Program f08kcfe ! F08KCF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. 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, & rank ! .. 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) 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 f08kcfe