Program f08chfe

!     F08CHF Example Program Text

!     Mark 29.1 Release. NAG Copyright 2023.

!     .. Use Statements ..
      Use nag_library, Only: dgerqf, dormrq, dtrtrs, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Real (Kind=nag_wp), Parameter    :: zero = 0.0E0_nag_wp
      Integer, Parameter               :: nb = 64, nin = 5, nout = 6
!     .. Local Scalars ..
      Integer                          :: i, info, lda, lwork, m, n
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:), tau(:), work(:), x(:)
!     .. Executable Statements ..
      Write (nout,*) 'F08CHF 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 dgerqf is f08chf
      Call dgerqf(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 dtrtrs is f07tef
      Call dtrtrs('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

        x(1:n-m) = zero

!       Compute the minimum-norm solution x = (Q**T)*y
!       The NAG name equivalent of dormrq is f08ckf
        Call dormrq('Left','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 (1X,8F9.4)
    End Program f08chfe