PROGRAM f08cvfe

!      F08CVF Example Program Text

!      Mark 23 Release. NAG Copyright 2011.

!      .. Use Statements ..
       USE nag_library, ONLY : nag_wp, zgerqf, ztrtrs, zunmrq
!      .. Implicit None Statement ..
       IMPLICIT NONE
!      .. Parameters ..
       COMPLEX (KIND=nag_wp), PARAMETER :: zero = (0.0_nag_wp,0.0_nag_wp)
       INTEGER, PARAMETER              :: nb = 64, nin = 5, nout = 6
!      .. Local Scalars ..
       INTEGER                         :: i, info, lda, lwork, m, n
!      .. Local Arrays ..
       COMPLEX (KIND=nag_wp), ALLOCATABLE :: a(:,:), b(:), tau(:), work(:), x(:)
!      .. Executable Statements ..
       WRITE (nout,*) 'F08CVF Example Program Results'
       WRITE (nout,*)
!      Skip heading in data file
       READ (nin,*)
       READ (nin,*) m, n
       lda = m
       lwork = nb*m
       ALLOCATE (a(lda,n),b(m),tau(m),work(lwork),x(n))

!      Read the matrix A and the vector b from data file

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

!      Compute the RQ factorization of A
!      The NAG name equivalent of zgerqf is f08cvf
       CALL zgerqf(m,n,a,lda,tau,work,lwork,info)

!      Copy the m-element vector b into elements x(n-m+1), ..., x(n) of x

       x(n-m+1:n) = b(1:m)

!      Solve R*y2 = b, storing the result in x2
!      The NAG name equivalent of ztrtrs is f07tsf
       CALL ztrtrs('Upper','No transpose','Non-Unit',m,1,a(1,n-m+1),lda, &
          x(n-m+1),m,info)

       IF (info>0) THEN
          WRITE (nout,*) 'The upper triangular factor, R, of A is singular, '
          WRITE (nout,*) 'the least squares solution could not be computed'
       ELSE

!         Set y1 to zero (stored in x(1:n-m))

          x(1:n-m) = zero

!         Compute minimum-norm solution x = (Q**H)*y
!         The NAG name equivalent of zunmrq is f08cxf
          CALL zunmrq('Left','Conjugate transpose',n,1,m,a,lda,tau,x,n,work, &
             lwork,info)

!         Print minimum-norm solution

          WRITE (nout,*) 'Minimum-norm solution'
          WRITE (nout,99999) x(1:n)
       END IF

99999  FORMAT (4(' (',F8.4,',',F8.4,')':))
    END PROGRAM f08cvfe