Program f08xsfe

!     F08XSF Example Program Text

!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
      Use nag_library, Only: m01daf, m01edf, nag_wp, x04dbf, zgeqrf, zggbal,   &
                             zgghd3, zhgeqz, zunmqr
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Integer                          :: i, ifail, ihi, ilo, info, irows,     &
                                          jwork, lda, ldb, ldq, ldz, lwork, n, &
                                          ni
      Character (1)                    :: compq, compz, job
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: a(:,:), alpha(:), b(:,:), beta(:), &
                                          e(:), q(:,:), tau(:), work(:),       &
                                          z(:,:)
      Real (Kind=nag_wp), Allocatable  :: emod(:), lscale(:), rscale(:),       &
                                          rwork(:)
      Integer, Allocatable             :: irank(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: abs, 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 zgghd3 is f08wuf
      Call zgghd3(compq,compz,irows,1,irows,a(ilo,ilo),lda,b(ilo,ilo),ldb,q,   &
        ldq,z,ldz,work,lwork,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,*)
      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 in descending size order
!       Note: the actual values of beta are real and non-negative

!       Calculate the moduli of the finite eigenvalues.
        Allocate (e(n),emod(n),irank(n))
        ni = 0
        Do i = 1, n
          If (real(beta(i))/=0.0_nag_wp) Then
            ni = ni + 1
            e(ni) = alpha(i)/beta(i)
            emod(ni) = abs(e(ni))
          Else
            Write (nout,99996) i
          End If
        End Do

!       Rearrange the finite eigenvalues in descending order of modulus.
        ifail = 0
        Call m01daf(emod,1,ni,'Descending',irank,ifail)
        ifail = 0
        Call m01edf(e,1,ni,irank,ifail)

        Write (nout,99995)(i,'(',real(e(i)),',',aimag(e(i)),')',i=1,ni)
      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