!   F08XBF Example Program Text
!   Mark 26 Release. NAG Copyright 2016.

    Module f08xbfe_mod

!     F08XBF 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
    Contains
      Function selctg(ar,ai,b)

!       Logical function selctg for use with DGGESX (F08XBF)
!       Returns the value .TRUE. if the eigenvalue is real and positive

!       .. Function Return Value ..
        Logical                        :: selctg
!       .. Scalar Arguments ..
        Real (Kind=nag_wp), Intent (In) :: ai, ar, b
!       .. Executable Statements ..
        selctg = (ar>0._nag_wp .And. ai==0._nag_wp .And. b/=0._nag_wp)
        Return
      End Function selctg
    End Module f08xbfe_mod
    Program f08xbfe

!     F08XBF Example Main Program

!     .. Use Statements ..
      Use nag_library, Only: dgemm, dggesx, dlange => f06raf, f06bnf, nag_wp,  &
                             x02ajf, x04caf
      Use f08xbfe_mod, Only: nb, nin, nout, selctg
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: abnorm, alph, anorm, bet, bnorm,     &
                                          eps, normd, norme, tol
      Integer                          :: i, ifail, info, lda, ldb, ldc, ldd,  &
                                          lde, ldvsl, ldvsr, liwork, lwork, n, &
                                          sdim
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), alphai(:), alphar(:),        &
                                          b(:,:), beta(:), c(:,:), d(:,:),     &
                                          e(:,:), vsl(:,:), vsr(:,:), work(:)
      Real (Kind=nag_wp)               :: rconde(2), rcondv(2), rdum(1)
      Integer                          :: idum(1)
      Integer, Allocatable             :: iwork(:)
      Logical, Allocatable             :: bwork(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max, nint
!     .. Executable Statements ..
      Write (nout,*) 'F08XBF 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),alphai(n),alphar(n),b(ldb,n),beta(n),vsl(ldvsl,n),    &
        vsr(ldvsr,n),bwork(n),c(ldc,n),d(ldd,n),e(lde,n))

!     Use routine workspace query to get optimal workspace.
      lwork = -1
      liwork = -1
!     The NAG name equivalent of dggesx is f08xbf
      Call dggesx('Vectors (left)','Vectors (right)','Sort',selctg,            &
        'Both reciprocal condition numbers',n,a,lda,b,ldb,sdim,alphar,alphai,  &
        beta,vsl,ldvsl,vsr,ldvsr,rconde,rcondv,rdum,lwork,idum,liwork,bwork,   &
        info)

!     Make sure that there is enough workspace for block size nb.
      lwork = max(8*(n+1)+16+n*nb+n*n/2,nint(rdum(1)))
      liwork = max(n+6,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)

!     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)

!     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 x04caf('General',' ',n,n,a,lda,'Matrix A',ifail)
      Write (nout,*)
      Flush (nout)

      ifail = 0
      Call x04caf('General',' ',n,n,b,ldb,'Matrix B',ifail)
      Write (nout,*)
      Flush (nout)

!     Find the Frobenius norms of A and B
!     The NAG name equivalent of the LAPACK auxiliary dlange is f06raf
      anorm = dlange('Frobenius',n,n,a,lda,work)
      bnorm = dlange('Frobenius',n,n,b,ldb,work)

!     Find the generalized Schur form
!     The NAG name equivalent of dggesx is f08xbf
      Call dggesx('Vectors (left)','Vectors (right)','Sort',selctg,            &
        'Both reciprocal condition numbers',n,a,lda,b,ldb,sdim,alphar,alphai,  &
        beta,vsl,ldvsl,vsr,ldvsr,rconde,rcondv,work,lwork,iwork,liwork,bwork,  &
        info)

