NAG Library Manual, Mark 27.3
Interfaces:  FL   CL   CPP   AD
```    Program f08fgfe

!     F08FGF Example Program Text

!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
Use nag_library, Only: dormtr, dstebz, dstein, dsytrd, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Real (Kind=nag_wp), Parameter    :: zero = 0.0E0_nag_wp
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: vl, vu
Integer                          :: i, ifail, info, lda, ldc, lwork, m,  &
n, nsplit
Character (1)                    :: uplo
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), c(:,:), d(:), e(:), tau(:),  &
w(:), work(:)
Integer, Allocatable             :: iblock(:), ifailv(:), isplit(:),     &
iwork(:)
!     .. Executable Statements ..
Write (nout,*) 'F08FGF Example Program Results'
!     Skip heading in data file
lda = n
ldc = n
lwork = 64*n
Allocate (a(lda,n),c(ldc,n),d(n),e(n),tau(n),w(n),work(lwork),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**T)*A*Q
Call dsytrd(uplo,n,a,lda,d,e,tau,work,lwork,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,work,  &
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 dstein is f08jkf
Call dstein(n,d,e,m,w,iblock,isplit,c,ldc,work,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 dormtr is f08fgf
Call dormtr('Left',uplo,'No transpose',n,m,a,lda,tau,c,ldc,work,     &
lwork,info)

!         Print eigenvectors

Write (nout,*)
Flush (nout)

!         ifail: behaviour on error exit
!                =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04caf('General',' ',n,m,c,ldc,'Eigenvectors',ifail)

End If
End If

99999 Format (3X,(9F8.4))
End Program f08fgfe
```