Program f08kafe ! F08KAF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. 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