Program f08khfe ! F08KHF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: ddisna, dgejsv, nag_wp, x02ajf, x04caf ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nb = 64, nin = 5, nout = 6 ! .. Local Scalars .. Real (Kind=nag_wp) :: eps, serrbd Integer :: i, ifail, info, j, lda, ldu, ldv, & lwork, m, n ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: a(:,:), rcondu(:), rcondv(:), s(:), & u(:,:), v(:,:), work(:) Integer, Allocatable :: iwork(:) ! .. Intrinsic Procedures .. Intrinsic :: abs, max ! .. Executable Statements .. Write (nout,*) 'F08KHF Example Program Results' Write (nout,*) Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) m, n lda = m ldu = m ldv = n lwork = max(3*n+n*n+m,3*n+n*n+n*nb,7) Allocate (a(lda,n),rcondu(m),rcondv(m),s(n),u(ldu,n),v(ldv,n), & work(lwork),iwork(m+3*n)) ! Read the m by n matrix A from data file Read (nin,*)((a(i,j),j=1,n),i=1,m) ! Compute the singular values and left and right singular vectors ! of A (A = U*S*V^T, m.ge.n) ! The NAG name equivalent of dgejsv is f08khf Call dgejsv('E','U','V','R','N','N',m,n,a,lda,s,u,ldu,v,ldv,work,lwork, & iwork,info) If (info==0) Then ! Compute the approximate error bound for the computed singular values ! using the 2-norm, s(1) = norm(A), and machine precision, eps. eps = x02ajf() serrbd = eps*s(1) ! Print solution If (abs(work(1)-work(2))<2.0_nag_wp*eps) Then ! No scaling required Write (nout,'(1X,A)') 'Singular values' Write (nout,99999)(s(j),j=1,n) Else Write (nout,'(/1X,A)') 'Scaled singular values' Write (nout,99999)(s(j),j=1,n) Write (nout,'(/1X,A)') 'For true singular values, multiply by a/b,' Write (nout,99996) ' where a = ', work(1), ' and b = ', work(2) End If ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft Write (nout,*) Flush (nout) ifail = 0 Call x04caf('General',' ',m,n,u,ldu,'Left singular vectors',ifail) Write (nout,*) Flush (nout) ifail = 0 Call x04caf('General',' ',n,n,v,ldv,'Right singular vectors',ifail) ! Call DDISNA (F08FLF) to estimate reciprocal condition numbers for ! the singular vectors. Call ddisna('Left',m,n,s,rcondu,info) Call ddisna('Right',m,n,s,rcondv,info) ! Print the approximate error bounds for the singular values ! and vectors. Write (nout,*) Write (nout,'(/1X,A)') & 'Estimate of the condition number of column equilibrated A' Write (nout,99998) work(3) Write (nout,'(/1X,A)') 'Error estimate for the singular values' Write (nout,99998) serrbd Write (nout,'(/1X,A)') 'Error estimates for left singular vectors' Write (nout,99998)(serrbd/rcondu(i),i=1,n) Write (nout,'(/1X,A)') 'Error estimates for right singular vectors' Write (nout,99998)(serrbd/rcondv(i),i=1,n) Else Write (nout,99997) 'Failure in DGEJSV. INFO =', info End If 99999 Format (3X,8F8.4) 99998 Format (4X,1P,6E11.1) 99997 Format (1X,A,I4) 99996 Format (1X,2(A,1P,E13.5)) End Program f08khfe