NAG Library Manual, Mark 27.3
```    Program f08tbfe

!     F08TBF Example Program Text

!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
Use nag_library, Only: blas_damax_val, dspgvx, nag_wp, x04caf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Real (Kind=nag_wp), Parameter    :: zero = 0.0E+0_nag_wp
Integer, Parameter               :: nin = 5, nout = 6
Character (1), Parameter         :: uplo = 'U'
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: abstol, r, vl, vu
Integer                          :: i, ifail, il, info, iu, j, k, ldz,   &
m, n
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: ap(:), bp(:), w(:), work(:), z(:,:)
Integer, Allocatable             :: iwork(:), jfail(:)
!     .. Executable Statements ..
Write (nout,*) 'F08TBF Example Program Results'
Write (nout,*)
!     Skip heading in data file
ldz = n
m = n
Allocate (ap((n*(n+1))/2),bp((n*(n+1))/2),w(n),work(8*n),z(ldz,m),iwork( &
5*n),jfail(n))

!     Read the lower and upper bounds of the interval to be searched,
!     and read the upper or lower triangular parts of the matrices A
!     and B from data file

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

!     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 dspgvx is f08tbf
Call dspgvx(1,'Vectors','Values in range',uplo,n,ap,bp,vl,vu,il,iu,      &
abstol,m,w,z,ldz,work,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, largest positive
Do i = 1, m
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,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 DSPGVX. 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 f08tbfe
```