NAG Library Manual, Mark 28.4
```    Program f08wqfe

!     F08WQF Example Program Text

!     Mark 28.4 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: dznrm2, m01daf, m01edf, nag_wp, x02ajf, x04daf,   &
zggev3
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Complex (Kind=nag_wp)            :: scal
Integer                          :: i, ifail, info, j, k, lda, ldb,      &
ldvr, lwork, n
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), alpha(:), b(:,:), beta(:), &
temp(:), vr(:,:), work(:)
Complex (Kind=nag_wp)            :: dummy(1,1)
Real (Kind=nag_wp), Allocatable  :: rwork(:)
Integer, Allocatable             :: irank(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: abs, all, conjg, maxloc, nint, real
!     .. Executable Statements ..
Write (nout,*) 'F08WQF Example Program Results'
Write (nout,*)
Flush (nout)
!     Skip heading in data file
lda = n
ldb = n
ldvr = n
Allocate (a(lda,n),alpha(n),b(ldb,n),beta(n),vr(ldvr,n),rwork(8*n))

!     Use routine workspace query to get optimal workspace.
lwork = -1
!     The NAG name equivalent of zggev3 is f08wqf
Call zggev3('No left vectors','Vectors (right)',n,a,lda,b,ldb,alpha,     &
beta,dummy,1,vr,ldvr,dummy,lwork,rwork,info)

lwork = nint(real(dummy(1,1)))
Allocate (work(lwork))

!     Read in the matrices A and B

!     Solve the generalized eigenvalue problem

!     The NAG name equivalent of zggev3 is f08wqf
Call zggev3('No left vectors','Vectors (right)',n,a,lda,b,ldb,alpha,     &
beta,dummy,1,vr,ldvr,work,lwork,rwork,info)

If (info>0) Then
Write (nout,*)
Write (nout,99999) 'Failure in ZGGEV3. INFO =', info
Else If (all(abs(beta(1:n))>x02ajf())) Then
!       Re-normalize the eigenvectors, largest absolute element real
Do i = 1, n
rwork(1:n) = abs(vr(1:n,i))
k = maxloc(rwork(1:n),1)
scal = conjg(vr(k,i))/rwork(k)/dznrm2(n,vr(1,i),1)
vr(1:n,i) = vr(1:n,i)*scal
End Do
alpha(1:n) = alpha(1:n)/beta(1:n)

!       Reorder eigenvalues by descending absolute value
rwork(1:n) = abs(alpha(1:n))
Allocate (irank(n),temp(n))
ifail = 0
Call m01daf(rwork,1,n,'Descending',irank,ifail)
Call m01edf(alpha,1,n,irank,ifail)

!       Reorder eigenvectors accordingly
Do j = 1, n
temp(1:n) = vr(j,1:n)
Call m01edf(temp,1,n,irank,ifail)
vr(j,1:n) = temp(1:n)
End Do

ifail = 0
Call x04daf('Gen',' ',1,n,alpha,1,'Eigenvalues:',ifail)
Write (nout,*)
Flush (nout)
Call x04daf('Gen',' ',n,n,vr,ldvr,'Right Eigenvectors (columns):',     &
ifail)
Else
Write (nout,*) 'Some of the eigenvalues are infinite.'
Write (nout,*)
Flush (nout)
ifail = 0
Call x04daf('Gen',' ',1,n,alpha,1,'Alpha',ifail)
Call x04daf('Gen',' ',1,n,beta,1,'Beta',ifail)
End If

99999 Format (1X,A,I4)
End Program f08wqfe
```