    PROGRAM f08vafe

!      F08VAF Example Program Text

!      Mark 23 Release. NAG Copyright 2011.

!      .. 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
       READ (nin,*)
       READ (nin,*) m, n, p
       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

       READ (nin,*) (a(i,1:n),i=1,m)
       READ (nin,*) (b(i,1:n),i=1,p)

!      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', &
             'Non singular 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
