```    Program f08ngfe

!     F08NGF Example Program Text

!     Mark 25 Release. NAG Copyright 2014.

!     .. Use Statements ..
Use nag_library, Only: dgehrd, dhsein, dhseqr, dormhr, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Complex (Kind=nag_wp)            :: eig, eig1
Real (Kind=nag_wp)               :: thresh
Integer                          :: i, ifail, info, j, k, lda, ldc, ldh, &
ldvl, ldz, lwork, m, n
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), c(:,:), h(:,:), tau(:),      &
vl(:,:), wi(:), work(:), wr(:), z(:,:)
Integer, Allocatable             :: ifaill(:), ifailr(:)
Logical, Allocatable             :: select(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: aimag, cmplx, real
!     .. Executable Statements ..
Write (nout,*) 'F08NGF Example Program Results'
!     Skip heading in data file
ldz = 1
lda = n
ldc = n
ldh = n
ldvl = n
lwork = 64*n
Allocate (a(lda,n),c(ldc,n),h(ldh,n),tau(n),vl(ldvl,n),wi(n), &
work(lwork),wr(n),z(ldz,1),ifaill(n),ifailr(n),select(n))

!     Read A from data file

!     Reduce A to upper Hessenberg form H = (Q**T)*A*Q
!     The NAG name equivalent of dgehrd is f08nef
Call dgehrd(n,1,n,a,lda,tau,work,lwork,info)

!     Copy A to H
h(1:n,1:n) = a(1:n,1:n)

!     Calculate the eigenvalues of H (same as A)
!     The NAG name equivalent of dhseqr is f08pef
Call dhseqr('Eigenvalues','No vectors',n,1,n,h,ldh,wr,wi,z,ldz,work, &
lwork,info)

Write (nout,*)
If (info>0) Then
Write (nout,*) 'Failure to converge.'
Else
Write (nout,*) 'Eigenvalues'
Write (nout,99999)(' (',wr(i),',',wi(i),')',i=1,n)

Do i = 1, n
select(i) = wr(i) < thresh
End Do

!       Calculate the eigenvectors of H (as specified by SELECT),
!       storing the result in C
!       The NAG name equivalent of dhsein is f08pkf
Call dhsein('Right','QR','No initial vectors',select,n,a,lda,wr,wi,vl, &
ldvl,c,ldc,n,m,work,ifaill,ifailr,info)

!       Calculate the eigenvectors of A = Q * (eigenvectors of H)
!       The NAG name equivalent of dormhr is f08ngf
Call dormhr('Left','No transpose',n,m,1,n,a,lda,tau,c,ldc,work,lwork, &
info)

!       Print eigenvectors

Write (nout,*)
Flush (nout)

!       Normalize selected eigenvectors
j = 0
k = 1
Do While (k<=n)
If (select(k)) Then
j = j + 1
If (wi(k)==0.0_nag_wp) Then
Do i = 2, n
c(i,j) = c(i,j)/c(1,j)
End Do
c(1,j) = 1.0_nag_wp
Else
eig1 = cmplx(c(1,j),c(1,j+1),kind=nag_wp)
c(1,j) = 1.0_nag_wp
c(1,j+1) = 0.0_nag_wp
Do i = 2, n
eig = cmplx(c(i,j),c(i,j+1),kind=nag_wp)
eig = eig/eig1
c(i,j) = real(eig)
c(i,j+1) = aimag(eig)
End Do
j = j + 1
k = k + 1
End If
End If
k = k + 1
End Do

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,m,c,ldc,'Contents of array C',ifail)

End If

99999 Format (1X,A,F8.4,A,F8.4,A)
End Program f08ngfe
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