```    Program f08fafe

!     F08FAF Example Program Text

!     Mark 26 Release. NAG Copyright 2016.

!     .. Use Statements ..
Use nag_library, Only: blas_damax_val, ddisna, dsyev, nag_wp, x02ajf,    &
x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Real (Kind=nag_wp), Parameter    :: zero = 0.0_nag_wp
Integer, Parameter               :: nb = 64, nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: eerrbd, eps, r
Integer                          :: i, ifail, info, k, lda, lwork, n
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), rcondz(:), w(:), work(:),    &
zerrbd(:)
Real (Kind=nag_wp)               :: dummy(1)
!     .. Intrinsic Procedures ..
Intrinsic                        :: abs, max, nint
!     .. Executable Statements ..
Write (nout,*) 'F08FAF Example Program Results'
Write (nout,*)
!     Skip heading in data file
lda = n
Allocate (a(lda,n),rcondz(n),w(n),zerrbd(n))

!     Use routine workspace query to get optimal workspace.
!     The NAG name equivalent of dsyev is f08faf
lwork = -1
Call dsyev('Vectors','Upper',n,a,lda,w,dummy,lwork,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 upper triangular part of the matrix A from data file

!     Solve the symmetric eigenvalue problem
!     The NAG name equivalent of dsyev is f08faf
Call dsyev('Vectors','Upper',n,a,lda,w,work,lwork,info)

If (info==0) Then

!       Print solution

Write (nout,*) 'Eigenvalues'
Write (nout,99999) w(1:n)
Flush (nout)

!       Normalize the eigenvectors: largest element positive
Do i = 1, n
Call blas_damax_val(n,a(1,i),1,k,r)
If (a(k,i)<zero) Then
a(1:n,i) = -a(1:n,i)
End If
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,n,a,lda,'Eigenvectors',ifail)

!       Get the machine precision, EPS and compute the approximate
!       error bound for the computed eigenvalues.  Note that for
!       the 2-norm, max( abs(W(i)) ) = norm(A), and since the
!       eigenvalues are returned in ascending order
!       max( abs(W(i)) ) = max( abs(W(1)), abs(W(n)))

eps = x02ajf()
eerrbd = eps*max(abs(w(1)),abs(w(n)))

!       Call DDISNA (F08FLF) to estimate reciprocal condition
!       numbers for the eigenvectors
Call ddisna('Eigenvectors',n,n,w,rcondz,info)

!       Compute the error estimates for the eigenvectors

Do i = 1, n
zerrbd(i) = eerrbd/rcondz(i)
End Do

!       Print the approximate error bounds for the eigenvalues
!       and vectors

Write (nout,*)
Write (nout,*) 'Error estimate for the eigenvalues'
Write (nout,99998) eerrbd
Write (nout,*)
Write (nout,*) 'Error estimates for the eigenvectors'
Write (nout,99998) zerrbd(1:n)
Else
Write (nout,99997) 'Failure in DSYEV. INFO =', info
End If

99999 Format (3X,(8F8.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4)
End Program f08fafe
```