PROGRAM f08yxfe ! F08YXF Example Program Text ! Mark 23 Release. NAG Copyright 2011. ! .. Use Statements .. USE nag_library, ONLY : f06tff, f06thf, nag_wp, x04dbf, zgeqrf, zggbak, & zggbal, zgghrd, zhgeqz, ztgevc, zungqr, zunmqr ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. COMPLEX (KIND=nag_wp), PARAMETER :: cone = (1.0E0_nag_wp,0.0E0_nag_wp) COMPLEX (KIND=nag_wp), PARAMETER :: czero = (0.0E0_nag_wp,0.0E0_nag_wp) INTEGER, PARAMETER :: nin = 5, nout = 6 ! .. Local Scalars .. COMPLEX (KIND=nag_wp) :: e INTEGER :: i, icols, ifail, ihi, ilo, info, & irows, jwork, lda, ldb, ldvl, ldvr, & lwork, m, n LOGICAL :: ileft, iright CHARACTER (1) :: compq, compz, howmny, job, side ! .. Local Arrays .. COMPLEX (KIND=nag_wp), ALLOCATABLE :: a(:,:), alpha(:), b(:,:), & beta(:), tau(:), vl(:,:), & vr(:,:), work(:) REAL (KIND=nag_wp), ALLOCATABLE :: lscale(:), rscale(:), rwork(:) LOGICAL, ALLOCATABLE :: select(:) CHARACTER (1) :: clabs(1), rlabs(1) ! .. Intrinsic Functions .. INTRINSIC aimag, nint, real ! .. Executable Statements .. WRITE (nout,*) 'F08YXF Example Program Results' FLUSH (nout) ! ileft is TRUE if left eigenvectors are required ! iright is TRUE if right eigenvectors are required ileft = .TRUE. iright = .TRUE. ! Skip heading in data file READ (nin,*) READ (nin,*) n lda = n ldb = n ldvl = n ldvr = n lwork = 6*n ALLOCATE (a(lda,n),alpha(n),b(ldb,n),beta(n),tau(n),vl(ldvl,ldvl), & vr(ldvr,ldvr),work(lwork),lscale(n),rscale(n),rwork(6*n),select(n)) ! READ matrix A from data file READ (nin,*) (a(i,1:n),i=1,n) ! READ matrix B from data file READ (nin,*) (b(i,1:n),i=1,n) ! Balance matrix pair (A,B) job = 'B' ! The NAG name equivalent of zggbal is f08wvf CALL zggbal(job,n,a,lda,b,ldb,ilo,ihi,lscale,rscale,rwork,info) ! Matrix A after balancing ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 CALL x04dbf('General',' ',n,n,a,lda,'Bracketed','F7.4', & 'Matrix A after balancing','Integer',rlabs,'Integer',clabs,80,0, & ifail) WRITE (nout,*) FLUSH (nout) ! Matrix B after balancing ifail = 0 CALL x04dbf('General',' ',n,n,b,ldb,'Bracketed','F7.4', & 'Matrix B after balancing','Integer',rlabs,'Integer',clabs,80,0, & ifail) WRITE (nout,*) FLUSH (nout) ! Reduce B to triangular form using QR irows = ihi + 1 - ilo icols = n + 1 - ilo ! The NAG name equivalent of zgeqrf is f08asf CALL zgeqrf(irows,icols,b(ilo,ilo),ldb,tau,work,lwork,info) ! Apply the orthogonal transformation to A ! The NAG name equivalent of zunmqr is f08auf CALL zunmqr('L','C',irows,icols,irows,b(ilo,ilo),ldb,tau,a(ilo,ilo), & lda,work,lwork,info) ! Initialize VL (for left eigenvectors) IF (ileft) THEN CALL f06thf('General',n,n,czero,cone,vl,ldvl) CALL f06tff('Lower',irows-1,irows-1,b(ilo+1,ilo),ldb,vl(ilo+1,ilo), & ldvl) ! The NAG name equivalent of zungqr is f08atf CALL zungqr(irows,irows,irows,vl(ilo,ilo),ldvl,tau,work,lwork,info) END IF ! Initialize VR for right eigenvectors IF (iright) CALL f06thf('General',n,n,czero,cone,vr,ldvr) ! Compute the generalized Hessenberg form of (A,B) compq = 'V' compz = 'V' ! The NAG