```    Program f08safe

!     F08SAF Example Program Text

!     Mark 27.0 Release. NAG Copyright 2019.

!     .. Use Statements ..
Use nag_library, Only: blas_damax_val, ddisna, dsygv, dtrcon, f06rcf,    &
nag_wp, x02ajf, 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)               :: anorm, bnorm, eps, r, rcond, rcondb, &
t1, t2, t3
Integer                          :: i, ifail, info, k, lda, ldb, lwork,  &
n
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:,:), eerbnd(:),           &
rcondz(:), w(:), work(:), zerbnd(:)
Real (Kind=nag_wp)               :: dummy(1)
Integer, Allocatable             :: iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: abs, max, nint
!     .. Executable Statements ..
Write (nout,*) 'F08SAF Example Program Results'
Write (nout,*)
!     Skip heading in data file
Read (nin,*)
Read (nin,*) n
lda = n
ldb = n
Allocate (a(lda,n),b(ldb,n),eerbnd(n),rcondz(n),w(n),zerbnd(n),iwork(n))

!     Use routine workspace query to get optimal workspace.
lwork = -1
!     The NAG name equivalent of dsygv is f08saf
Call dsygv(1,'Vectors','Upper',n,a,lda,b,ldb,w,dummy,lwork,info)

!     Make sure that there is enough workspace for block size nb.
lwork = max((nb+2)*n,nint(dummy(1)))
Allocate (work(lwork))

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

Read (nin,*)(a(i,i:n),i=1,n)
Read (nin,*)(b(i,i:n),i=1,n)

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

anorm = f06rcf('One norm','Upper',n,a,lda,work)
bnorm = f06rcf('One norm','Upper',n,b,ldb,work)

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

!     The NAG name equivalent of dsygv is f08saf
Call dsygv(1,'Vectors','Upper',n,a,lda,b,ldb,w,work,lwork,info)

If (info==0) Then

!       Print solution

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

Write (nout,*)
Flush (nout)

!       Normalize the eigenvectors, largest positive
Do i = 1, n
Call blas_damax_val(n,a(1,i),1,k,r)
If (a(k,i)<zero) Then
a(1:n,i) = -a(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,a,lda,'Eigenvectors',ifail)

!       Call DTRCON (F07TGF) to estimate the reciprocal condition
!       number of the Cholesky factor of B.  Note that:
!       cond(B) = 1/rcond**2

!       The NAG name equivalent of dtrcon is f07tgf
Call dtrcon('One norm','Upper','Non-unit',n,b,ldb,rcond,work,iwork,    &
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
Flush (nout)

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

eps = x02ajf()
If (rcond>=eps) Then

!         Call DDISNA (F08FLF) to estimate reciprocal condition
!         numbers for the eigenvectors of (A - lambda*B)

Call ddisna('Eigenvectors',n,n,w,rcondz,info)

!         Compute the error estimates for the eigenvalues and
!         eigenvectors

t1 = eps/rcondb
t2 = anorm/bnorm
t3 = t2/rcond
Do i = 1, n
eerbnd(i) = t1*(t2+abs(w(i)))
zerbnd(i) = t1*(t3+abs(w(i)))/rcondz(i)
End Do

!         Print the approximate error bounds for the eigenvalues
!         and vectors

Write (nout,*)
Write (nout,*) 'Error estimates for the eigenvalues'
Write (nout,99998) eerbnd(1:n)
Write (nout,*)
Write (nout,*) 'Error estimates for the eigenvectors'
Write (nout,99998) zerbnd(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 DSYGV. 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 f08safe
```