```    Program f08sbfe

!     F08SBF Example Program Text

!     Mark 25 Release. NAG Copyright 2014.

!     .. Use Statements ..
Use nag_library, Only: dsygvx, nag_wp, 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)               :: abstol, vl, vu
Integer                          :: i, ifail, il, info, iu, lda, ldb,    &
ldz, lwork, m, n
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:,:), w(:), work(:), z(:,:)
Real (Kind=nag_wp)               :: dummy(1)
Integer, Allocatable             :: iwork(:), jfail(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max, nint
!     .. Executable Statements ..
Write (nout,*) 'F08SBF Example Program Results'
Write (nout,*)
!     Skip heading in data file
lda = n
ldb = n
ldz = n
m = n
Allocate (a(lda,n),b(ldb,n),w(n),z(ldz,m),iwork(5*n),jfail(n))

!     Read the lower and upper bounds of the interval to be searched.

!     Use routine workspace query to get optimal workspace.
lwork = -1
!     The NAG name equivalent of dsygvx is f08sbf
Call dsygvx(1,'Vectors','Values in range','Upper',n,a,lda,b,ldb,vl,vu, &
il,iu,abstol,m,w,z,ldz,dummy,lwork,iwork,jfail,info)

!     Make sure that there is enough workspace for blocksize nb.
lwork = max((nb+3)*n,nint(dummy(1)))
Allocate (work(lwork))

!     Read the upper triangular parts of the matrices A and B

!     Set the absolute error tolerance for eigenvalues.  With ABSTOL
!     set to zero, the default value is used instead

abstol = zero

!     Solve the generalized symmetric eigenvalue problem
!     A*x = lambda*B*x (ITYPE = 1)

!     The NAG name equivalent of dsygvx is f08sbf
Call dsygvx(1,'Vectors','Values in range','Upper',n,a,lda,b,ldb,vl,vu, &
il,iu,abstol,m,w,z,ldz,work,lwork,iwork,jfail,info)

If (info>=0 .And. info<=n) Then

!       Print solution

Write (nout,99999) 'Number of eigenvalues found =', m
Write (nout,*)
Write (nout,*) 'Eigenvalues'
Write (nout,99998) w(1:m)
Flush (nout)

!       Normalize the eigenvectors
Do i = 1, m
z(1:n,i) = z(1:n,i)/z(1,i)
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,m,z,ldz,'Selected eigenvectors',ifail)

If (info>0) Then
Write (nout,99999) 'INFO eigenvectors failed to converge, INFO =', &
info
Write (nout,*) 'Indices of eigenvectors that did not converge'
Write (nout,99997) jfail(1:m)
End If
Else If (info>n .And. info<=2*n) Then
i = info - n
Write (nout,99996) 'The leading minor of order ', i, &
' of B is not positive definite'
Else
Write (nout,99999) 'Failure in DSYGVX. INFO =', info
End If

99999 Format (1X,A,I5)
99998 Format (3X,(8F8.4))
99997 Format (3X,(8I8))
99996 Format (1X,A,I4,A)
End Program f08sbfe
```