!   F08XPF Example Program Text
!   Mark 26 Release. NAG Copyright 2016.

    Module f08xpfe_mod

!     F08XPF 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                           :: selctg
!     .. Parameters ..
      Integer, Parameter, Public       :: nb = 64, nin = 5, nout = 6
      Logical, Parameter, Public       :: chkfac = .False., prcond = .False.,  &
                                          prmat = .False.
    Contains
      Function selctg(a,b)

!       Logical function selctg for use with ZGGESX (F08XPF)
!       Returns the value .TRUE. if the absolute value of the eigenvalue
!       a/b < 6.0

!       .. Function Return Value ..
        Logical                        :: selctg
!       .. Scalar Arguments ..
        Complex (Kind=nag_wp), Intent (In) :: a, b
!       .. Intrinsic Procedures ..
        Intrinsic                      :: abs
!       .. Executable Statements ..
        selctg = (abs(a)<6.0_nag_wp*abs(b))
        Return
      End Function selctg
    End Module f08xpfe_mod
    Program f08xpfe

!     F08XPF Example Main Program

!     .. Use Statements ..
      Use nag_library, Only: f06bnf, m01daf, m01edf, nag_wp, x02ajf, x04dbf,   &
                             zgemm, zggesx, zlange => f06uaf
      Use f08xpfe_mod, Only: chkfac, nb, nin, nout, prcond, prmat, selctg
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Complex (Kind=nag_wp)            :: alph, bet
      Real (Kind=nag_wp)               :: abnorm, anorm, bnorm, eps, normd,    &
                                          norme, tol
      Integer                          :: i, ifail, info, lda, ldb, ldc, ldd,  &
                                          lde, ldvsl, ldvsr, liwork, lwork, n, &
                                          sdim
      Logical                          :: factor
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: a(:,:), alpha(:), b(:,:), beta(:), &
                                          c(:,:), d(:,:), e(:,:), vsl(:,:),    &
                                          vsr(:,:), work(:)
      Complex (Kind=nag_wp)            :: dummy(1)
      Real (Kind=nag_wp)               :: rconde(2), rcondv(2)
      Real (Kind=nag_wp), Allocatable  :: rwork(:)
      Integer                          :: idum(1)
      Integer, Allocatable             :: iwork(:)
      Logical, Allocatable             :: bwork(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: abs, cmplx, max, nint, real
!     .. Executable Statements ..
      Write (nout,*) 'F08XPF Example Program Results'
      Write (nout,*)
      Flush (nout)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n
      lda = n
      ldb = n
      ldc = n
      ldd = n
      lde = n
      ldvsl = n
      ldvsr = n
      Allocate (a(lda,n),alpha(n),b(ldb,n),beta(n),c(ldc,n),d(ldd,n),e(lde,n), &
        vsl(ldvsl,n),vsr(ldvsr,n),rwork(8*n),bwork(n))

!     Use routine workspace query to get optimal workspace.
      lwork = -1
      liwork = -1
!     The NAG name equivalent of zggesx is f08xpf
      Call zggesx('Vectors (left)','Vectors (right)','Sort',selctg,            &
        'Both reciprocal condition numbers',n,a,lda,b,ldb,sdim,alpha,beta,vsl, &
        ldvsl,vsr,ldvsr,rconde,rcondv,dummy,lwork,rwork,idum,liwork,bwork,     &
        info)

!     Make sure that there is enough workspace for block size nb.
      lwork = max(n*nb+n*n/2,nint(real(dummy(1))))
      liwork = max(n+2,idum(1))
      Allocate (work(lwork),iwork(liwork))

!     Read in the matrices A and B
      Read (nin,*)(a(i,1:n),i=1,n)
      Read (nin,*)(b(i,1:n),i=1,n)

      If (chkfac) Then
!       Copy A and B into D and E respectively
        d(1:n,1:n) = a(1:n,1:n)
        e(1:n,1:n) = b(1:n,1:n)
      End If

!     Find the Frobenius norms of A and B
!     The NAG name equivalent of the LAPACK auxiliary zlange is f06uaf
      anorm = zlange('Frobenius',n,n,a,lda,rwork)
      bnorm = zlange('Frobenius',n,n,b,ldb,rwork)

      If (prmat) Then
!       Print matrices A and B
!       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','F8.4','Matrix A',     &
          'Integer',rlabs,'Integer',clabs,80,0,ifail)
        Write (nout,*)
        Flush (nout)

        ifail = 0
        Call x04dbf('General',' ',n,n,b,ldb,'Bracketed','F8.4','Matrix B',     &
          'Integer',rlabs,'Integer',clabs,80,0,ifail)
        Write (nout,*)
        Flush (nout)
      End If

      factor = .True.
!     Find the generalized Schur form
!     The NAG name equivalent of zggesx is f08xpf
      Call zggesx('Vectors (left)','Vectors (right)','Sort',selctg,            &
        'Both reciprocal condition numbers',n,a,lda,b,ldb,sdim,alpha,beta,vsl, &
        ldvsl,vsr,ldvsr,rconde,rcondv,work,lwork,rwork,iwork,liwork,bwork,     &
        info)

