! F12AEF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE f12aefe_mod ! F12AEF 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 :: three = 3.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: two = 2.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: zero = 0.0_nag_wp INTEGER, PARAMETER :: nin = 5, nout = 6 CONTAINS SUBROUTINE mv(n,v) ! Compute the in-place matrix vector multiplication X<---M*X, ! where M is mass matrix formed by using piecewise linear elements ! on [0,1]. ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: n ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (INOUT) :: v(n) ! .. Local Scalars .. REAL (KIND=nag_wp) :: vm1, vv INTEGER :: j ! .. Executable Statements .. vm1 = v(1) v(1) = four*v(1) + v(2) DO j = 2, n - 1 vv = v(j) v(j) = vm1 + four*vv + v(j+1) vm1 = vv END DO v(n) = vm1 + four*v(n) RETURN END SUBROUTINE mv SUBROUTINE av(n,v,w) ! .. 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 .. INTEGER :: j ! .. Executable Statements .. w(1) = two*v(1) + three*v(2) DO j = 2, n - 1 w(j) = -two*v(j-1) + two*v(j) + three*v(j+1) END DO w(n) = -two*v(n-1) + two*v(n) RETURN END SUBROUTINE av END MODULE f12aefe_mod PROGRAM f12aefe ! F12AEF Example Main Program ! .. Use Statements .. USE nag_library, ONLY : ddot, dnrm2, f06bnf, f12aaf, f12abf, f12acf, & f12adf, f12aef, zgttrf, zgttrs USE f12aefe_mod, ONLY : av, four, mv, nag_wp, nin, nout, three, two, zero ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. COMPLEX (KIND=nag_wp) :: c1, c2, c3, csig REAL (KIND=nag_wp) :: deni, denr, nev_nrm, numi, numr, & sigmai, sigmar INTEGER :: ifail, ifail1, info, irevcm, j, & lcomm, ldv, licomm, n, nconv, & ncv, nev, niter, nshift LOGICAL :: first ! .. Local Arrays .. COMPLEX (KIND=nag_wp), ALLOCATABLE :: cdd(:), cdl(:), cdu(:), cdu2(:), & ctemp(:) REAL (KIND=nag_wp), ALLOCATABLE :: ax(:), comm(:), d(:,:), mx(:), & resid(:), v(:,:), x(:) INTEGER, ALLOCATABLE :: icomm(:), ipiv(:) ! .. Intrinsic Functions .. INTRINSIC cmplx, real ! .. Executable Statements .. WRITE (nout,*) 'F12AEF Example Program Results' WRITE (nout,*) ! Skip heading in data file READ (nin,*) READ (nin,*) n, nev, ncv, sigmar, sigmai ldv = n licomm = 140 lcomm = 3*n + 3*ncv*ncv + 6*ncv + 60 ALLOCATE (cdd(n),cdl(n),cdu(n),cdu2(n),ctemp(n),ax(n),comm(lcomm), & d(ncv,3),mx(n),resid(n),v(ldv,ncv),x(n),icomm(licomm),ipiv(n)) ! 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 mode. ifail = 0 CALL f12adf('SHIFTED REAL',icomm,comm,ifail) ! Set problem type CALL f12adf('GENERALIZED',icomm,comm,ifail) ! Solve A*x = lambda*B*x in shift-invert mode. ! The shift, sigma, is a complex number (sigmar, sigmai). ! OP = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M and B = M. csig = cmplx(sigmar,sigmai,kind=nag_wp) c1 = cmplx(-two,kind=nag_wp) - csig c2 = cmplx(two,kind=nag_wp) - cmplx(four,kind=nag_wp)*csig