```    Program f08vafe

!     F08VAF Example Program Text

!     Mark 27.0 Release. NAG Copyright 2019.

!     .. Use Statements ..
Use nag_library, Only: dggsvd, dtrcon, nag_wp, x02ajf, x04cbf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: eps, rcond, serrbd
Integer                          :: i, ifail, info, irank, j, k, l, lda, &
ldb, ldq, ldu, ldv, m, n, p
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), alpha(:), b(:,:), beta(:),   &
q(:,:), u(:,:), v(:,:), work(:)
Integer, Allocatable             :: iwork(:)
Character (1)                    :: clabs(1), rlabs(1)
!     .. Executable Statements ..
Write (nout,*) 'F08VAF Example Program Results'
Write (nout,*)
Flush (nout)
!     Skip heading in data file
lda = m
ldb = p
ldq = n
ldu = m
ldv = p
Allocate (a(lda,n),alpha(n),b(ldb,n),beta(n),q(ldq,n),u(ldu,m),v(ldv,p), &
work(m+3*n),iwork(n))

!     Read the m by n matrix A and p by n matrix B from data file

!     Compute the generalized singular value decomposition of (A, B)
!     (A = U*D1*(0 R)*(Q**T), B = V*D2*(0 R)*(Q**T), m>=n)
!     The NAG name equivalent of dggsvd is f08vaf
Call dggsvd('U','V','Q',m,n,p,k,l,a,lda,b,ldb,alpha,beta,u,ldu,v,ldv,q,  &
ldq,work,iwork,info)

If (info==0) Then

!       Print solution

irank = k + l
Write (nout,*) 'Number of infinite generalized singular values (K)'
Write (nout,99999) k
Write (nout,*) 'Number of finite generalized singular values (L)'
Write (nout,99999) l
Write (nout,*) 'Numerical rank of (A**T B**T)**T (K+L)'
Write (nout,99999) irank
Write (nout,*)
Write (nout,*) 'Finite generalized singular values'
Write (nout,99998)(alpha(j)/beta(j),j=k+1,irank)

Write (nout,*)
Flush (nout)

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04cbf('General',' ',m,m,u,ldu,'1P,E12.4','Orthogonal matrix U',  &
'Integer',rlabs,'Integer',clabs,80,0,ifail)

Write (nout,*)
Flush (nout)

Call x04cbf('General',' ',p,p,v,ldv,'1P,E12.4','Orthogonal matrix V',  &
'Integer',rlabs,'Integer',clabs,80,0,ifail)

Write (nout,*)
Flush (nout)

Call x04cbf('General',' ',n,n,q,ldq,'1P,E12.4','Orthogonal matrix Q',  &
'Integer',rlabs,'Integer',clabs,80,0,ifail)

Write (nout,*)
Flush (nout)

Call x04cbf('Upper triangular','Non-unit',irank,irank,a(1,n-irank+1),  &
lda,'1P,E12.4','Nonsingular upper triangular matrix R','Integer',    &
rlabs,'Integer',clabs,80,0,ifail)

!       Call DTRCON (F07TGF) to estimate the reciprocal condition
!       number of R

Call dtrcon('Infinity-norm','Upper','Non-unit',irank,a(1,n-irank+1),   &
lda,rcond,work,iwork,info)

Write (nout,*)
Write (nout,*) 'Estimate of reciprocal condition number for R'
Write (nout,99997) rcond
Write (nout,*)

!       So long as irank = n, get the machine precision, eps, and
!       compute the approximate error bound for the computed
!       generalized singular values

If (irank==n) Then
eps = x02ajf()
serrbd = eps/rcond
Write (nout,*) 'Error estimate for the generalized singular values'
Write (nout,99997) serrbd
Else
Write (nout,*) '(A**T B**T)**T is not of full rank'
End If
Else
Write (nout,99996) 'Failure in DGGSVD. INFO =', info
End If

99999 Format (1X,I5)
99998 Format (3X,8(1P,E12.4))
99997 Format (1X,1P,E11.1)
99996 Format (1X,A,I4)
End Program f08vafe
```