name equivalent of zgghrd is f08wsf CALL zgghrd(compq,compz,n,ilo,ihi,a,lda,b,ldb,vl,ldvl,vr,ldvr,info) ! Matrix A in generalized Hessenberg form ifail = 0 CALL x04dbf('General',' ',n,n,a,lda,'Bracketed','F7.3', & 'Matrix A in Hessenberg form','Integer',rlabs,'Integer',clabs,80,0, & ifail) WRITE (nout,*) FLUSH (nout) ! Matrix B in generalized Hessenberg form ifail = 0 CALL x04dbf('General',' ',n,n,b,ldb,'Bracketed','F7.3', & 'Matrix B in Hessenberg form','Integer',rlabs,'Integer',clabs,80,0, & ifail) ! Routine ZHGEQZ ! Workspace query: jwork = -1 jwork = -1 job = 'S' ! The NAG name equivalent of zhgeqz is f08xsf CALL zhgeqz(job,compq,compz,n,ilo,ihi,a,lda,b,ldb,alpha,beta,vl,ldvl, & vr,ldvr,work,jwork,rwork,info) WRITE (nout,*) WRITE (nout,99999) nint(real(work(1))) WRITE (nout,99998) lwork WRITE (nout,*) FLUSH (nout) ! Compute the generalized Schur form ! if the workspace lwork is adequate IF (nint(real(work(1)))<=lwork) THEN ! The NAG name equivalent of zhgeqz is f08xsf CALL zhgeqz(job,compq,compz,n,ilo,ihi,a,lda,b,ldb,alpha,beta,vl, & ldvl,vr,ldvr,work,lwork,rwork,info) ! Print the generalized eigenvalues ! Note: the actual values of beta are real and non-negative WRITE (nout,99997) DO i = 1, n IF (real(beta(i))/=0.0E0_nag_wp) THEN e = alpha(i)/beta(i) WRITE (nout,99995) i, '(', real(e), ',', aimag(e), ')' ELSE WRITE (nout,99996) i END IF END DO WRITE (nout,*) FLUSH (nout) ! Compute left and right generalized eigenvectors ! of the balanced matrix howmny = 'B' IF (ileft .AND. iright) THEN side = 'B' ELSE IF (ileft) THEN side = 'L' ELSE IF (iright) THEN side = 'R' END IF ! The NAG name equivalent of ztgevc is f08yxf CALL ztgevc(side,howmny,select,n,a,lda,b,ldb,vl,ldvl,vr,ldvr,n,m, & work,rwork,info) ! Compute right eigenvectors of the original matrix IF (iright) THEN job = 'B' side = 'R' ! The NAG name equivalent of zggbak is f08wwf CALL zggbak(job,side,n,ilo,ihi,lscale,rscale,n,vr,ldvr,info) ! Normalize the right eigenvectors DO i = 1, n vr(1:n,i) = vr(1:n,i)/vr(1,i) END DO ! Print the right eigenvectors ifail = 0 CALL x04dbf('General',' ',n,n,vr,ldvr,'Bracketed','F7.4', & 'Right eigenvectors','Integer',rlabs,'Integer',clabs,80,0, & ifail) WRITE (nout,*) FLUSH (nout) END IF ! Compute left eigenvectors of the original matrix IF (iright) THEN job = 'B' side = 'L' ! The NAG name equivalent of zggbak is f08wwf CALL zggbak(job,side,n,ilo,ihi,lscale,rscale,n,vl,ldvl,info) ! Normalize the left eigenvectors DO i = 1, n vl(1:n,i) = vl(1:n,i)/vl(1,i) END DO ! Print the left eigenvectors ifail = 0 CALL x04dbf('General',' ',n,n,vl,ldvl,'Bracketed','F7.4', & 'Left eigenvectors','Integer',rlabs,'Integer',clabs,80,0, & ifail) END IF ELSE WRITE (nout,99994) END IF 99999 FORMAT (1X,'Minimal required LWORK = ',I6) 99998 FORMAT (1X,'Actual value of LWORK = ',I6) 99997 FORMAT (1X,'Generalized eigenvalues') 99996 FORMAT (1X,I4,' Infinite eigenvalue') 99995 FORMAT (1X,I4,5X,A,F7.3,A,F7.3,A) 99994 FORMAT (1X,'Insufficient workspace for array WORK'/' in F08XSF/', & 'ZHGEQZ') END PROGRAM f08yxfe