c3 = cmplx(three,kind=nag_wp) - csig cdl(1:n-1) = c1 cdd(1:n-1) = c2 cdu(1:n-1) = c3 cdd(n) = c2 ! The NAG name equivalent of zgttrf is f07crf CALL zgttrf(n,cdl,cdd,cdu,cdu2,ipiv,info) irevcm = 0 ifail = -1 LOOP: DO CALL f12abf(irevcm,resid,v,ldv,x,mx,nshift,comm,icomm,ifail) IF (irevcm/=5) THEN SELECT CASE (irevcm) CASE (-1) ! Perform x <--- OP*x = inv[A-SIGMA*M]*M*x CALL mv(n,x) ctemp(1:n) = cmplx(x(1:n),kind=nag_wp) ! The NAG name equivalent of zgttrs is f07csf CALL zgttrs('N',n,1,cdl,cdd,cdu,cdu2,ipiv,ctemp,n,info) x(1:n) = real(ctemp(1:n)) CASE (1) ! Perform x <--- OP*x = inv[A-SIGMA*M]*M*x, ! M*X stored in MX. ctemp(1:n) = cmplx(mx(1:n),kind=nag_wp) ! The NAG name equivalent of zgttrs is f07csf CALL zgttrs('N',n,1,cdl,cdd,cdu,cdu2,ipiv,ctemp,n,info) x(1:n) = real(ctemp(1:n)) CASE (2) ! Perform y <--- M*x CALL mv(n,x) CASE (4) ! Output monitoring information CALL f12aef(niter,nconv,d,d(1,2),d(1,3),icomm,comm) ! The NAG name equivalent of dnrm2 is f06ejf nev_nrm = dnrm2(nev,d(1,3),1) WRITE (6,99999) niter, nconv, nev_nrm END SELECT ELSE EXIT LOOP END IF END DO LOOP IF (ifail==0) THEN ! Post-Process using F12ACF to compute eigenvalues/vectors. ifail1 = 0 CALL f12acf(nconv,d,d(1,2),v,ldv,sigmar,sigmai,resid,v,ldv,comm, & icomm,ifail1) first = .TRUE. DO j = 1, nconv ! Use Rayleigh Quotient to recover eigenvalues of the original ! problem. ! The NAG name equivalent of ddot is f06eaf IF (d(j,2)==zero) THEN ! Ritz value is real. x = v(:,j); eig = x'Ax/x'Mx. CALL av(n,v(1,j),ax) numr = ddot(n,v(1,j),1,ax,1) mx(1:n) = v(1:n,j) CALL mv(n,mx) denr = ddot(n,v(1,j),1,mx,1) d(j,1) = numr/denr ELSE IF (first) THEN ! Ritz value is complex: x = v(:,j) - i v(:,j+1). ! Compute x'(Ax): ! first (xr,xi)'*(A xr) CALL av(n,v(1,j),ax) numr = ddot(n,v(1,j),1,ax,1) numi = ddot(n,v(1,j+1),1,ax,1) ! then add (xi,-xr)'*(A xi) CALL av(n,v(1,j+1),ax) numr = numr + ddot(n,v(1,j+1),1,ax,1) numi = -numi + ddot(n,v(1,j),1,ax,1) ! Compute x'(Mx) as above using mv in, place of av. mx(1:n) = v(1:n,j) CALL mv(n,mx) denr = ddot(n,v(1,j),1,mx,1) deni = ddot(n,v(1,j+1),1,mx,1) mx(1:n) = v(1:n,j+1) CALL mv(n,mx) denr = denr + ddot(n,v(1,j+1),1,mx,1) deni = -deni + ddot(n,v(1,j),1,mx,1) ! Rayleigh quotient, d=x'(Ax)/x'(Mx), (complex division). d(j,1) = (numr*denr+numi*deni)/f06bnf(denr,deni) d(j,2) = (numi*denr-numr*deni)/f06bnf(denr,deni) first = .FALSE. ELSE ! Second of complex conjugate pair. d(j,1) = d(j-1,1) d(j,2) = -d(j-1,2) first = .TRUE. END IF END DO ! Print computed eigenvalues. WRITE (nout,99998) nconv, sigmar, sigmai WRITE (nout,99997) (j,d(j,1:2),j=1,nconv) END IF 99999 FORMAT (1X,'Iteration',1X,I3,', No. converged =',1X,I3,', norm o', & 'f estimates =',E12.4) 99998 FORMAT (1X/' The ',I4,' generalized Ritz values closest to (',F8.4, & ', ',F8.4,') are:'/) 99997 FORMAT (1X,I8,5X,'(',F7.4,',',F7.4,')') END PROGRAM f12aefe