! D02NEF Example Program Text ! Mark 24 Release. NAG Copyright 2012. Module d02nefe_mod ! D02NEF Example Program Module: ! Parameters and User-defined Routines ! .. Use Statements .. Use nag_library, Only: nag_wp ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Real (Kind=nag_wp), Parameter :: alpha = 0.04_nag_wp Real (Kind=nag_wp), Parameter :: beta = 1.0E4_nag_wp Real (Kind=nag_wp), Parameter :: gamma = 3.0E7_nag_wp Real (Kind=nag_wp), Parameter :: one = 1.0_nag_wp Real (Kind=nag_wp), Parameter :: two = 2.0_nag_wp Integer, Parameter :: ml = 1, mu = 2, neq1 = 3, & neq2 = 1, nin = 5, nout = 6 Contains Subroutine myjac1(neq,ml,mu,t,y,ydot,pd,cj) ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: cj, t Integer, Intent (In) :: ml, mu, neq ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Out) :: pd(2*ml+mu+1,neq) Real (Kind=nag_wp), Intent (In) :: y(neq), ydot(neq) ! .. Local Scalars .. Integer :: md, ms ! .. Executable Statements .. ! Main diagonal pdfull(i,i), i=1,neq md = mu + ml + 1 pd(md,1) = -alpha - cj pd(md,2) = -beta*y(3) - two*gamma*y(2) - cj pd(md,3) = -cj ! 1 Sub-diagonal pdfull(i+1:i), i=1,neq-1 ms = md + 1 pd(ms,1) = alpha pd(ms,2) = two*gamma*y(2) ! First super-diagonal pdfull(i-1,i), i=2, neq ms = md - 1 pd(ms,2) = beta*y(3) pd(ms,3) = -beta*y(2) ! Second super-diagonal pdfull(i-2,i), i=3, neq ms = md - 2 pd(ms,3) = beta*y(2) Return End Subroutine myjac1 Subroutine myjac2(neq,t,y,ydot,pd,cj) ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: cj, t Integer, Intent (In) :: neq ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Out) :: pd(neq*neq) Real (Kind=nag_wp), Intent (In) :: y(neq), ydot(neq) ! .. Intrinsic Procedures .. Intrinsic :: exp ! .. Executable Statements .. pd(1) = -two*y(1) + 0.1E0_nag_wp*t*y(1)*exp(y(1)) Return End Subroutine myjac2 Subroutine res1(neq,t,y,ydot,r,ires,iuser,ruser) ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: t Integer, Intent (Inout) :: ires Integer, Intent (In) :: neq ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Out) :: r(neq) Real (Kind=nag_wp), Intent (Inout) :: ruser(*) Real (Kind=nag_wp), Intent (In) :: y(neq), ydot(neq) Integer, Intent (Inout) :: iuser(*) ! .. Executable Statements .. r(1) = -alpha*y(1) + beta*y(2)*y(3) - ydot(1) r(2) = alpha*y(1) - beta*y(2)*y(3) - gamma*y(2)*y(2) - ydot(2) r(3) = gamma*y(2)*y(2) - ydot(3) Return End Subroutine res1 Subroutine jac1(neq,t,y,ydot,pd,cj,iuser,ruser) ! .. Use Statements .. Use nag_library, Only: d02nez ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: cj, t Integer, Intent (In) :: neq ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Inout) :: pd(*), ruser(*) Real (Kind=nag_wp), Intent (In) :: y(neq), ydot(neq) Integer, Intent (Inout) :: iuser(*) ! .. Local Scalars .. Integer :: ijac, ml, mu ! .. Executable Statements .. ml = iuser(1) mu = iuser(2) ijac = iuser(3) If (ijac==1) Then Call myjac1(neq,ml,mu,t,y,ydot,pd,cj) Else Call d02nez(neq,t,y,ydot,pd,cj,iuser,ruser) End If Return End Subroutine jac1 Subroutine res2(neq,t,y,ydot,r,ires,iuser,ruser) ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: t Integer, Intent (Inout) :: ires Integer, Intent (In) :: neq ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Out) :: r(neq) Real (Kind=nag_wp), Intent (Inout) :: ruser(*) Real (Kind=nag_wp), Intent (In) :: y(neq), ydot(neq) Integer, Intent (Inout) :: iuser(*) ! .. Intrinsic Procedures .. Intrinsic :: exp ! .. Executable Statements .. r(1) = 4.0_nag_wp - y(1)**2 + t*0.1E0_nag_wp*exp(y(1)) Return End Subroutine res2 Subroutine jac2(neq,t,y,ydot,pd,cj,iuser,ruser) ! .. Use Statements .. Use nag_library, Only: d02nez ! .. Scalar Arguments .. Real (Kind=nag_wp), Intent (In) :: cj, t Integer, Intent (In) :: neq ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Inout) :: pd(*), ruser(*) Real (Kind=nag_wp), Intent (In) :: y(neq), ydot(neq) Integer, Intent (Inout) :: iuser(*) ! .. Local Scalars .. Integer :: ijac ! .. Executable Statements .. ijac = iuser(1) If (ijac==1) Then Call myjac2(neq,t,y,ydot,pd,cj) Else Call d02nez(neq,t,y,ydot,pd,cj,iuser,ruser) End If Return End Subroutine jac2 End Module d02nefe_mod Program d02nefe ! D02NEF Example Main Program ! .. Use Statements .. Use d02nefe_mod, Only: nout ! .. Implicit None Statement .. Implicit