* F08AEF Example Program Text * Mark 21 Release. NAG Copyright 2004. * .. Parameters .. INTEGER NIN, NOUT PARAMETER (NIN=5,NOUT=6) INTEGER MMAX, NB, NMAX PARAMETER (MMAX=8,NB=64,NMAX=8) INTEGER LDA, LDB, NRHSMX, LWORK PARAMETER (LDA=MMAX,LDB=MMAX,NRHSMX=NMAX,LWORK=NB*NMAX) * .. Local Scalars .. INTEGER I, IFAIL, INFO, J, M, N, NRHS * .. Local Arrays .. DOUBLE PRECISION A(LDA,NMAX), B(LDB,NRHSMX), RNORM(NRHSMX), + TAU(NMAX), WORK(LWORK) * .. External Functions .. DOUBLE PRECISION DNRM2 EXTERNAL DNRM2 * .. External Subroutines .. EXTERNAL DGEQRF, DORMQR, DTRTRS, X04CAF * .. Executable Statements .. WRITE (NOUT,*) 'F08AEF Example Program Results' WRITE (NOUT,*) * Skip heading in data file READ (NIN,*) READ (NIN,*) M, N, NRHS IF (M.LE.MMAX .AND. N.LE.NMAX .AND. M.GE.N .AND. NRHS.LE.NRHSMX) + THEN * * Read A and B from data file * READ (NIN,*) ((A(I,J),J=1,N),I=1,M) READ (NIN,*) ((B(I,J),J=1,NRHS),I=1,M) * * Compute the QR factorization of A * CALL DGEQRF(M,N,A,LDA,TAU,WORK,LWORK,INFO) * * Compute C = (C1) = (Q**T)*B, storing the result in B * (C2) * 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 * CALL DTRTRS('Upper','No transpose','Non-Unit',N,NRHS,A,LDA,B, + LDB,INFO) * IF (INFO.GT.0) THEN WRITE (NOUT,*) + 'The upper triangular factor, R, of A is singular, ' WRITE (NOUT,*) + 'the least squares solution could not be computed' GO TO 40 END IF * * Print least-squares solutions * 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 * DO 20 J = 1, NRHS RNORM(J) = DNRM2(M-N,B(N+1,J),1) 20 CONTINUE * WRITE (NOUT,*) WRITE (NOUT,*) + 'Square root(s) of the residual sum(s) of squares' WRITE (NOUT,99999) (RNORM(J),J=1,NRHS) ELSE WRITE (NOUT,*) + 'One or more of MMAX, NMAX or NRHSMX is too small, ', + 'and/or M.LT.N' END IF 40 CONTINUE * 99999 FORMAT (5X,1P,7E11.2) END