Mercurial > octave-nkf
view libcruft/qrupdate/sqrder.f @ 7961:a5d1e27ee1f4 ss-3-1-51
3.1.51 snapshot
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 22 Jul 2008 11:40:48 -0400 |
parents | 82be108cc558 |
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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 sqrder(m,n,Q,Q1,R,R1,j) c purpose: updates a QR factorization after deleting a row. c i.e., given an m-by-m orthogonal matrix Q, an m-by-n c upper trapezoidal matrix R and index j in the range c 1:m, this subroutine forms the (m-1)-by-(m-1) matrix c Q1 and an (m-1)-by-n matrix R1 so that Q1 is again c orthogonal, R1 upper trapezoidal, and c Q1*R1 = [A(1:j-1,:); A(j+1:m,:)], where A = Q*R. c (real version) c c arguments: c m (in) number of rows of the matrix R. c n (in) number of columns of the matrix R c Q (in) the orthogonal matrix Q c Q1 (out) the updated matrix Q1 c R (in) the upper trapezoidal matrix R c R1 (out) the updated matrix R1 c j (in) the position of the new row in R1 c integer m,n,j real Q(m,m),Q1(m-1,m-1),R(m,n),R1(m-1,n) real c real s,rr,w external xerbla,slacpy,slartg,srot,sscal,saxpy integer i c quick return if possible if (m == 1) return c check arguments info = 0 if (m < 1) then info = 1 else if (j < 1 .or. j > n) then info = 7 end if if (info /= 0) then call xerbla('SQRDER',info) end if c setup the new matrix Q1 c permute the columns of Q and rows of R so that the deleted row ends c up being the topmost row. if (j > 1) then call slacpy('0',j-1,m-1,Q(1,2),m,Q1(1,1),m-1) end if if (j < m) then call slacpy('0',m-j,m-1,Q(j+1,2),m,Q1(j,1),m-1) end if c setup the new matrix R1 call slacpy('0',m-1,n,R(2,1),m,R1(1,1),m-1) c eliminate Q(j,2:m) w = Q(j,m) do i = m-1,2,-1 call slartg(Q(j,i),w,c,s,rr) w = rr c apply rotation to rows of R1 if (i <= n) then call srot(n-i+1,R1(i-1,i),m-1,R1(i,i),m-1,c,s) end if c apply rotation to columns of Q1 call srot(m-1,Q1(1,i-1),1,Q1(1,i),1,c,s) end do c the last iteration is special, as we don't have the first row of c R and first column of Q call slartg(Q(j,1),w,c,s,rr) w = rr call sscal(n,c,R1(1,1),m-1) call saxpy(n,-s,R(1,1),m,R1(1,1),m-1) c apply rotation to columns of Q1 call sscal(m-1,c,Q1(1,1),1) if (j > 1) then call saxpy(j-1,-s,Q(1,1),1,Q1(1,1),1) end if if (j < m) then call saxpy(m-j,-s,Q(j+1,1),1,Q1(j,1),1) end if end