Mercurial > octave-nkf
view libcruft/qrupdate/dqr1up.f @ 7553:56be6f31dd4e
implementation of QR factorization updating
author | Jaroslav Hajek <highegg@gmail.com> |
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date | Tue, 04 Mar 2008 21:47:11 -0500 |
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c Copyright (C) 2008 VZLU Prague, a.s., Czech Republic c c Author: Jaroslav Hajek <highegg@gmail.com> c c This source is free software; you can redistribute it and/or modify c it under the terms of the GNU General Public License as published by c the Free Software Foundation; either version 2 of the License, or c (at your option) any later version. c c This program is distributed in the hope that it will be useful, c but WITHOUT ANY WARRANTY; without even the implied warranty of c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the c GNU General Public License for more details. c c You should have received a copy of the GNU General Public License c along with this software; see the file COPYING. If not, see c <http://www.gnu.org/licenses/>. c subroutine dqr1up(m,n,k,Q,R,u,v) c purpose: updates a QR factorization after rank-1 modification c i.e., given a m-by-k orthogonal Q and m-by-n upper c trapezoidal R, an m-vector u and n-vector v, c this subroutine updates Q -> Q1 and R -> R1 so that c Q1*R1 = Q*R + Q*Q'u*v', and Q1 is again orthonormal c and R1 upper trapezoidal. c (real version) c arguments: c m (in) number of rows of the matrix Q. c n (in) number of columns of the matrix R. c k (in) number of columns of Q, and rows of R. k <= m. c Q (io) on entry, the orthogonal m-by-k matrix Q. c on exit, the updated matrix Q1. c R (io) on entry, the upper trapezoidal m-by-n matrix R.. c on exit, the updated matrix R1. c u (in) the left m-vector. c v (in) the right n-vector. c integer m,n,k double precision Q(m,k),R(k,n),u(m),v(n) double precision w external dqrqhv,dqhqr,daxpy c quick return if possible if (m <= 0 .or. n <= 0) return c eliminate tail of Q'*u call dqrqhv(m,n,k,Q,m,R,m,u,w) c update R call daxpy(n,w,v,1,R(1,1),m) c retriangularize R call dqhqr(m,n,k,Q,m,R,k) end