! F12FBF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE f12fbfe_mod ! F12FBF 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 :: one = 1.0_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, licomm = 140, nin = 5, & nout = 6 CONTAINS SUBROUTINE av(m,n,x,w) ! Computes w <- A*x. ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: m, n ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: w(m) REAL (KIND=nag_wp), INTENT (IN) :: x(n) ! .. Local Scalars .. REAL (KIND=nag_wp) :: h, k, s, t INTEGER :: i, j ! .. Intrinsic Functions .. INTRINSIC real ! .. Executable Statements .. h = one/real(m+1,kind=nag_wp) k = one/real(n+1,kind=nag_wp) w(1:m) = zero t = zero DO j = 1, n t = t + k s = zero DO i = 1, j s = s + h w(i) = w(i) + k*s*(t-one)*x(j) END DO DO i = j + 1, m s = s + h w(i) = w(i) + k*t*(s-one)*x(j) END DO END DO RETURN END SUBROUTINE av SUBROUTINE atv(m,n,w,y) ! Computes y <- A'*w. ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: m, n ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: w(m) REAL (KIND=nag_wp), INTENT (OUT) :: y(n) ! .. Local Scalars .. REAL (KIND=nag_wp) :: h, k, s, t INTEGER :: i, j ! .. Intrinsic Functions .. INTRINSIC real ! .. Executable Statements .. h = one/real(m+1,kind=nag_wp) k = one/real(n+1,kind=nag_wp) y(1:n) = zero t = zero DO j = 1, n t = t + k s = zero DO i = 1, j s = s + h y(j) = y(j) + k*s*(t-one)*w(i) END DO DO i = j + 1, m s = s + h y(j) = y(j) + k*t*(s-one)*w(i) END DO END DO RETURN END SUBROUTINE atv END MODULE f12fbfe_mod PROGRAM f12fbfe ! F12FBF Example Main Program ! .. Use Statements .. USE f12fbfe_mod, ONLY : nout ! .. Implicit None Statement .. IMPLICIT NONE ! .. Executable Statements .. WRITE (nout,*) 'F12FBF Example Program Results' CALL ex1 CALL ex2 CONTAINS SUBROUTINE ex1 ! .. Use Statements .. USE nag_library, ONLY : dgttrf, dgttrs, dnrm2, f12faf, f12fbf, & f12fcf, f12fdf, f12fef USE f12fbfe_mod, ONLY : imon, licomm, nag_wp, nin, one, two, zero ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. REAL (KIND=nag_wp) :: h2, 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,*) WRITE (nout,*) 'F12FBF Example 1' WRITE (nout,*) FLUSH (nout) ! Skip heading in data file READ (nin,*) READ (nin,*) READ (nin,*) n, nev, ncv ldv = n lcomm = 3*n + ncv*ncv + 8*ncv + 60 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) ! Set the region of the spectrum that is required. CALL f12fdf('LARGEST MAGNITUDE',icomm,comm,ifail) ! Use the Shifted Inverse mode. CALL f12fdf('SHIFTED INVERSE',icomm,comm,ifail) h2 = one/real((n+1)*(n+1),kind=nag_wp) sigma = zero ad(1:n) = two/h2 - sigma adl(1:n) = -one/h2 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 .OR. irevcm==1) THEN ! Perform matrix vector multiplication ! y <--- inv[A-sigma*I]*x ! The NAG name equivalent of dgttrs is f07cef CALL dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,x,n,info) 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) FLUSH (nout) END IF END DO REVCM IF (ifail==0) THEN ! Post-Process using F12FCF to compute eigenvalues/vectors. 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 DEALLOCATE (ad,adl,adu,adu2,comm,d,mx,resid,v,x,ipiv) RETURN 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 SUBROUTINE ex1 SUBROUTINE ex2 ! .. Use Statements .. USE nag_library, ONLY : daxpy, dnrm2, dscal, f12faf, f12fbf, f12fcf, & x04caf USE f12fbfe_mod, ONLY : atv, av, licomm, nag_wp, nin, one ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. REAL (KIND=nag_wp) :: sigma, temp INTEGER :: ifail, ifail1, irevcm, j, & lcomm, ldu, ldv, m, n, nconv, & ncv, nev, nshift ! .. Local Arrays .. REAL (KIND=nag_wp), ALLOCATABLE :: ax(:), comm(:), d(:,:), & mx(:), resid(:), u(:,:), & v(:,:), x(:) INTEGER :: icomm(licomm) ! .. Intrinsic Functions .. INTRINSIC sqrt ! .. Executable Statements .. WRITE (nout,*) WRITE (nout,*) 'F12FBF Example 2' WRITE (nout,*) FLUSH (nout) ! Skip heading in data file READ (nin,*) READ (nin,*) m, n, nev, ncv ldu = m ldv = n lcomm = 3*n + ncv*ncv + 8*ncv + 60 ALLOCATE (ax(m),comm(lcomm),d(ncv,2),mx(m),resid(n),u(ldu,nev), & v(ldv,ncv),x(m)) ! Initialize for problem. ifail = 0 CALL f12faf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail) ! Main reverse communication loop. 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 .OR. irevcm==1) THEN ! Perform the operation X <- A'AX CALL av(m,n,x,ax) CALL atv(m,n,ax,x) END IF END DO REVCM IF (ifail==0) THEN ! Post-Process using F12FCF. ! Computed singular values may be extracted. ! Singular vectors may also be computed now if desired. ifail1 = 0 CALL f12fcf(nconv,d,v,ldv,sigma,resid,v,ldv,comm,icomm,ifail1) ! Singular values (squared) are returned in the first column ! of D and the corresponding right singular vectors are ! returned in the first NEV columns of V. DO j = 1, nconv d(j,1) = sqrt(d(j,1)) ! Compute the left singular vectors from the formula ! u = Av/sigma/norm(Av). CALL av(m,n,v(1,j),ax) u(1:m,j) = ax(1:m) ! The NAG name equivalent of dnrm2 is f06ejf temp = one/dnrm2(m,u(1,j),1) ! The NAG name equivalent of dscal is f06edf CALL dscal(m,temp,u(1,j),1) ! Compute the residual norm ||A*v - sigma*u|| for the nconv ! accurately computed singular values and vectors. ! Store the result in 2nd column of array D. ! The NAG name equivalent of daxpy is f06ecf CALL daxpy(m,-d(j,1),u(1,j),1,ax,1) d(j,2) = dnrm2(m,ax,1) END DO ! Print computed residuals CALL x04caf('G','N',nconv,2,d,ncv, & ' Singular values and direct residuals',ifail1) END IF DEALLOCATE (ax,comm,d,mx,resid,u,v,x) RETURN END SUBROUTINE ex2 END PROGRAM f12fbfe