      If (info/=0 .And. info/=(n+2)) Then
        Write (nout,99999) 'Failure in ZGGESX. INFO =', info
        factor = .False.
      Else If (chkfac) Then
!       Compute A - Q*S*Z^H from the factorization of (A,B) and store in
!       matrix D
!       The NAG name equivalent of zgemm is f06zaf
        alph = cmplx(1,kind=nag_wp)
        bet = cmplx(0,kind=nag_wp)
        Call zgemm('N','N',n,n,n,alph,vsl,ldvsl,a,lda,bet,c,ldc)
        alph = cmplx(-1,kind=nag_wp)
        bet = cmplx(1,kind=nag_wp)
        Call zgemm('N','C',n,n,n,alph,c,ldc,vsr,ldvsr,bet,d,ldd)

!       Compute B - Q*T*Z^H from the factorization of (A,B) and store in
!       matrix E
        alph = cmplx(1,kind=nag_wp)
        bet = cmplx(0,kind=nag_wp)
        Call zgemm('N','N',n,n,n,alph,vsl,ldvsl,b,ldb,bet,c,ldc)
        alph = cmplx(-1,kind=nag_wp)
        bet = cmplx(1,kind=nag_wp)
        Call zgemm('N','C',n,n,n,alph,c,ldc,vsr,ldvsr,bet,e,lde)

!       Find norms of matrices D and E and warn if either is too large
        normd = zlange('O',ldd,n,d,ldd,rwork)
        If (normd>x02ajf()**0.75_nag_wp) Then
          Write (nout,*) 'Norm of A-(Q*S*Z^T) is much greater than 0.'
          factor = .False.
          Write (nout,*) 'Schur factorization has failed.'
        End If
        norme = zlange('O',lde,n,e,lde,rwork)
        If (norme>x02ajf()**0.75_nag_wp) Then
          Write (nout,*) 'Norm of B-(Q*T*Z^T) is much greater than 0.'
          factor = .False.
        End If
      End If

      If (factor) Then
!       Print eigenvalue details
        Write (nout,99999) 'Number of eigenvalues for which SELCTG is true = ' &
          , sdim, '(dimension of deflating subspaces)'

        Write (nout,*)
!       Print selected (finite) generalized eigenvalues
        Write (nout,*) 'Selected generalized eigenvalues'

!       Store absolute values of eigenvalues for ranking
        work(1:n) = alpha(1:n)/beta(1:n)
        rwork(1:n) = abs(work(1:n))

!       Rank eigenvalues
        ifail = 0
        Call m01daf(rwork,1,sdim,'Descending',iwork,ifail)

!       Sort eigenvalues in work(1:n)
        Call m01edf(work,1,sdim,iwork,ifail)
        Do i = 1, sdim
          Write (nout,99998) i, work(i)
        End Do

        If (info==(n+2)) Then
          Write (nout,99997) '*** Note that rounding errors mean ',            &
            'that leading eigenvalues in the',                                 &
            'generalized Schur form no longer satisfy SELCTG = .TRUE.'
          Write (nout,*)
        End If
        Flush (nout)

        If (prcond) Then
!         Compute the machine precision and sqrt(anorm**2+bnorm**2)
          eps = x02ajf()
          abnorm = f06bnf(anorm,bnorm)
          tol = eps*abnorm

!         Print out the reciprocal condition numbers and error bound for
!         selected eigenvalues
          Write (nout,*)
          Write (nout,99996)                                                   &
            'Reciprocal condition numbers for the average of the',             &
            'selected eigenvalues and their asymptotic error bound',           &
            'rcond-left = ', rconde(1), ', rcond-right = ', rconde(2),         &
            ', error = ', tol/rconde(1)

          Write (nout,*)
          Write (nout,99996)                                                   &
            'Reciprocal condition numbers for the deflating subspaces',        &
            'and their approximate asymptotic error bound', 'rcond-left = ',   &
            rcondv(1), ', rcond-right = ', rcondv(2), ', error = ',            &
            tol/rcondv(2)
        End If

      Else
        Write (nout,*) 'Schur factorization has failed.'
      End If

99999 Format (1X,A,I4,/,1X,A)
99998 Format (1X,I2,1X,'(',F6.2,',',F6.2,')')
99997 Format (1X,2A,/,1X,A)
99996 Format (1X,A,/,1X,A,/,1X,3(A,1P,E8.1))
    End Program f08xpfe