! F12FDF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE f12fdfe_mod ! F12FDF 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 :: four = 4.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: one = 1.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: six = 6.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: two = 2.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: zero = 0.0_nag_wp INTEGER, PARAMETER :: imon = 0, ipoint = 1, & licomm = 140, nin = 5, nout = 6 CONTAINS SUBROUTINE mv(n,v,w) ! .. Use Statements .. USE nag_library, ONLY : dscal ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: n ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: v(n) REAL (KIND=nag_wp), INTENT (OUT) :: w(n) ! .. Local Scalars .. REAL (KIND=nag_wp) :: h INTEGER :: j ! .. Intrinsic Functions .. INTRINSIC real ! .. Executable Statements .. h = one/(real(n+1,kind=nag_wp)*six) w(1) = four*v(1) + v(2) DO j = 2, n - 1 w(j) = v(j-1) + four*v(j) + v(j+1) END DO j = n w(j) = v(j-1) + four*v(j) ! The NAG name equivalent of dscal is f06edf CALL dscal(n,h,w,1) RETURN END SUBROUTINE mv END MODULE f12fdfe_mod PROGRAM f12fdfe ! F12FDF Example Main Program ! .. Use Statements .. USE nag_library, ONLY : dcopy, dgttrf, dgttrs, dnrm2, f12faf, f12fbf, & f12fcf, f12fdf, f12fef USE f12fdfe_mod, ONLY : four, imon, ipoint, licomm, mv, nag_wp, nin, & nout, one, six, two, zero ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. REAL (KIND=nag_wp) :: h, r1, r2, sigma INTEGER :: ifail, info, irevcm, j, lcomm, & ldv, n, nconv, ncv, nev, niter, & nshift ! .. Local Arrays .. REAL (KIND=nag_wp), ALLOCATABLE :: ad(:), adl(:), adu(:), adu2(:), & comm(:), d(:,:), mx(:), & resid(:), v(:,:), x(:) INTEGER :: icomm(licomm) INTEGER, ALLOCATABLE :: ipiv(:) ! .. Intrinsic Functions .. INTRINSIC real ! .. Executable Statements .. WRITE (nout,*) 'F12FDF Example Program Results' WRITE (nout,*) ! Skip heading in data file READ (nin,*) READ (nin,*) n, nev, ncv lcomm = 3*n + ncv*ncv + 8*ncv + 60 ldv = n ALLOCATE (ad(n),adl(n),adu(n),adu2(n),comm(lcomm),d(ncv,2),mx(n), & resid(n),v(ldv,ncv),x(n),ipiv(n)) ifail = 0 CALL f12faf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail) ! We are solving a generalized problem ifail = 0 CALL f12fdf('GENERALIZED',icomm,comm,ifail) ! Indicate that we are using the shift and invert mode. CALL f12fdf('SHIFTED INVERSE',icomm,comm,ifail) IF (ipoint==1) THEN ! Use pointers to Workspace in calculating matrix vector ! products rather than interfacing through the array X CALL f12fdf('POINTERS=YES',icomm,comm,ifail) END IF h = one/real(n+1,kind=nag_wp) r1 = (four/six)*h r2 = (one/six)*h sigma = zero ad(1:n) = two/h - sigma*r1 adl(1:n) = -one/h - sigma*r2 adu(1:n) = adl(1:n) ! The NAG name equivalent of dgttrf is f07cdf CALL dgttrf(n,adl,ad,adu,adu2,ipiv,info) irevcm = 0 ifail = -1 REVCM: DO CALL f12fbf(irevcm,resid,v,ldv,x,mx,nshift,comm,icomm,ifail) IF (irevcm==5) THEN EXIT REVCM ELSE IF (irevcm==-1) THEN ! Perform y <--- OP*x = inv[A-SIGMA*M]*M*x ! The NAG name equivalent of dgttrs is f07cef IF (ipoint==0) THEN CALL mv(n,x,mx) x(1:n) = mx(1:n) CALL dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,x,n,info) ELSE CALL mv(n,comm(icomm(1)),comm(icomm(2))) CALL dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,comm(icomm(2)),n, & info) END IF ELSE IF (irevcm==1) THEN ! Perform y <-- OP*x = inv[A-sigma*M]*M*x ! The NAG name equivalent of dgttrs is f07cef. ! M*x has been saved in COMM(ICOMM(3)) or MX. IF (ipoint==0) THEN x(1:n) = mx(1:n) CALL dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,x,n,info) ELSE ! The NAG name equivalent of dcopy is f06eff CALL dcopy(n,comm(icomm(3)),1,comm(icomm(2)),1) CALL dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,comm(icomm(2)),n, & info) END IF ELSE IF (irevcm==2) THEN ! Perform y <--- M*x. IF (ipoint==0) THEN CALL mv(n,x,mx) ELSE CALL mv(n,comm(icomm(1)),comm(icomm(2))) END IF ELSE IF (irevcm==4 .AND. imon/=0) THEN ! Output monitoring information CALL f12fef(niter,nconv,d,d(1,2),icomm,comm) ! The NAG name equivalent of dnrm2 is f06ejf WRITE (6,99999) niter, nconv, dnrm2(nev,d(1,2),1) END IF END DO REVCM IF (ifail==0) THEN ! Post-Process using F12FCF to compute eigenvalues/values. ifail = 0 CALL f12fcf(nconv,d,v,ldv,sigma,resid,v,ldv,comm,icomm,ifail) WRITE (nout,99998) nconv, sigma WRITE (nout,99997) (j,d(j,1),j=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 closest to ',F8.4,' are:'/) 99997 FORMAT (1X,I8,5X,F12.4) END PROGRAM f12fdfe