!   F08YKF Example Program Text
!   Mark 26 Release. NAG Copyright 2016.

    Module f08ykfe_mod

!     F08YKF Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
      Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Accessibility Statements ..
      Private
      Public                           :: normalize
!     .. Parameters ..
      Real (Kind=nag_wp), Parameter, Public :: one = 1.0_nag_wp
      Real (Kind=nag_wp), Parameter, Public :: zero = 0.0_nag_wp
      Integer, Parameter, Public       :: nin = 5, nout = 6
    Contains
      Subroutine normalize(n,alphai,v,ldv)

!       .. Use Statements ..
        Use nag_library, Only: dnrm2
!       .. Implicit None Statement ..
        Implicit None
!       .. Scalar Arguments ..
        Integer, Intent (In)           :: ldv, n
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (In) :: alphai(n)
        Real (Kind=nag_wp), Intent (Inout) :: v(ldv,*)
!       .. Local Scalars ..
        Real (Kind=nag_wp)             :: a, b, r, r1, r2, v1, v2
        Integer                        :: i, j, k
!       .. Intrinsic Procedures ..
        Intrinsic                      :: sqrt
!       .. Executable Statements ..

        Do j = 1, n

          If (alphai(j)>=0.0_nag_wp) Then
            If (alphai(j)==0.0_nag_wp) Then
!             Real eigenvalue
!             The 2-norm of Q is calculated using dnrm2 (f06ejf).
              r = dnrm2(n,v(1,j),1)
              v(1:n,j) = v(1:n,j)/r
            Else
!             Complex eigenvalue (positive imaginary part)
!             Make largest element real and positive
              r1 = dnrm2(n,v(1,j),1)
              r2 = dnrm2(n,v(1,j+1),1)
              r1 = sqrt(r1**2+r2**2)
              r2 = -1.0_nag_wp
              Do i = 1, n
                r = v(i,j)**2 + v(i,j+1)**2
                If (r>r2) Then
                  r2 = r
                  k = i
                End If
              End Do
              r = r1*sqrt(r2)
              a = v(k,j)/r
              b = v(k,j+1)/r
              Do i = 1, n
                v1 = v(i,j)
                v2 = v(i,j+1)
                v(i,j) = v1*a + v2*b
                v(i,j+1) = v2*a - v1*b
              End Do
            End If
          End If
        End Do
      End Subroutine normalize
    End Module f08ykfe_mod
    Program f08ykfe

!     F08YKF Example Main Program

!     .. Use Statements ..
      Use nag_library, Only: dgeqrf, dggbak, dggbal, dgghrd, dhgeqz, dorgqr,   &
                             dormqr, dtgevc, f06qff, f06qhf, nag_wp, x04cbf
      Use f08ykfe_mod, Only: nin, normalize, nout, one, zero
!     .. Implicit None Statement ..
      Implicit None
!     .. 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(:)
      Character (0)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      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 x04cbf('General',' ',n,n,a,lda,'F8.4','Matrix A after balancing',   &
        'I',rlabs,'I',clabs,80,0,ifail)
      Write (nout,*)
      Flush (nout)

!     Matrix B after balancing
      ifail = 0
      Call x04cbf('General',' ',n,n,b,ldb,'F8.4','Matrix B after balancing',   &
        'I',rlabs,'I',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 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) Then
        Call f06qhf('General',n,n,zero,one,vr,ldvr)
      End If

!     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 x04cbf('General',' ',n,n,a,lda,'F8.4','Matrix A in Hessenberg form' &
        ,'I',rlabs,'I',clabs,80,0,ifail)
      Write (nout,*)
      Flush (nout)

!     Matrix B in generalized Hessenberg form
      ifail = 0
      Call x04cbf('General',' ',n,n,b,ldb,'F8.4','Matrix B in Hessenberg form' &
        ,'I',rlabs,'I',clabs,80,0,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)

          Call normalize(n,alphai,vr,ldvr)
!         Print the right eigenvectors

          ifail = 0
          Call x04cbf('General',' ',n,n,vr,ldvr,'F8.4','Right eigenvectors',   &
            'I',rlabs,'I',clabs,80,0,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)

          Call normalize(n,alphai,vl,ldvl)
!         Print the left eigenvectors

          ifail = 0
          Call x04cbf('General',' ',n,n,vl,ldvl,'F8.4','Left eigenvectors',    &
            'I',rlabs,'I',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,I4,5X,'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