Program f08vafe ! F08VAF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: dggsvd, dtrcon, nag_wp, x02ajf, x04cbf ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nin = 5, nout = 6 ! .. Local Scalars .. Real (Kind=nag_wp) :: eps, rcond, serrbd Integer :: i, ifail, info, irank, j, k, l, lda, & ldb, ldq, ldu, ldv, m, n, p ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: a(:,:), alpha(:), b(:,:), beta(:), & q(:,:), u(:,:), v(:,:), work(:) Integer, Allocatable :: iwork(:) Character (1) :: clabs(1), rlabs(1) ! .. Executable Statements .. Write (nout,*) 'F08VAF Example Program Results' Write (nout,*) Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) m, n, p lda = m ldb = p ldq = n ldu = m ldv = p Allocate (a(lda,n),alpha(n),b(ldb,n),beta(n),q(ldq,n),u(ldu,m),v(ldv,p), & work(m+3*n),iwork(n)) ! Read the m by n matrix A and p by n matrix B from data file Read (nin,*)(a(i,1:n),i=1,m) Read (nin,*)(b(i,1:n),i=1,p) ! Compute the generalized singular value decomposition of (A, B) ! (A = U*D1*(0 R)*(Q**T), B = V*D2*(0 R)*(Q**T), m>=n) ! The NAG name equivalent of dggsvd is f08vaf Call dggsvd('U','V','Q',m,n,p,k,l,a,lda,b,ldb,alpha,beta,u,ldu,v,ldv,q, & ldq,work,iwork,info) If (info==0) Then ! Print solution irank = k + l Write (nout,*) 'Number of infinite generalized singular values (K)' Write (nout,99999) k Write (nout,*) 'Number of finite generalized singular values (L)' Write (nout,99999) l Write (nout,*) 'Numerical rank of (A**T B**T)**T (K+L)' Write (nout,99999) irank Write (nout,*) Write (nout,*) 'Finite generalized singular values' Write (nout,99998)(alpha(j)/beta(j),j=k+1,irank) Write (nout,*) Flush (nout) ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call x04cbf('General',' ',m,m,u,ldu,'1P,E12.4','Orthogonal matrix U', & 'Integer',rlabs,'Integer',clabs,80,0,ifail) Write (nout,*) Flush (nout) Call x04cbf('General',' ',p,p,v,ldv,'1P,E12.4','Orthogonal matrix V', & 'Integer',rlabs,'Integer',clabs,80,0,ifail) Write (nout,*) Flush (nout) Call x04cbf('General',' ',n,n,q,ldq,'1P,E12.4','Orthogonal matrix Q', & 'Integer',rlabs,'Integer',clabs,80,0,ifail) Write (nout,*) Flush (nout) Call x04cbf('Upper triangular','Non-unit',irank,irank,a(1,n-irank+1), & lda,'1P,E12.4','Non singular upper triangular matrix R','Integer', & rlabs,'Integer',clabs,80,0,ifail) ! Call DTRCON (F07TGF) to estimate the reciprocal condition ! number of R Call dtrcon('Infinity-norm','Upper','Non-unit',irank,a(1,n-irank+1), & lda,rcond,work,iwork,info) Write (nout,*) Write (nout,*) 'Estimate of reciprocal condition number for R' Write (nout,99997) rcond Write (nout,*) ! So long as irank = n, get the machine precision, eps, and ! compute the approximate error bound for the computed ! generalized singular values If (irank==n) Then eps = x02ajf() serrbd = eps/rcond Write (nout,*) 'Error estimate for the generalized singular values' Write (nout,99997) serrbd Else Write (nout,*) '(A**T B**T)**T is not of full rank' End If Else Write (nout,99996) 'Failure in DGGSVD. INFO =', info End If 99999 Format (1X,I5) 99998 Format (3X,8(1P,E12.4)) 99997 Format (1X,1P,E11.1) 99996 Format (1X,A,I4) End Program f08vafe