```    Program f08nbfe

!     F08NBF Example Program Text

!     Mark 26 Release. NAG Copyright 2016.

!     .. Use Statements ..
Use nag_library, Only: dgeevx, nag_wp, x02ajf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nb = 64, nin = 5, nout = 6
!     .. Local Scalars ..
Complex (Kind=nag_wp)            :: eig
Real (Kind=nag_wp)               :: abnrm, eps, tol
Integer                          :: i, ihi, ilo, info, j, k, lda, ldvl,  &
ldvr, lwork, n
Logical                          :: pair
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), rconde(:), rcondv(:),        &
scale(:), vl(:,:), vr(:,:), wi(:),   &
work(:), wr(:)
Real (Kind=nag_wp)               :: dummy(1)
Integer, Allocatable             :: iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: cmplx, max, maxloc, nint
!     .. Executable Statements ..
Write (nout,*) 'F08NBF Example Program Results'
!     Skip heading in data file
lda = n
ldvl = n
ldvr = n
lwork = (2+nb)*n
Allocate (a(lda,n),rconde(n),rcondv(n),scale(n),vl(ldvl,n),vr(ldvr,n),   &
wi(n),wr(n),iwork(2*n-2))

!     Use routine workspace query to get optimal workspace.
lwork = -1
!     The NAG name equivalent of dgeevx is f08nbf
Call dgeevx('Balance','Vectors (left)','Vectors (right)',                &
'Both reciprocal condition numbers',n,a,lda,wr,wi,vl,ldvl,vr,ldvr,ilo, &
ihi,scale,abnrm,rconde,rcondv,dummy,lwork,iwork,info)

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

!     Read the matrix A from data file

!     Solve the eigenvalue problem
!     The NAG name equivalent of dgeevx is f08nbf
Call dgeevx('Balance','Vectors (left)','Vectors (right)',                &
'Both reciprocal condition numbers',n,a,lda,wr,wi,vl,ldvl,vr,ldvr,ilo, &
ihi,scale,abnrm,rconde,rcondv,work,lwork,iwork,info)

If (info==0) Then

!       Compute the machine precision
eps = x02ajf()
tol = eps*abnrm
pair = .False.

!       Print the eigenvalues and vectors, and associated condition
!       number and bounds

Write (nout,*)
Write (nout,*) 'Eigenvalues'
Write (nout,*)
Write (nout,*) '         Eigenvalue           rcond    error'

Do j = 1, n

!         Print information on j-th eigenvalue

If (wi(j)==0.0_nag_wp) Then
If (rconde(j)>0.0_nag_wp) Then
If (tol/rconde(j)<10.0_nag_wp*eps) Then
Write (nout,99999) j, wr(j), rconde(j), '-'
Else
Write (nout,99998) j, wr(j), rconde(j), tol/rconde(j)
End If
Else
Write (nout,99998) j, wr(j), rconde(j), 'Inf'
End If
Else
If (rconde(j)>0.0_nag_wp) Then
If (tol/rconde(j)<10.0_nag_wp*eps) Then
Write (nout,99997) j, wr(j), wi(j), rconde(j), '-'
Else
Write (nout,99996) j, wr(j), wi(j), rconde(j), tol/rconde(j)
End If
Else
Write (nout,99997) j, wr(j), wi(j), rconde(j), 'Inf'
End If
End If
End Do

Write (nout,*)
Write (nout,*) 'Eigenvectors'
Write (nout,*)
Write (nout,*) '         Eigenvector          rcond    error'

Do j = 1, n

!         Print information on j-th eigenvector
Write (nout,*)

If (wi(j)==0.0E0_nag_wp) Then
!           Make real eigenvectors have positive first entry
If (vr(1,j)<0.0_nag_wp) Then
vr(1:n,j) = -vr(1:n,j)
End If
If (rcondv(j)>0.0_nag_wp) Then
If (tol/rcondv(j)<10.0_nag_wp*eps) Then
Write (nout,99999) j, vr(1,j), rcondv(j), '-'
Else
Write (nout,99998) j, vr(1,j), rcondv(j), tol/rcondv(j)
End If
Else
Write (nout,99998) j, vr(1,j), rcondv(j), 'Inf'
End If
Write (nout,99995) vr(2:n,j)
Else
If (pair) Then
eig = cmplx(vr(1,j-1),-vr(1,j),kind=nag_wp)
Else
!             Make largest eigenvector element have positive first entry
work(1:n) = vr(1:n,j)**2 + vr(1:n,j+1)**2
k = maxloc(work(1:n),1)
If (vr(k,j)<0.0_nag_wp) Then
vr(1:n,j) = -vr(1:n,j)
End If
eig = cmplx(vr(1,j),vr(1,j+1),kind=nag_wp)
End If
If (rcondv(j)>0.0_nag_wp) Then
If (tol/rcondv(j)<10.0_nag_wp*eps) Then
Write (nout,99997) j, eig, rcondv(j), '-'
Else
Write (nout,99996) j, eig, rcondv(j), tol/rcondv(j)
End If
Else
Write (nout,99997) j, eig, rcondv(j), 'Inf'
End If
If (pair) Then
Write (nout,99994)(vr(i,j-1),-vr(i,j),i=2,n)
Else
Write (nout,99994)(vr(i,j),vr(i,j+1),i=2,n)
End If
pair = .Not. pair
End If
End Do
Write (nout,*)
Write (nout,*) 'Errors below 10*machine precision are not displayed'
Else
Write (nout,*)
Write (nout,99993) 'Failure in DGEEVX.  INFO = ', info
End If

99999 Format (1X,I2,2X,1P,E11.4,14X,0P,F7.4,4X,A)
99998 Format (1X,I2,2X,1P,E11.4,11X,0P,F7.4,1X,1P,E8.1)
99997 Format (1X,I2,1X,'(',1P,E11.4,',',E11.4,')',1X,0P,F7.4,4X,A)
99996 Format (1X,I2,1X,'(',1P,E11.4,',',E11.4,')',1X,0P,F7.4,1X,1P,E8.1)
99995 Format (1X,4X,1P,E11.4)
99994 Format (1X,3X,'(',1P,E11.4,',',E11.4,')')
99993 Format (1X,A,I4)
End Program f08nbfe
```