Program f08aefe ! F08AEF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: dgeqrf, dnrm2, dormqr, dtrtrs, nag_wp, x04caf ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nb = 64, nin = 5, nout = 6 ! .. Local Scalars .. Integer :: i, ifail, info, j, lda, ldb, lwork, & m, n, nrhs ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), rnorm(:), tau(:), & work(:) ! .. Executable Statements .. Write (nout,*) 'F08AEF Example Program Results' Write (nout,*) Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) m, n, nrhs lda = m ldb = m lwork = nb*n Allocate (a(lda,n),b(ldb,nrhs),rnorm(nrhs),tau(n),work(lwork)) ! Read A and B from data file Read (nin,*)(a(i,1:n),i=1,m) Read (nin,*)(b(i,1:nrhs),i=1,m) ! Compute the QR factorization of A ! The NAG name equivalent of dgeqrf is f08aef Call dgeqrf(m,n,a,lda,tau,work,lwork,info) ! Compute C = (C1) = (Q**T)*B, storing the result in B ! (C2) ! The NAG name equivalent of dormqr is f08agf Call dormqr('Left','Transpose',m,nrhs,n,a,lda,tau,b,ldb,work,lwork,info) ! Compute least-squares solutions by backsubstitution in ! R*X = C1 ! The NAG name equivalent of dtrtrs is f07tef Call dtrtrs('Upper','No transpose','Non-Unit',n,nrhs,a,lda,b,ldb,info) If (info>0) Then Write (nout,*) 'The upper triangular factor, R, of A is singular, ' Write (nout,*) 'the least squares solution could not be computed' Else ! Print least-squares solutions ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call x04caf('General',' ',n,nrhs,b,ldb,'Least-squares solution(s)', & ifail) ! Compute and print estimates of the square roots of the residual ! sums of squares ! The NAG name equivalent of dnrm2 is f06ejf Do j = 1, nrhs rnorm(j) = dnrm2(m-n,b(n+1,j),1) End Do Write (nout,*) Write (nout,*) 'Square root(s) of the residual sum(s) of squares' Write (nout,99999) rnorm(1:nrhs) End If 99999 Format (5X,1P,7E11.2) End Program f08aefe