Program f08xsfe ! F08XSF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: nag_wp, x04dbf, zgeqrf, zggbal, zgghrd, zhgeqz, & zunmqr ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nin = 5, nout = 6 ! .. Local Scalars .. Complex (Kind=nag_wp) :: e Integer :: i, ifail, ihi, ilo, info, irows, & jwork, lda, ldb, ldq, ldz, lwork, n Character (1) :: compq, compz, job ! .. Local Arrays .. Complex (Kind=nag_wp), Allocatable :: a(:,:), alpha(:), b(:,:), beta(:), & q(:,:), tau(:), work(:), z(:,:) Real (Kind=nag_wp), Allocatable :: lscale(:), rscale(:), rwork(:) Character (1) :: clabs(1), rlabs(1) ! .. Intrinsic Procedures .. Intrinsic :: aimag, nint, real ! .. Executable Statements .. Write (nout,*) 'F08XSF Example Program Results' Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) n ldq = 1 ldz = 1 lda = n ldb = n lwork = 6*n Allocate (a(lda,n),alpha(n),b(ldb,n),beta(n),q(ldq,ldq),tau(n), & work(lwork),z(ldz,ldz),lscale(n),rscale(n),rwork(6*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' 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 ! The NAG name equivalent of zgeqrf is f08asf Call zgeqrf(irows,irows,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,irows,irows,b(ilo,ilo),ldb,tau,a(ilo,ilo),lda, & work,lwork,info) ! Compute the generalized Hessenberg form of (A,B) -> (H,T) compq = 'N' compz = 'N' ! The NAG name equivalent of zgghrd is f08wsf Call zgghrd(compq,compz,irows,1,irows,a(ilo,ilo),lda,b(ilo,ilo),ldb,q, & ldq,z,ldz,info) ! Matrix A (H) 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 (T) in generalized Hessenberg form ifail = 0 Call x04dbf('General',' ',n,n,b,ldb,'Bracketed','F7.3', & 'Matrix B is triangular','Integer',rlabs,'Integer',clabs,80,0,ifail) ! Routine ZHGEQZ ! Workspace query: jwork = -1 jwork = -1 job = 'E' ! The NAG name equivalent of zhgeqz is f08xsf Call zhgeqz(job,compq,compz,n,ilo,ihi,a,lda,b,ldb,alpha,beta,q,ldq,z, & ldz,work,jwork,rwork,info) Write (nout,*) Write (nout,99999) nint(real(work(1))) Write (nout,99998) lwork Write (nout,*) Write (nout,99997) Write (nout,99996) 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,q,ldq,z, & ldz,work,lwork,rwork,info) ! Print the generalized eigenvalues ! Note: the actual values of beta are real and non-negative 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 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 allocated for call to F08XSF/ZHGEQZ') End Program f08xsfe