NAG Library Manual, Mark 29.2
```    Program f08jgfe

!     F08JGF Example Program Text

!     Mark 29.2 Release. NAG Copyright 2023.

!     .. Use Statements ..
Use nag_library, Only: blas_damax_val, dpteqr, 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, ldz, n
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: d(:), e(:), work(:), z(:,:)
!     .. Executable Statements ..
Write (nout,*) 'F08JGF Example Program Results'
!     Skip heading in data file
ldz = n
Allocate (d(n),e(n-1),work(4*n),z(ldz,n))

!     Read T from data file

!     Calculate all the eigenvalues and eigenvectors of T
!     The NAG name equivalent of dpteqr is f08jgf
Call dpteqr('I',n,d,e,z,ldz,work,info)

Write (nout,*)
If (info>0 .And. info<=n) Then
Write (nout,*) 'T is not positive definite.'
Else If (info>n) 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 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 f08jgfe
```