:*) Integer, Intent (In) :: m(neq) ! .. Executable Statements .. dgbdy(1,1,0) = one Return End Subroutine gbjac Subroutine guess(x,neq,m,y,dym) ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: x Integer, Intent (In) :: neq ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Out) :: dym(neq) Real (Kind=nag_wp), Intent (Inout) :: y(neq,0:*) Integer, Intent (In) :: m(neq) ! .. Executable Statements .. y(1,0) = alpha + (beta-alpha)*x y(1,1) = (beta-alpha) dym(1) = 0.0_nag_wp Return End Subroutine guess End Module d02tzfe_mod Program d02tzfe ! D02TZF Example Main Program ! .. Use Statements .. Use nag_library, Only: d02tkf, d02tvf, d02txf, d02tyf, d02tzf, nag_wp Use d02tzfe_mod, Only: alpha, beta, eps, ffun, fjac, gafun, gajac, & gbfun, gbjac, guess, m, mmax, neq, nin, nlbc, & nout, nrbc ! .. Implicit None Statement .. Implicit None ! .. Local Scalars .. Real (Kind=nag_wp) :: ermx Integer :: i, iermx, ifail, ijermx, j, & liwork, lrwork, mxmesh, ncol, & nmesh Logical :: failed ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: mesh(:), rwork(:), tol(:), y(:,:) Integer, Allocatable :: ipmesh(:), iwork(:) ! .. Executable Statements .. Write (nout,*) 'D02TZF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) Read (nin,*) ncol, nmesh, mxmesh liwork = mxmesh*(11*neq+6) lrwork = mxmesh*(109*neq**2+78*neq+7) Allocate (mesh(mxmesh),tol(neq),rwork(lrwork),y(neq,0:mmax-1), & ipmesh(mxmesh),iwork(liwork)) Read (nin,*) alpha, beta, eps Read (nin,*) mesh(1:nmesh) Read (nin,*) ipmesh(1:nmesh) Read (nin,*) tol(1:neq) ! Initialize ifail = 0 Call d02tvf(neq,m,nlbc,nrbc,ncol,tol,mxmesh,nmesh,mesh,ipmesh,rwork, & lrwork,iwork,liwork,ifail) eps = 0.1_nag_wp*eps contn: Do j = 1, 2 Write (nout,99997) tol(1), eps ! Solve ifail = -1 Call d02tkf(ffun,fjac,gafun,gbfun,gajac,gbjac,guess,rwork,iwork,ifail) failed = ifail /= 0 ! Extract mesh. ifail = -1 Call d02tzf(mxmesh,nmesh,mesh,ipmesh,ermx,iermx,ijermx,rwork,iwork, & ifail) ! Print mesh statistics. Write (nout,99996) nmesh, ermx, iermx, ijermx If (failed) Exit contn ! Print solution at every second point on final mesh. Write (nout,99999) Do i = 1, nmesh, 2 ifail = -1 Call d02tyf(mesh(i),y,neq,mmax,rwork,iwork,ifail) Write (nout,99998) mesh(i), y(1,0), y(1,1) End Do If (j==1) Then ! Halve final mesh for new initial mesh and set up for continuation. nmesh = (nmesh+1)/2 ifail = 0 Call d02txf(mxmesh,nmesh,mesh,ipmesh,rwork,iwork,ifail) ! Reduce continuation parameter. eps = 0.1_nag_wp*eps End If End Do contn 99999 Format (/' Solution and derivative at every second point:'/ & ' x u u''') 99998 Format (' ',F8.4,2F11.5) 99997 Format (//' Tolerance = ',E8.1,' EPS = ',E10.3) 99996 Format (/' Used a mesh of ',I4,' points'/' Maximum error = ',E10.2, & ' in interval ',I4,' for component ',I4) End Program d02tzfe