NAG Library Manual, Mark 28.7
```    Program f08gufe

!     F08GUF Example Program Text

!     Mark 28.7 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: dstebz, dznrm2, nag_wp, x04dbf, zhptrd, zstein,   &
zupmtr
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Real (Kind=nag_wp), Parameter    :: zero = 0.0E0_nag_wp
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Complex (Kind=nag_wp)            :: scal
Real (Kind=nag_wp)               :: vl, vu
Integer                          :: i, ifail, info, j, k, ldc, m, n,     &
nsplit
Character (1)                    :: uplo
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: ap(:), c(:,:), tau(:), work(:)
Real (Kind=nag_wp), Allocatable  :: d(:), e(:), rwork(:), w(:)
Integer, Allocatable             :: iblock(:), ifailv(:), isplit(:),     &
iwork(:)
Character (1)                    :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
Intrinsic                        :: abs, conjg, maxloc
!     .. Executable Statements ..
Write (nout,*) 'F08GUF Example Program Results'
!     Skip heading in data file
ldc = n
Allocate (ap(n*(n+1)/2),c(ldc,n),tau(n),work(n),d(n),e(n),rwork(5*n),w(n &
),iblock(n),ifailv(n),isplit(n),iwork(3*n))

!     Read A from data file

If (uplo=='U') Then
Else If (uplo=='L') Then
End If

!     Reduce A to tridiagonal form T = (Q**H)*A*Q
!     The NAG name equivalent of zhptrd is f08gsf
Call zhptrd(uplo,n,ap,d,e,tau,info)

!     Calculate the two smallest eigenvalues of T (same as A)

!     The NAG name equivalent of dstebz is f08jjf
Call dstebz('I','B',n,vl,vu,1,2,zero,d,e,m,nsplit,w,iblock,isplit,rwork, &
iwork,info)

Write (nout,*)
If (info>0) Then
Write (nout,*) 'Failure to converge.'
Else
Write (nout,*) 'Eigenvalues'
Write (nout,99999) w(1:m)

!       Calculate the eigenvectors of T, storing the result in C
!       The NAG name equivalent of zstein is f08jxf
Call zstein(n,d,e,m,w,iblock,isplit,c,ldc,rwork,iwork,ifailv,info)

If (info>0) Then
Write (nout,*) 'Failure to converge.'
Else

!         Calculate the eigenvectors of A = Q * (eigenvectors of T)
!         The NAG name equivalent of zupmtr is f08guf
Call zupmtr('Left',uplo,'No transpose',n,m,ap,tau,c,ldc,work,info)

!         Print eigenvectors

Write (nout,*)
Flush (nout)

!         Normalize the eigenvectors, largest element real
Do i = 1, m
rwork(1:n) = abs(c(1:n,i))
k = maxloc(rwork(1:n),1)
scal = conjg(c(k,i))/abs(c(k,i))/dznrm2(n,c(1,i),1)
c(1:n,i) = c(1:n,i)*scal
End Do

!         ifail: behaviour on error exit
!                =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04dbf('General',' ',n,m,c,ldc,'Bracketed','F7.4',              &
'Eigenvectors','Integer',rlabs,'Integer',clabs,80,0,ifail)

End If
End If

99999 Format (8X,4(F7.4,11X,:))
End Program f08gufe
```