NAG Library Manual, Mark 29
```    Program f08fffe

!     F08FFF Example Program Text

!     Mark 29.0 Release. NAG Copyright 2023.

!     .. Use Statements ..
Use nag_library, Only: blas_damax_val, dorgtr, dsteqr, dsytrd, f06qff,   &
nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Real (Kind=nag_wp), Parameter    :: zero = 0.0_nag_wp
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: r
Integer                          :: i, ifail, info, k, lda, ldz, lwork,  &
n
Character (1)                    :: uplo
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), d(:), e(:), tau(:), work(:), &
z(:,:)
!     .. Executable Statements ..
Write (nout,*) 'F08FFF Example Program Results'
!     Skip heading in data file
lda = n
ldz = n
lwork = 64*n
Allocate (a(lda,n),d(n),e(n),tau(n),work(lwork),z(ldz,n))

!     Read A from data file

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

!     Reduce A to tridiagonal form T = (Q**T)*A*Q
!     The NAG name equivalent of dsytrd is f08fef
Call dsytrd(uplo,n,a,lda,d,e,tau,work,lwork,info)

!     Copy A into Z
Call f06qff(uplo,n,n,a,lda,z,ldz)

!     Form Q explicitly, storing the result in Z
!     The NAG name equivalent of dorgtr is f08fff
Call dorgtr(uplo,n,z,ldz,tau,work,lwork,info)

!     Calculate all the eigenvalues and eigenvectors of A
!     The NAG name equivalent of dsteqr is f08jef
Call dsteqr('V',n,d,e,z,ldz,work,info)

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

!       Print eigenvalues and eigenvectors

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

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

End If

99999 Format (3X,(8F8.4))
End Program f08fffe
```