NAG Library Manual, Mark 29.3
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description
    Program f08kcfe

!     F08KCF Example Program Text

!     Mark 29.3 Release. NAG Copyright 2023.

!     .. Use Statements ..
      Use nag_library, Only: dgelsd, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: rcond
      Integer                          :: i, info, lda, liwork, lwork, m, n,   &
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), b(:), s(:), work(:)
      Real (Kind=nag_wp)               :: lw(1)
      Integer, Allocatable             :: iwork(:)
      Integer                          :: liw(1)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: nint
!     .. Executable Statements ..
      Write (nout,*) 'F08KCF Example Program Results'
      Write (nout,*)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) m, n
      lda = m
      Allocate (a(lda,n),b(n),s(m))

!     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

!     Call f08kcf/dgelsd in workspace query mode.
      lwork = -1
!     The NAG name equivalent of dgelsd is f08kcf
      Call dgelsd(m,n,1,a,lda,b,n,s,rcond,rank,lw,lwork,liw,info)
      lwork = nint(lw(1))
      liwork = liw(1)
      Allocate (work(lwork),iwork(liwork))

!     Now Solve the least squares problem min( norm2(b - Ax) ) for the
!     x of minimum norm.
      Call dgelsd(m,n,1,a,lda,b,n,s,rcond,rank,work,lwork,iwork,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:m)
        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 f08kcfe