!   F08PPF Example Program Text
!   Mark 26 Release. NAG Copyright 2016.

    Module f08ppfe_mod

!     F08PPF 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                           :: select
!     .. Parameters ..
      Integer, Parameter, Public       :: nb = 64, nin = 5, nout = 6
      Logical, Parameter, Public       :: check_fac = .True.,                  &
                                          print_cond = .False.
    Contains
      Function select(w)

!       Logical function select for use with ZGEESX (F08PPF)
!       Returns the value .TRUE. if the real part of the eigenvalue
!       w is positive.

!       .. Function Return Value ..
        Logical                        :: select
!       .. Scalar Arguments ..
        Complex (Kind=nag_wp), Intent (In) :: w
!       .. Intrinsic Procedures ..
        Intrinsic                      :: real
!       .. Executable Statements ..
        select = (real(w)>0._nag_wp)
        Return
      End Function select
    End Module f08ppfe_mod
    Program f08ppfe

!     F08PPF Example Main Program

!     .. Use Statements ..
      Use nag_library, Only: nag_wp, x02ajf, x04dbf, zgeesx, zgemm,            &
                             zlange => f06uaf
      Use f08ppfe_mod, Only: check_fac, nb, nin, nout, print_cond, select
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Complex (Kind=nag_wp)            :: alpha, beta
      Real (Kind=nag_wp)               :: anorm, eps, norm, rconde, rcondv,    &
                                          tol
      Integer                          :: i, ifail, info, lda, ldc, ldd, ldvs, &
                                          lwork, n, sdim
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: a(:,:), c(:,:), d(:,:), vs(:,:),   &
                                          w(:), work(:)
      Complex (Kind=nag_wp)            :: dummy(1)
      Real (Kind=nag_wp), Allocatable  :: rwork(:)
      Logical, Allocatable             :: bwork(:)
      Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: cmplx, max, nint, real
!     .. Executable Statements ..
      Write (nout,*) 'F08PPF Example Program Results'
      Write (nout,*)
      Flush (nout)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n
      lda = n
      ldc = n
      ldd = n
      ldvs = n
      Allocate (a(lda,n),c(ldc,n),d(ldd,n),vs(ldvs,n),w(n),rwork(n),bwork(n))

!     Use routine workspace query to get optimal workspace.
      lwork = -1
!     The NAG name equivalent of zgeesx is f08ppf
      Call zgeesx('Vectors (Schur)','Sort',select,                             &
        'Both reciprocal condition numbers',n,a,lda,sdim,w,vs,ldvs,rconde,     &
        rcondv,dummy,lwork,rwork,bwork,info)

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

!     Read in the matrix A
      Read (nin,*)(a(i,1:n),i=1,n)

!     Copy A into D
      d(1:n,1:n) = a(1:n,1:n)

!     Print matrix A
!     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',       &
        'Integer',rlabs,'Integer',clabs,80,0,ifail)

      Write (nout,*)
      Flush (nout)

!     Find the Frobenius norm of A
!     The NAG name equivalent of the LAPACK auxiliary zlange is f06uaf
      anorm = zlange('Frobenius',n,n,a,lda,rwork)

!     Find the Schur factorization of A
!     The NAG name equivalent of zgeesx is f08ppf
      Call zgeesx('Vectors (Schur)','Sort',select,                             &
        'Both reciprocal condition numbers',n,a,lda,sdim,w,vs,ldvs,rconde,     &
        rcondv,work,lwork,rwork,bwork,info)

      If (info/=0 .And. info/=(n+2)) Then
        Write (nout,99993) 'Failure in ZGEESX. INFO =', info
        Go To 100
      End If

      If (check_fac) Then
!       Compute A - Z*T*Z^H from the factorization of A and store in matrix D
!       The NAG name equivalent of zgemm is f06zaf
        alpha = cmplx(1,kind=nag_wp)
        beta = cmplx(0,kind=nag_wp)
        Call zgemm('N','N',n,n,n,alpha,vs,ldvs,a,lda,beta,c,ldc)
        alpha = cmplx(-1,kind=nag_wp)
        beta = cmplx(1,kind=nag_wp)
        Call zgemm('N','C',n,n,n,alpha,c,ldc,vs,ldvs,beta,d,ldd)

!       Find norm of matrix D and print warning if it is too large
!       f06uaf is the NAG name equivalent of the LAPACK auxiliary zlange
        norm = zlange('O',ldd,n,d,ldd,rwork)
        If (norm>x02ajf()**0.5_nag_wp) Then
          Write (nout,*) 'Norm of A-(Z*T*Z^H) is much greater than 0.'
          Write (nout,*) 'Schur factorization has failed.'
          Go To 100
        End If
      End If

!     Print solution
      Write (nout,99999) 'Number of eigenvalues for which SELECT is true = ',  &
        sdim, '(dimension of invariant subspace)'

      Write (nout,*)
!     Print eigenvalues.
      Write (nout,*) 'Selected eigenvalues'
      Write (nout,99998)(i,w(i),i=1,sdim)
      Write (nout,*)

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

      If (print_cond) Then
!       Print out the reciprocal condition numbers
        Write (nout,99996) 'Reciprocal of projection norm onto the invariant', &
          'subspace for the selected eigenvalues', 'RCONDE = ', rconde
        Write (nout,*)
        Write (nout,99995)                                                     &
          'Reciprocal condition number for the invariant subspace',            &
          'RCONDV = ', rcondv

!       Compute the machine precision
        eps = x02ajf()
        tol = eps*anorm

!       Print out the approximate asymptotic error bound on the
!       average absolute error of the selected eigenvalues given by
!       eps*norm(A)/RCONDE
        Write (nout,*)
        Write (nout,99994) 'Approximate asymptotic error bound for selected ', &
          'eigenvalues   = ', tol/rconde

!       Print out an approximate asymptotic bound on the maximum
!       angular error in the computed invariant subspace given by
!       eps*norm(A)/RCONDV
        Write (nout,99994)                                                     &
          'Approximate asymptotic error bound for the invariant ',             &
          'subspace = ', tol/rcondv
      End If
100   Continue

99999 Format (1X,A,I4,/,1X,A)
99998 Format (1X,I4,2X,' (',F7.4,',',F7.4,')',:)
99997 Format (1X,2A,/,1X,A)
99996 Format (1X,A,/,1X,A,/,1X,A,1P,E8.1)
99995 Format (1X,A,/,1X,A,1P,E8.1)
99994 Format (1X,2A,1P,E8.1)
99993 Format (1X,A,I4)
    End Program f08ppfe