Program f08kdfe ! F08KDF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: ddisna, dgesdd, 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, lda, ldu, lwork, m, n ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: a(:,:), rcondu(:), rcondv(:), s(:), & u(:,:), uerrbd(:), verrbd(:), work(:) Real (Kind=nag_wp) :: dummy(1,1) Integer, Allocatable :: iwork(:) ! .. Intrinsic Procedures .. Intrinsic :: max, min, nint ! .. Executable Statements .. Write (nout,*) 'F08KDF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) Read (nin,*) m, n lda = m ldu = m Allocate (a(lda,n),rcondu(m),rcondv(m),s(m),u(ldu,m),uerrbd(m), & verrbd(m),iwork(8*min(m,n))) ! Use routine workspace query to get optimal workspace. lwork = -1 ! The NAG name equivalent of dgesdd is f08kdf Call dgesdd('Overwrite A by tranpose(V)',m,n,a,lda,s,u,ldu,dummy,1, & dummy,lwork,iwork,info) ! Make sure that there is enough workspace for blocksize nb. lwork = max((5*m+9)*m+n+nb*(m+n),nint(dummy(1,1))) Allocate (work(lwork)) ! Read the m by n matrix A from data file Read (nin,*)(a(i,1:n),i=1,m) ! Compute the singular values and left and right singular vectors ! of A (A = U*S*(V**T), m.le.n) ! The NAG name equivalent of dgesdd is f08kdf Call dgesdd('Overwrite A by tranpose(V)',m,n,a,lda,s,u,ldu,dummy,1,work, & lwork,iwork,info) If (info==0) Then ! Print solution Write (nout,*) 'Singular values' Write (nout,99999) s(1:m) Flush (nout) ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call x04caf('General',' ',m,m,u,ldu,'Left singular vectors',ifail) Write (nout,*) Flush (nout) Call x04caf('General',' ',m,n,a,lda,'Right singular vectors by row '// & '(first m rows of V**T)',ifail) ! Get the machine precision, EPS and compute the approximate ! error bound for the computed singular values. Note that for ! the 2-norm, S(1) = norm(A) eps = x02ajf() serrbd = eps*s(1) ! 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) ! Compute the error estimates for the singular vectors Do i = 1, m uerrbd(i) = serrbd/rcondu(i) verrbd(i) = serrbd/rcondv(i) End Do ! Print the approximate error bounds for the singular values ! and vectors Write (nout,*) Write (nout,*) 'Error estimate for the singular values' Write (nout,99998) serrbd Write (nout,*) Write (nout,*) 'Error estimates for the left singular vectors' Write (nout,99998) uerrbd(1:m) Write (nout,*) Write (nout,*) 'Error estimates for the right singular vectors' Write (nout,99998) verrbd(1:m) Else Write (nout,99997) 'Failure in DGESDD. INFO =', info End If 99999 Format (3X,(8F8.4)) 99998 Format (4X,1P,6E11.1) 99997 Format (1X,A,I4) End Program f08kdfe