NAG Library Manual, Mark 28.7
```    Program f08npfe

!     F08NPF Example Program Text

!     Mark 28.7 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: nag_wp, x02ajf, zgeevx
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nb = 64, nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: abnrm, eps, tol
Integer                          :: i, ihi, ilo, info, j, lda, ldvl,     &
ldvr, lwork, n
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), vl(:,:), vr(:,:), w(:),    &
work(:)
Complex (Kind=nag_wp)            :: dummy(1)
Real (Kind=nag_wp), Allocatable  :: rconde(:), rcondv(:), rwork(:),      &
scale(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, nint, real
!     .. Executable Statements ..
Write (nout,*) 'F08NPF Example Program Results'
!     Skip heading in data file
lda = n
ldvl = n
ldvr = n
Allocate (a(lda,n),vl(ldvl,n),vr(ldvr,n),w(n),rconde(n),rcondv(n),       &
rwork(2*n),scale(n))

!     Use routine workspace query to get optimal workspace.
lwork = -1
!     The NAG name equivalent of zgeevx is f08npf
Call zgeevx('Balance','Vectors (left)','Vectors (right)',                &
'Both reciprocal condition numbers',n,a,lda,w,vl,ldvl,vr,ldvr,ilo,ihi, &
scale,abnrm,rconde,rcondv,dummy,lwork,rwork,info)

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

!     Read the matrix A from data file

!     Solve the eigenvalue problem

!     The NAG name equivalent of zgeevx is f08npf
Call zgeevx('Balance','Vectors (left)','Vectors (right)',                &
'Both reciprocal condition numbers',n,a,lda,w,vl,ldvl,vr,ldvr,ilo,ihi, &
scale,abnrm,rconde,rcondv,work,lwork,rwork,info)

If (info==0) Then

!       Compute the machine precision

eps = x02ajf()
tol = eps*abnrm

!       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 (rconde(j)>0.0_nag_wp) Then
If (tol/rconde(j)<10.0_nag_wp*eps) Then
Write (nout,99999) j, w(j), rconde(j), '-'
Else
Write (nout,99998) j, w(j), rconde(j), tol/rconde(j)
End If
Else
Write (nout,99999) j, w(j), rconde(j), 'Inf'
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,*)

!         Make first real part component be positive
If (real(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,99999) j, vr(1,j), rcondv(j), 'Inf'
End If

Write (nout,99997) vr(2:n,j)

End Do
Write (nout,*)
Write (nout,*) 'Errors below 10*machine precision are not displayed'
Else
Write (nout,*)
Write (nout,99996) 'Failure in ZGEEVX. INFO =', info
End If

99999 Format (1X,I2,1X,'(',1P,E11.4,',',E11.4,')',1X,0P,F7.4,4X,A)
99998 Format (1X,I2,1X,'(',1P,E11.4,',',E11.4,')',1X,0P,F7.4,1X,1P,E8.1)
99997 Format (1X,3X,'(',1P,E11.4,',',E11.4,')')
99996 Format (1X,A,I4)

End Program f08npfe
```