Program f08kafe

!     F08KAF Example Program Text

!     Mark 28.3 Release. NAG Copyright 2022.

!     .. Use Statements ..
      Use nag_library, Only: dgelss, dnrm2, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nb = 64, nin = 5, nout = 6
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: rcond, rnorm
      Integer                          :: i, info, lda, lwork, m, n, rank
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:), s(:), work(:)
!     .. Executable Statements ..
      Write (nout,*) 'F08KAF Example Program Results'
      Write (nout,*)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) m, n
      lda = m
      lwork = 3*n + nb*(m+n)
      Allocate (a(lda,n),b(m),s(n),work(lwork))

!     Read A and B from data file

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

!     Choose RCOND to reflect the relative accuracy of the input data

      rcond = 0.01_nag_wp

!     Solve the least squares problem min( norm2(b - Ax) ) for the x
!     of minimum norm.

!     The NAG name equivalent of dgelss is f08kaf
      Call dgelss(m,n,1,a,lda,b,m,s,rcond,rank,work,lwork,info)

      If (info==0) Then

!       Print solution

        Write (nout,*) 'Least squares solution'
        Write (nout,99999) b(1:n)

!       Print the effective rank of A

        Write (nout,*)
        Write (nout,*) 'Tolerance used to estimate the rank of A'
        Write (nout,99998) rcond
        Write (nout,*) 'Estimated rank of A'
        Write (nout,99997) rank

!       Print singular values of A

        Write (nout,*)
        Write (nout,*) 'Singular values of A'
        Write (nout,99999) s(1:n)

!       Compute and print estimate of the square root of the
!       residual sum of squares

        If (rank==n) Then
!         The NAG name equivalent of dnrm2 is f06ejf
          rnorm = dnrm2(m-n,b(n+1),1)
          Write (nout,*)
          Write (nout,*) 'Square root of the residual sum of squares'
          Write (nout,99998) rnorm
        End If
      Else
        Write (nout,*) 'The SVD algorithm failed to converge'
      End If

99999 Format (1X,7F11.4)
99998 Format (3X,1P,E11.2)
99997 Format (1X,I6)
    End Program f08kafe