None ! .. Executable Statements .. Write (nout,*) 'D02NEF Example Program Results' Call ex1 Call ex2 Contains Subroutine ex1 ! .. Use Statements .. Use nag_library, Only: d02mcf, d02mwf, d02nef, d02npf, nag_wp Use d02nefe_mod, Only: jac1, ml, mu, neq1, nin, res1 ! .. Local Scalars .. Real (Kind=nag_wp) :: h0, hmax, t, tout Integer :: i, ifail, ijac, itask, itol, & j, lcom, licom, maxord, neq Character (8) :: jceval ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: atol(:), com(:), rtol(:), & y(:), ydot(:) Real (Kind=nag_wp) :: ruser(1) Integer, Allocatable :: icom(:) Integer :: iuser(3) ! .. Executable Statements .. Write (nout,*) Write (nout,*) 'D02NEF Example 1' ! Skip heading in data file Read (nin,*) Read (nin,*) maxord neq = neq1 lcom = 40 + (maxord+4)*neq + (2*ml+mu+1)*neq + 2*(neq/(ml+mu+1)+1) licom = 50 + neq Allocate (atol(neq),com(lcom),rtol(neq),y(neq),ydot(neq),icom(licom)) Read (nin,*) ijac, itol Read (nin,*) rtol(1:neq) Read (nin,*) atol(1:neq) Read (nin,*) ydot(1:neq) If (ijac==1) Then jceval = 'Analytic' Else jceval = 'Numeric' End If ! Set initial values Read (nin,*) y(1:neq) ! Initialize the problem, specifying that the Jacobian is to be ! evaluated analytically using the provided routine jac. Read (nin,*) hmax, h0 Read (nin,*) t, tout ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call d02mwf(neq,maxord,jceval,hmax,h0,itol,icom,licom,com,lcom,ifail) ! Specify that the Jacobian is banded. ifail = 0 Call d02npf(neq,ml,mu,icom,licom,ifail) ! Use the iuser array to pass the band dimensions through to jac. ! An alternative would be to hard code values for ml and mu in jac. iuser(1) = ml iuser(2) = mu iuser(3) = ijac Write (nout,99999)(i,i=1,neq) Write (nout,99998) t, (y(i),i=1,neq) itask = 0 ! Obtain the solution at 5 equally spaced values of T. loop: Do j = 1, 5 ifail = -1 Call d02nef(neq,t,tout,y,ydot,rtol,atol,itask,res1,jac1,icom,com, & lcom,iuser,ruser,ifail) Write (nout,99998) t, (y(i),i=1,neq) If (ifail/=0) Then Write (nout,99997) ifail Exit loop End If tout = tout + 0.02_nag_wp Call d02mcf(icom) End Do loop Write (nout,*) Write (nout,99996) itask 99999 Format (/1X,' t ',5X,3(' Y(',I1,') ')) 99998 Format (1X,F8.4,3X,3(F12.6)) 99997 Format (1X,' ** D02NEF returned with IFAIL = ',I5) 99996 Format (1X,'The integrator completed task, ITASK = ',I4) End Subroutine ex1 Subroutine ex2 ! .. Use Statements .. Use nag_library, Only: d02mcf, d02mwf, d02nef, nag_wp Use d02nefe_mod, Only: jac2, neq2, nin, res2 ! .. Local Scalars .. Real (Kind=nag_wp) :: h0, hmax, t, tout Integer :: i, ifail, ijac, itask, itol, & j, lcom, licom, maxord, neq Character (8) :: jceval ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: atol(:), com(:), rtol(:), & y(:), ydot(:) Real (Kind=nag_wp) :: ruser(1) Integer, Allocatable :: icom(:) Integer :: iuser(1) ! .. Executable Statements .. Write (nout,*) Write (nout,*) 'D02NEF Example 2' Write (nout,*) Read (nin,*) Read (nin,*) maxord neq = neq2 lcom = 40 + (maxord+4)*neq + neq*neq licom = 50 + neq Allocate (atol(neq),com(lcom),rtol(neq),y(neq),ydot(neq),icom(licom)) Read (nin,*) ijac, itol Read (nin,*) rtol(1:neq) Read (nin,*) atol(1:neq) Read (nin,*) ydot(1:neq) If (ijac==1) Then jceval = 'Analytic' Else jceval = 'Numeric' End If ! Initialize the problem, specifying that the Jacobian is to be ! evaluated analytically using the provided routine jac. Read (nin,*) y(1:neq) Read (nin,*) hmax, h0 Read (nin,*) t, tout ifail = 0 Call d02mwf(neq,maxord,jceval,hmax,h0,itol,icom,licom,com,lcom,ifail) ! Use the iuser array to pass whether numerical or analytic Jacobian ! is to be used. iuser(1) = ijac Write (nout,99999)(i,i=1,neq) Write (nout,99998) t, y(1:neq) itask = 0 ! Obtain the solution at 5 equally spaced values of t. loop: Do j = 1, 5 ifail = -1 Call d02nef(neq,t,tout,y,ydot,rtol,atol,itask,res2,jac2,icom,com, & lcom,iuser,ruser,ifail) Write (nout,99998) t, y(1:neq) If (ifail/=0) Then Write (nout,99997) ifail Exit loop End If tout = tout + 0.2_nag_wp Call d02mcf(icom) End Do loop Write (nout,*) Write (nout,99996) itask 99999 Format (/1X,' t y(',I1,')') 99998 Format (1X,F8.4,3X,3(F12.6)) 99997 Format (1X,' ** D02NEF returned with IFAIL = ',I5) 99996 Format (1X,'The integrator completed task, ITASK = ',I4) End Subroutine ex2 End Program d02nefe