Program f08yxfe ! F08YXF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. 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 Procedures .. 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