NAG Library Manual, Mark 28.5
```    Program f08hefe

!     F08HEF Example Program Text

!     Mark 28.5 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: dsbtrd, dsteqr, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Integer                          :: i, ifail, info, j, kd, ldab, ldq, n
Character (1)                    :: uplo
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: ab(:,:), d(:), e(:), q(:,:), work(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, min
!     .. Executable Statements ..
Write (nout,*) 'F08HEF Example Program Results'
!     Skip heading in data file
ldab = kd + 1
ldq = n
Allocate (ab(ldab,n),d(n),e(n-1),q(ldq,n),work(2*n-2))

!     Read A from data file

If (uplo=='U') Then
Do i = 1, n
End Do
Else If (uplo=='L') Then
Do i = 1, n
End Do
End If

!     Reduce A to tridiagonal form T = (Q**T)*A*Q (and form Q)
!     The NAG name equivalent of dsbtrd is f08hef
Call dsbtrd('V',uplo,n,kd,ab,ldab,d,e,q,ldq,work,info)

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

!       Standardize the eigenvectors so that first elements are non-negative.
Do i = 1, n
If (q(1,i)<0.0_nag_wp) Then
q(1:n,i) = -q(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,q,ldq,'Eigenvectors',ifail)

End If

99999 Format (3X,(8F8.4))
End Program f08hefe
```