Mercurial > octave-nkf
comparison 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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| 7552:6070c3bd69c4 | 7553:56be6f31dd4e |
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| 1 c Copyright (C) 2008 VZLU Prague, a.s., Czech Republic | |
| 2 c | |
| 3 c Author: Jaroslav Hajek <highegg@gmail.com> | |
| 4 c | |
| 5 c This source is free software; you can redistribute it and/or modify | |
| 6 c it under the terms of the GNU General Public License as published by | |
| 7 c the Free Software Foundation; either version 2 of the License, or | |
| 8 c (at your option) any later version. | |
| 9 c | |
| 10 c This program is distributed in the hope that it will be useful, | |
| 11 c but WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
| 13 c GNU General Public License for more details. | |
| 14 c | |
| 15 c You should have received a copy of the GNU General Public License | |
| 16 c along with this software; see the file COPYING. If not, see | |
| 17 c <http://www.gnu.org/licenses/>. | |
| 18 c | |
| 19 subroutine dqr1up(m,n,k,Q,R,u,v) | |
| 20 c purpose: updates a QR factorization after rank-1 modification | |
| 21 c i.e., given a m-by-k orthogonal Q and m-by-n upper | |
| 22 c trapezoidal R, an m-vector u and n-vector v, | |
| 23 c this subroutine updates Q -> Q1 and R -> R1 so that | |
| 24 c Q1*R1 = Q*R + Q*Q'u*v', and Q1 is again orthonormal | |
| 25 c and R1 upper trapezoidal. | |
| 26 c (real version) | |
| 27 c arguments: | |
| 28 c m (in) number of rows of the matrix Q. | |
| 29 c n (in) number of columns of the matrix R. | |
| 30 c k (in) number of columns of Q, and rows of R. k <= m. | |
| 31 c Q (io) on entry, the orthogonal m-by-k matrix Q. | |
| 32 c on exit, the updated matrix Q1. | |
| 33 c R (io) on entry, the upper trapezoidal m-by-n matrix R.. | |
| 34 c on exit, the updated matrix R1. | |
| 35 c u (in) the left m-vector. | |
| 36 c v (in) the right n-vector. | |
| 37 c | |
| 38 integer m,n,k | |
| 39 double precision Q(m,k),R(k,n),u(m),v(n) | |
| 40 double precision w | |
| 41 external dqrqhv,dqhqr,daxpy | |
| 42 c quick return if possible | |
| 43 if (m <= 0 .or. n <= 0) return | |
| 44 c eliminate tail of Q'*u | |
| 45 call dqrqhv(m,n,k,Q,m,R,m,u,w) | |
| 46 c update R | |
| 47 | |
| 48 call daxpy(n,w,v,1,R(1,1),m) | |
| 49 | |
| 50 c retriangularize R | |
| 51 call dqhqr(m,n,k,Q,m,R,k) | |
| 52 end |