! F12AQF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE f12aqfe_mod ! F12AQF Example Program Module: ! Parameters and User-defined Routines ! .. Use Statements .. USE nag_library, ONLY : nag_wp ! .. 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 :: & one = (1.0E+0_nag_wp,0.0E+0_nag_wp) COMPLEX (KIND=nag_wp), PARAMETER :: two = (2.0_nag_wp,0.0_nag_wp) INTEGER, PARAMETER :: imon = 0, licomm = 140, & nerr = 6, nin = 5, nout = 6 CONTAINS SUBROUTINE av(nx,v,w) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. COMPLEX (KIND=nag_wp), PARAMETER :: rho = (10.0_nag_wp,0.0_nag_wp) ! .. 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) :: dd, dl, du, h, s INTEGER :: j, n ! .. Intrinsic Functions .. INTRINSIC cmplx ! .. Executable Statements .. n = nx*nx h = one/cmplx(n+1,kind=nag_wp) s = rho/two dd = two/h dl = -one/h - s du = -one/h + s w(1) = dd*v(1) + du*v(2) DO j = 2, n - 1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) END DO w(n) = dl*v(n-1) + dd*v(n) RETURN END SUBROUTINE av SUBROUTINE mv(nx,v,w) ! .. Use Statements .. USE nag_library, ONLY : zscal ! .. 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) :: h INTEGER :: j, n ! .. Intrinsic Functions .. INTRINSIC cmplx ! .. Executable Statements .. n = nx*nx w(1) = four*v(1) + one*v(2) DO j = 2, n - 1 w(j) = one*v(j-1) + four*v(j) + one*v(j+1) END DO w(n) = one*v(n-1) + four*v(n) h = one/cmplx(n+1,kind=nag_wp) ! The NAG name equivalent of zscal is f06gdf CALL zscal(n,h,w,1) RETURN END SUBROUTINE mv END MODULE f12aqfe_mod PROGRAM f12aqfe ! F12AQF Example Main Program ! .. Use Statements .. USE nag_library, ONLY : dznrm2, f12anf, f12apf, f12aqf, f12arf, f12asf, & zgttrf, zgttrs USE f12aqfe_mod, ONLY : av, four, imon, licomm, mv, nag_wp, nerr, nin, & nout, one ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. COMPLEX (KIND=nag_wp) :: h, sigma INTEGER :: ifail, ifail1, info, irevcm, j, & lcomm, ldv, n, nconv, ncv, nev, & niter, nshift, nx ! .. Local Arrays .. COMPLEX (KIND=nag_wp), ALLOCATABLE :: comm(:), d(:,:), dd(:), dl(:), & du(:), du2(:), mx(:), resid(:), & v(:,:), x(:) INTEGER :: icomm(licomm) INTEGER, ALLOCATABLE :: ipiv(:) ! .. Intrinsic Functions .. INTRINSIC cmplx ! .. Executable Statements .. WRITE (nout,*) 'F12AQF Example Program Results' WRITE (nout,*) ! Skip heading in data file READ (nin,*) READ (nin,*) nx, nev, ncv n = nx*nx lcomm = 3*n + 3*ncv*ncv + 5*ncv + 60 ldv = n ALLOCATE (comm(lcomm),d(ncv,2),dd(n),dl(n),du(n),du2(n),mx(n),resid(n), & v(ldv,ncv),x(n),ipiv(n)) ifail = 0 CALL f12anf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail) ! Set the mode. ifail = 0 CALL f12arf('REGULAR INVERSE',icomm,comm,ifail) ! Set problem type. CALL f12arf('GENERALIZED',icomm,comm,ifail) ! Use pointers to Workspace rather than interfacing through the array X. CALL f12arf('POINTERS=YES',icomm,comm,ifail) h = one/cmplx(n+1,kind=nag_wp) dl(1:n-1) = h dd(1:n-1) = four*h du(1:n-1) = h dd(n) = four*h ! The NAG name equivalent of zgttrf is f07crf CALL zgttrf(n,dl,dd,du,du2,ipiv,info) IF (info/=0) THEN WRITE (nerr,99999) info GO TO 20 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 y <--- OP*x = inv[M]*A*x | CALL av(nx,comm(icomm(1)),comm(icomm(2))) ! The NAG name equivalent of zgttrs is f07csf CALL zgttrs('N',n,1,dl,dd,du,du2,ipiv,comm(icomm(2)),n,info) IF (info/=0) THEN WRITE (nerr,99998) info EXIT REVCM END IF ELSE IF (irevcm==2) THEN ! Perform y <--- M*x CALL mv(nx,comm(icomm(1)),comm(icomm(2))) 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 (6,99997) niter, nconv, dznrm2(nev,d(1,2),1) END IF END DO REVCM IF (ifail==0 .AND. info==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,99996) nconv WRITE (nout,99995) (j,d(j,1),j=1,nconv) END IF 20 CONTINUE 99999 FORMAT (1X,'** Error status returned by ZGTTRF, INFO =',I12) 99998 FORMAT (1X,'** Error status returned by ZGTTRS, INFO =',I12) 99997 FORMAT (1X,'Iteration',1X,I3,', No. converged =',1X,I3,', norm o', & 'f estimates =',E16.8) 99996 FORMAT (1X/' The ',I4,' Ritz values of largest magnitude are:'/) 99995 FORMAT (1X,I8,5X,'( ',F12.4,' , ',F12.4,' )') END PROGRAM f12aqfe