! F12AAF Example Program Text ! Mark 24 Release. NAG Copyright 2012. Module f12aafe_mod ! F12AAF Example Program Module: ! Parameters and User-defined Routines ! .. Use Statements .. Use nag_library, Only: nag_wp ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: imon = 0, ipoint = 0, nin = 5, & nout = 6 Contains Subroutine tv(nx,x,y) ! Compute the matrix vector multiplication y<---T*x where T is a nx ! by nx tridiagonal matrix with constant diagonals (DD, DL and DU). ! .. Parameters .. Real (Kind=nag_wp), Parameter :: half = 0.5_nag_wp Real (Kind=nag_wp), Parameter :: rho = 100.0_nag_wp ! .. Scalar Arguments .. Integer, Intent (In) :: nx ! .. Array Arguments .. Real (Kind=nag_wp), Intent (In) :: x(nx) Real (Kind=nag_wp), Intent (Out) :: y(nx) ! .. Local Scalars .. Real (Kind=nag_wp) :: dd, dl, du, nx1, nx2 Integer :: j ! .. Intrinsic Procedures .. Intrinsic :: real ! .. Executable Statements .. nx1 = real(nx+1,kind=nag_wp) nx2 = nx1*nx1 dd = 4.0_nag_wp*nx2 dl = -nx2 - half*rho*nx1 du = -nx2 + half*rho*nx1 y(1) = dd*x(1) + du*x(2) Do j = 2, nx - 1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) End Do y(nx) = dl*x(nx-1) + dd*x(nx) Return End Subroutine tv Subroutine av(nx,v,w) ! .. Use Statements .. Use nag_library, Only: daxpy ! .. Scalar Arguments .. Integer, Intent (In) :: nx ! .. Array Arguments .. Real (Kind=nag_wp), Intent (In) :: v(nx*nx) Real (Kind=nag_wp), Intent (Out) :: w(nx*nx) ! .. Local Scalars .. Real (Kind=nag_wp) :: nx2 Integer :: j, lo ! .. Intrinsic Procedures .. Intrinsic :: real ! .. Executable Statements .. nx2 = -real((nx+1)*(nx+1),kind=nag_wp) Call tv(nx,v(1),w(1)) ! The NAG name equivalent of daxpy is f06ecf Call daxpy(nx,nx2,v(nx+1),1,w(1),1) Do j = 2, nx - 1 lo = (j-1)*nx Call tv(nx,v(lo+1),w(lo+1)) Call daxpy(nx,nx2,v(lo-nx+1),1,w(lo+1),1) Call daxpy(nx,nx2,v(lo+nx+1),1,w(lo+1),1) End Do lo = (nx-1)*nx Call tv(nx,v(lo+1),w(lo+1)) Call daxpy(nx,nx2,v(lo-nx+1),1,w(lo+1),1) Return End Subroutine av End Module f12aafe_mod Program f12aafe ! F12AAF Example Main Program ! .. Use Statements .. Use nag_library, Only: dnrm2, f12aaf, f12abf, f12acf, f12adf, f12aef, & nag_wp Use f12aafe_mod, Only: av, imon, ipoint, nin, nout ! .. Implicit None Statement .. Implicit None ! .. Local Scalars .. Real (Kind=nag_wp) :: sigmai, sigmar Integer :: i, ifail, ifail1, irevcm, lcomm, & ldv, licomm, n, nconv, ncv, nev, & niter, nshift, nx ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: ax(:), comm(:), d(:,:), mx(:), & resid(:), v(:,:), x(:) Integer, Allocatable :: icomm(:) ! .. Executable Statements .. Write (nout,*) 'F12AAF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) Read (nin,*) nx, nev, ncv n = nx*nx ldv = n lcomm = 3*n + 3*ncv*ncv + 6*ncv + 60 licomm = 140 Allocate (ax(n),comm(lcomm),d(ncv,3),mx(n),resid(n),v(ldv,ncv),x(n), & icomm(licomm)) ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call f12aaf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail) ! Set the region of the spectrum that is required. ifail = 0 Call f12adf('SMALLEST MAG',icomm,comm,ifail) If (ipoint/=0) Then ! Use pointers to workspace in calculating matrix vector products ! rather than interfacing through the array X. ifail = 0 Call f12adf('POINTERS=YES',icomm,comm,ifail) End If irevcm = 0 ifail = -1 loop: Do Call f12abf(irevcm,resid,v,ldv,x,mx,nshift,comm,icomm,ifail) If (irevcm/=5) Then If (irevcm==-1 .Or. irevcm==1) Then ! Perform matrix vector multiplication y <--- Op*x If (ipoint==0) Then Call av(nx,x,ax) x(1:n) = ax(1:n) Else Call av(nx,comm(icomm(1)),comm(icomm(2))) End If Else If (irevcm==4 .And. imon/=0) Then ! Set IMON=1 to output monitoring information. Call f12aef(niter,nconv,d,d(1,2),d(1,3),icomm,comm) ! The NAG name equivalent of dnrm2 is f06ejf Write (6,99999) niter, nconv, dnrm2(nev,d(1,3),1) End If Else Exit loop End If End Do loop If (ifail==0) Then ! Post-Process using F12ACF to compute eigenvalues and ! (by default) the corresponding eigenvectors. ifail1 = 0 Call f12acf(nconv,d,d(1,2),v,ldv,sigmar,sigmai,resid,v,ldv,comm,icomm, & ifail1) Write (nout,99998) nconv Do i = 1, nconv Write (nout,99997) i, d(i,1), d(i,2) End Do End If 99999 Format (1X,'Iteration',1X,I3,', No. converged =',1X,I3,', norm o', & 'f estimates =',E16.8) 99998 Format (1X/' The ',I4,' Ritz values of smallest magnitude are:'/) 99997 Format (1X,I8,5X,'( ',F12.4,' , ',F12.4,' )') End Program f12aafe