PROGRAM f08ykfe ! F08YKF Example Program Text ! Mark 23 Release. NAG Copyright 2011. ! .. Use Statements .. USE nag_library, ONLY : dgeqrf, dggbak, dggbal, dgghrd, dhgeqz, dorgqr, & dormqr, dtgevc, f06qff, f06qhf, nag_wp, x04caf ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. REAL (KIND=nag_wp), PARAMETER :: one = 1.0E0_nag_wp REAL (KIND=nag_wp), PARAMETER :: zero = 0.0E0_nag_wp INTEGER, PARAMETER :: nin = 5, nout = 6 ! .. Local Scalars .. 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 .. REAL (KIND=nag_wp), ALLOCATABLE :: a(:,:), alphai(:), alphar(:), & b(:,:), beta(:), lscale(:), & rscale(:), tau(:), vl(:,:), vr(:,:), & work(:) LOGICAL, ALLOCATABLE :: select(:) ! .. Intrinsic Functions .. INTRINSIC nint ! .. Executable Statements .. WRITE (nout,*) 'F08YKF 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),alphai(n),alphar(n),b(ldb,n),beta(n),lscale(n), & rscale(n),tau(n),vl(ldvl,ldvl),vr(ldvr,ldvr),work(lwork),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 dggbal is f08whf CALL dggbal(job,n,a,lda,b,ldb,ilo,ihi,lscale,rscale,work,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 x04caf('General',' ',n,n,a,lda,'Matrix A after balancing',ifail) WRITE (nout,*) FLUSH (nout) ! Matrix B after balancing ifail = 0 CALL x04caf('General',' ',n,n,b,ldb,'Matrix B after balancing',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 dgeqrf is f08aef CALL dgeqrf(irows,icols,b(ilo,ilo),ldb,tau,work,lwork,info) ! Apply the orthogonal transformation to matrix A ! The NAG name equivalent of dormqr is f08agf CALL dormqr('L','T',irows,icols,irows,b(ilo,ilo),ldb,tau,a(ilo,ilo), & lda,work,lwork,info) ! Initialize VL (if left eigenvectors are required) IF (ileft) THEN CALL f06qhf('General',n,n,zero,one,vl,ldvl) CALL f06qff('Lower',irows-1,irows-1,b(ilo+1,ilo),ldb,vl(ilo+1,ilo), & ldvl) ! The NAG name equivalent of dorgqr is f08aff CALL dorgqr(irows,irows,irows,vl(ilo,ilo),ldvl,tau,work,lwork,info) END IF ! Initialize VR (if right eigenvectors are required) IF (iright) CALL f06qhf('General',n,n,zero,one,vr,ldvr) ! Compute the generalized Hessenberg form of (A,B) compq = 'V' compz = 'V' ! The NAG name equivalent of dgghrd is f08wef CALL dgghrd(compq,compz,n,ilo,ihi,a,lda,b,ldb,vl,ldvl,vr,ldvr,info) ! Matrix A in generalized Hessenberg form ifail = 0 CALL x04caf('General',' ',n,n,a,lda,'Matrix A in Hessenberg form', & ifail) WRITE (nout,*) FLUSH (nout) ! Matrix B in generalized Hessenberg form ifail = 0 CALL x04caf('General',' ',n,n,b,ldb,'Matrix B in Hessenberg form', & ifail) ! Routine DHGEQZ ! Workspace query: jwork = -1 jwork = -1 job = 'S' ! The NAG name equivalent of dhgeqz is f08xef CALL dhgeqz(job,compq,compz,n,ilo,ihi,a,lda,b,ldb,alphar,alphai,beta, & vl,ldvl,vr,ldvr,work,jwork,info) WRITE (nout,*) WRITE (nout,99999) nint(work(1)) WRITE (nout,99998) lwork WRITE (nout,*) WRITE (nout,99997) WRITE (nout,99996) ! Compute the generalized Schur form ! if the workspace lwork is adequate ! The Schur form also gives parameters ! required to compute generalized eigenvalues IF (nint(work(1))<=lwork) THEN ! The NAG name equivalent of dhgeqz is f08xef CALL dhgeqz(job,compq,compz,n,ilo,ihi,a,lda,b,ldb,alphar,alphai, & beta,vl,ldvl,vr,ldvr,work,lwork,info) ! Print the generalized eigenvalues DO i = 1, n IF (beta(i)/=0.0E0_nag_wp) THEN WRITE (nout,99995) i, '(', alphar(i)/beta(i), ',', & alphai(i)/beta(i), ')' 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 dtgevc is f08ykf CALL dtgevc(side,howmny,select,n,a,lda,b,ldb,vl,ldvl,vr,ldvr,n,m, & work,info) IF (iright) THEN ! Compute right eigenvectors of the original matrix job = 'B' side = 'R' ! The NAG name equivalent of dggbak is f08wjf CALL dggbak(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 x04caf('General',' ',n,n,vr,ldvr, & 'Right eigenvectors ',ifail) WRITE (nout,*) FLUSH (nout) END IF ! Compute left eigenvectors of the original matrix IF (ileft) THEN job = 'B' side = 'L' ! The NAG name equivalent of dggbak is f08wjf CALL dggbak(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 x04caf('General',' ',n,n,vl,ldvl,'Left eigenvectors',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,I4,5X,'Infinite eigenvalue') 99995 FORMAT (1X,I4,5X,A,F7.3,A,F7.3,A) 99994 FORMAT (1X,'Insufficient workspace for array WORK'/' in F08XEF/', & 'DHGEQZ') END PROGRAM f08ykfe