NAG Library Manual, Mark 28.5
```    Program f08tqfe

!     F08TQF Example Program Text

!     Mark 28.5 Release. NAG Copyright 2022.

!     .. Use Statements ..
Use nag_library, Only: f06udf, nag_wp, x02ajf, zhpgvd, ztpcon
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
Character (1), Parameter         :: uplo = 'U'
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: anorm, bnorm, eps, rcond, rcondb, t1
Integer                          :: aplen, i, info, j, liwork, lrwork,   &
lwork, n
!     .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: ap(:), bp(:), work(:)
Complex (Kind=nag_wp)            :: dummy(1,1)
Real (Kind=nag_wp), Allocatable  :: eerbnd(:), rwork(:), w(:)
Real (Kind=nag_wp)               :: rdum(1)
Integer                          :: idum(1)
Integer, Allocatable             :: iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: abs, max, nint, real
!     .. Executable Statements ..
Write (nout,*) 'F08TQF Example Program Results'
Write (nout,*)
!     Skip heading in data file
aplen = (n*(n+1))/2
Allocate (ap(aplen),bp(aplen),eerbnd(n),w(n))

!     Use routine workspace query to get optimal workspace.
lwork = -1
liwork = -1
lrwork = -1
!     The NAG name equivalent of zhpgvd is f08tqf
Call zhpgvd(2,'No vectors',uplo,n,ap,bp,w,dummy,1,dummy,lwork,rdum,      &
lrwork,idum,liwork,info)

!     Make sure that there is at least the minimum workspace
lwork = max(2*n,nint(real(dummy(1,1))))
lrwork = max(n,nint(rdum(1)))
liwork = max(1,idum(1))
Allocate (work(lwork),rwork(lrwork),iwork(liwork))

!     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

!     Compute the one-norms of the symmetric matrices A and B

anorm = f06udf('One norm',uplo,n,ap,rwork)
bnorm = f06udf('One norm',uplo,n,bp,rwork)

!     Solve the generalized symmetric eigenvalue problem
!     A*B*x = lambda*x (itype = 2)

!     The NAG name equivalent of zhpgvd is f08tqf
Call zhpgvd(2,'No vectors',uplo,n,ap,bp,w,dummy,1,work,lwork,rwork,      &
lrwork,iwork,liwork,info)

If (info==0) Then

!       Print solution

Write (nout,*) 'Eigenvalues'
Write (nout,99999) w(1:n)

!       Call ZTPCON (F07UUF) to estimate the reciprocal condition
!       number of the Cholesky factor of B.  Note that:
!       cond(B) = 1/rcond**2.  ZTPCON requires WORK and RWORK to be
!       of length at least 2*n and n respectively

Call ztpcon('One norm',uplo,'Non-unit',n,bp,rcond,work,rwork,info)

!       Print the reciprocal condition number of B

rcondb = rcond**2
Write (nout,*)
Write (nout,*) 'Estimate of reciprocal condition number for B'
Write (nout,99998) rcondb

!       Get the machine precision, eps, and if rcondb is not less
!       than eps**2, compute error estimates for the eigenvalues

eps = x02ajf()
If (rcond>=eps) Then
t1 = anorm*bnorm
Do i = 1, n
eerbnd(i) = t1 + abs(w(i))/rcondb
End Do

!         Print the approximate error bounds for the eigenvalues

Write (nout,*)
Write (nout,*) 'Error estimates (relative to machine precision)'
Write (nout,*) 'for the eigenvalues:'
Write (nout,99998) eerbnd(1:n)
Else
Write (nout,*)
Write (nout,*) 'B is very ill-conditioned, error ',                  &
'estimates have not been computed'
End If
Else If (info>n .And. info<=2*n) Then
i = info - n
Write (nout,99997) 'The leading minor of order ', i,                   &
' of B is not positive definite'
Else
Write (nout,99996) 'Failure in ZHPGVD. INFO =', info
End If

99999 Format (3X,(6F11.4))
99998 Format (4X,1P,6E11.1)
99997 Format (1X,A,I4,A)
99996 Format (1X,A,I4)
End Program f08tqfe
```