      If (info==0 .Or. info==(n+2)) Then

!       Compute A - Q*S*Z^T from the factorization of (A,B) and store in
!       matrix D
!       The NAG name equivalent of dgemm is f06yaf
        alph = 1.0_nag_wp
        bet = 0.0_nag_wp
        Call dgemm('N','N',n,n,n,alph,vsl,ldvsl,a,lda,bet,c,ldc)
        alph = -1.0_nag_wp
        bet = 1.0_nag_wp
        Call dgemm('N','T',n,n,n,alph,c,ldc,vsr,ldvsr,bet,d,ldd)

!       Compute B - Q*T*Z^T from the factorization of (A,B) and store in
!       matrix E
        alph = 1.0_nag_wp
        bet = 0.0_nag_wp
        Call dgemm('N','N',n,n,n,alph,vsl,ldvsl,b,ldb,bet,c,ldc)
        alph = -1.0_nag_wp
        bet = 1.0_nag_wp
        Call dgemm('N','T',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 = dlange('O',ldd,n,d,ldd,work)
        norme = dlange('O',lde,n,e,lde,work)
        If (normd>x02ajf()**0.8_nag_wp .Or. norme>x02ajf()**0.8_nag_wp) Then
          Write (nout,*)                                                       &
            'Norm of A-(Q*S*Z^T) or norm of B-(Q*T*Z^T) is much greater than 0.'
          Write (nout,*) 'Schur factorization has failed.'
        Else

!         Print solution
          Write (nout,99999)                                                   &
            'Number of eigenvalues for which SELCTG is true = ', sdim,         &
            '(dimension of deflating subspaces)'

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

          Do i = 1, sdim
            If (beta(i)/=0.0_nag_wp) Then
              Write (nout,99998) i, '(', alphar(i)/beta(i), ',',               &
                alphai(i)/beta(i), ')'
            Else
              Write (nout,99997) i
            End If
          End Do

          If (info==(n+2)) Then
            Write (nout,99996) '***Note that rounding errors mean ',           &
              'that leading eigenvalues in the generalized',                   &
              'Schur form no longer satisfy SELCTG = .TRUE.'
            Write (nout,*)
          End If
          Flush (nout)

!         Print out the reciprocal condition numbers
          Write (nout,*)
          Write (nout,99995)                                                   &
            'Reciprocals of left and right projection norms onto',             &
            'the deflating subspaces for the selected eigenvalues',            &
            'RCONDE(1) = ', rconde(1), ', RCONDE(2) = ', rconde(2)
          Write (nout,*)
          Write (nout,99995)                                                   &
            'Reciprocal condition numbers for the left and right',             &
            'deflating subspaces', 'RCONDV(1) = ', rcondv(1),                  &
            ', RCONDV(2) = ', rcondv(2)
          Flush (nout)

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

!         Print out the approximate asymptotic error bound on the
!         average absolute error of the selected eigenvalues given by
!         eps*norm((A, B))/PL,   where PL = RCONDE(1)
          Write (nout,*)
          Write (nout,99994)                                                   &
            'Approximate asymptotic error bound for selected ',                &
            'eigenvalues    = ', tol/rconde(1)

!         Print out an approximate asymptotic bound on the maximum
!         angular error in the computed deflating subspaces given by
!         eps*norm((A, B))/DIF(2),   where DIF(2) = RCONDV(2)
          Write (nout,99994)                                                   &
            'Approximate asymptotic error bound for the deflating ',           &
            'subspaces = ', tol/rcondv(2)

        End If

      Else
        Write (nout,99999) 'Failure in DGGESX. INFO =', info
      End If

99999 Format (1X,A,I4,/,1X,A)
99998 Format (1X,I4,5X,A,F7.3,A,F7.3,A)
99997 Format (1X,I4,'Eigenvalue is infinite')
99996 Format (1X,2A,/,1X,A)
99995 Format (1X,A,/,1X,A,/,1X,2(A,1P,E8.1))
99994 Format (1X,2A,1P,E8.1)
    End Program f08xbfe