! F12ANF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE f12anfe_mod ! F12ANF 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, & licomm = 140, 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. ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. COMPLEX (KIND=nag_wp), PARAMETER :: four = (4.0_nag_wp,0.0_nag_wp) COMPLEX (KIND=nag_wp), PARAMETER :: half = (0.5_nag_wp,0.0_nag_wp) COMPLEX (KIND=nag_wp), PARAMETER :: & rho = (100.0_nag_wp,0.0_nag_wp) ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: nx ! .. Array Arguments .. COMPLEX (KIND=nag_wp), INTENT (IN) :: x(nx) COMPLEX (KIND=nag_wp), INTENT (OUT) :: y(nx) ! .. Local Scalars .. COMPLEX (KIND=nag_wp) :: dd, dl, du, h, h2 INTEGER :: j ! .. Intrinsic Functions .. INTRINSIC cmplx ! .. Executable Statements .. h = cmplx(nx+1,kind=nag_wp) h2 = h*h dd = four*h2 dl = -h2 - half*rho*h du = -h2 + half*rho*h 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 : zaxpy ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: nx ! .. Array Arguments .. COMPLEX (KIND=nag_wp), INTENT (IN) :: v(nx*nx) COMPLEX (KIND=nag_wp), INTENT (OUT) :: w(nx*nx) ! .. Local Scalars .. COMPLEX (KIND=nag_wp) :: h2 INTEGER :: j, lo ! .. Intrinsic Functions .. INTRINSIC cmplx ! .. Executable Statements .. h2 = cmplx(-(nx+1)*(nx+1),kind=nag_wp) CALL tv(nx,v(1),w(1)) ! The NAG name equivalent of zaxpy is f06gcf CALL zaxpy(nx,h2,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 zaxpy(nx,h2,v(lo-nx+1),1,w(lo+1),1) CALL zaxpy(nx,h2,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 zaxpy(nx,h2,v(lo-nx+1),1,w(lo+1),1) RETURN END SUBROUTINE av END MODULE f12anfe_mod PROGRAM f12anfe ! F12ANF Example Main Program ! .. Use Statements .. USE nag_library, ONLY : dznrm2, f12anf, f12apf, f12aqf, f12arf, f12asf USE f12anfe_mod, ONLY : av, imon, ipoint, licomm, nag_wp, nin, nout ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. COMPLEX (KIND=nag_wp) :: sigma INTEGER :: i, ifail, ifail1, irevcm, lcomm, & ldv, n, nconv, ncv, nev, niter, & nshift, nx ! .. Local Arrays .. COMPLEX (KIND=nag_wp), ALLOCATABLE :: ax(:), comm(:), d(:,:), mx(:), & resid(:), v(:,:), x(:) INTEGER :: icomm(licomm) ! .. Executable Statements .. WRITE (nout,*) 'F12ANF 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 + 5*ncv + 60 ALLOCATE (ax(n),comm(lcomm),d(ncv,2),mx(n),resid(n),v(n,ncv),x(n)) ifail = 0 CALL f12anf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail) IF (ipoint/=0) THEN ! Use pointers to Workspace in calculating matrix vector ! products rather than interfacing through the array X. ifail = 0 CALL f12arf('POINTERS=YES',icomm,comm,ifail) END IF irevcm = 0 ifail = -1 REVCM: DO CALL f12apf(irevcm,resid,v,ldv,x,mx,nshift,comm,icomm,ifail) IF (irevcm==5) THEN EXIT REVCM ELSE 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 ! Output monitoring information. CALL f12asf(niter,nconv,d,d(1,2),icomm,comm) ! The NAG name equivalent of dznrm2 is f06jjf WRITE (6,99999) niter, nconv, dznrm2(nev,d(1,2),1) END IF END DO REVCM IF (ifail==0) THEN ! Post-Process using F12AQF to compute eigenvalues/vectors. ifail1 = 0 CALL f12aqf(nconv,d,v,ldv,sigma,resid,v,ldv,comm,icomm,ifail1) WRITE (nout,99998) nconv WRITE (nout,99997) (i,d(i,1),i=1,nconv) 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 largest magnitude are:'/) 99997 FORMAT (1X,I8,5X,'( ',F12.4,' , ',F12.4,' )') END PROGRAM f12anfe