octave-antonio: src/DLD-FUNCTIONS/qr.cc annotate

annotate src/DLD-FUNCTIONS/qr.cc @ 7553:56be6f31dd4e

implementation of QR factorization updating

author	Jaroslav Hajek <highegg@gmail.com>
date	Tue, 04 Mar 2008 21:47:11 -0500
parents	f5005d9510f4
children	40574114c514

rev	line source
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	1 /*
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	2
7017 a1dbe9d80eee [project @ 2007-10-12 21:27:11 by jwe] jwe parents: 7016 diff changeset	3 Copyright (C) 1996, 1997, 1999, 2000, 2005, 2006, 2007 John W. Eaton
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	4
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	5 This file is part of Octave.
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	6
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	7 Octave is free software; you can redistribute it and/or modify it
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	8 under the terms of the GNU General Public License as published by the
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6484 diff changeset	9 Free Software Foundation; either version 3 of the License, or (at your
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6484 diff changeset	10 option) any later version.
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	11
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	12 Octave is distributed in the hope that it will be useful, but WITHOUT
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	15 for more details.
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	16
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	17 You should have received a copy of the GNU General Public License
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6484 diff changeset	18 along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6484 diff changeset	19 <http://www.gnu.org/licenses/>.
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	20
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	21 */
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	22
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	23 // The qrupdate, qrinsert, and qrdelete functions were written by
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	24 // Jaroslav Hajek <highegg@gmail.com>, Copyright (C) 2008 VZLU
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	25 // Prague, a.s., Czech Republic.
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	26
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	27 #ifdef HAVE_CONFIG_H
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	28 #include <config.h>
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	29 #endif
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	30
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	31 #include "CmplxQR.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	32 #include "CmplxQRP.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	33 #include "dbleQR.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	34 #include "dbleQRP.h"
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	35 #include "SparseQR.h"
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	36 #include "SparseCmplxQR.h"
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	37
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	38
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	39 #include "defun-dld.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	40 #include "error.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	41 #include "gripes.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	42 #include "oct-obj.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	43 #include "utils.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	44
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	45 // [Q, R] = qr (X): form Q unitary and R upper triangular such
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	46 // that Q * R = X
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	47 //
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	48 // [Q, R] = qr (X, 0): form the economy decomposition such that if X is
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	49 // m by n then only the first n columns of Q are
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	50 // computed.
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	51 //
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	52 // [Q, R, P] = qr (X): form QRP factorization of X where
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	53 // P is a permutation matrix such that
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	54 // A * P = Q * R
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	55 //
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	56 // [Q, R, P] = qr (X, 0): form the economy decomposition with
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	57 // permutation vector P such that Q * R = X (:, P)
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	58 //
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	59 // qr (X) alone returns the output of the LAPACK routine dgeqrf, such
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	60 // that R = triu (qr (X))
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	61
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	62 DEFUN_DLD (qr, args, nargout,
3548 ab7fa5a8f23f [project @ 2000-02-03 01:17:15 by jwe] jwe parents: 3372 diff changeset	63 "-- texinfo --\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	64 @deftypefn {Loadable Function} {[@var{q}, @var{r}, @var{p}] =} qr (@var{a})\n\
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	65 @deftypefnx {Loadable Function} {[@var{q}, @var{r}, @var{p}] =} qr (@var{a}, '0')\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	66 @cindex QR factorization\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	67 Compute the QR factorization of @var{a}, using standard @sc{Lapack}\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	68 subroutines. For example, given the matrix @code{a = [1, 2; 3, 4]},\n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	69 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	70 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	71 [q, r] = qr (a)\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	72 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	73 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	74 @noindent\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	75 returns\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	76 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	77 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	78 q =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	79 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	80 -0.31623 -0.94868\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	81 -0.94868 0.31623\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	82 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	83 r =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	84 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	85 -3.16228 -4.42719\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	86 0.00000 -0.63246\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	87 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	88 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	89 The @code{qr} factorization has applications in the solution of least\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	90 squares problems\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	91 @iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	92 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	93 $$\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	94 \\min_x \\left\\Vert A x - b \\right\\Vert_2\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	95 $$\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	96 @end tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	97 @end iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	98 @ifinfo\n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	99 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	100 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	101 @code{min norm(A x - b)}\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	102 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	103 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	104 @end ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	105 for overdetermined systems of equations (i.e.,\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	106 @iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	107 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	108 $A$\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	109 @end tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	110 @end iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	111 @ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	112 @code{a}\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	113 @end ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	114 is a tall, thin matrix). The QR factorization is\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	115 @iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	116 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	117 $QR = A$ where $Q$ is an orthogonal matrix and $R$ is upper triangular.\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	118 @end tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	119 @end iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	120 @ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	121 @code{q * r = a} where @code{q} is an orthogonal matrix and @code{r} is\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	122 upper triangular.\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	123 @end ifinfo\n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	124 \n\
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	125 If given a second argument of '0', @code{qr} returns an economy-sized\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	126 QR factorization, omitting zero rows of @var{R} and the corresponding\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	127 columns of @var{Q}.\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	128 \n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	129 If the matrix @var{a} is full, the permuted QR factorization\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	130 @code{[@var{q}, @var{r}, @var{p}] = qr (@var{a})} forms the QR factorization\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	131 such that the diagonal entries of @code{r} are decreasing in magnitude\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	132 order. For example,given the matrix @code{a = [1, 2; 3, 4]},\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	133 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	134 @example\n\
3600 c11d138d654a [project @ 2000-02-24 03:55:32 by jwe] jwe parents: 3548 diff changeset	135 [q, r, p] = qr(a)\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	136 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	137 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	138 @noindent\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	139 returns\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	140 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	141 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	142 q = \n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	143 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	144 -0.44721 -0.89443\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	145 -0.89443 0.44721\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	146 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	147 r =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	148 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	149 -4.47214 -3.13050\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	150 0.00000 0.44721\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	151 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	152 p =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	153 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	154 0 1\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	155 1 0\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	156 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	157 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	158 The permuted @code{qr} factorization @code{[q, r, p] = qr (a)}\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	159 factorization allows the construction of an orthogonal basis of\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	160 @code{span (a)}.\n\
7491 7879ef1042a8 qr doc fix Jaroslav Hajek parents: 7017 diff changeset	161 \n\
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	162 If the matrix @var{a} is sparse, then compute the sparse QR factorization\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	163 of @var{a}, using @sc{CSparse}. As the matrix @var{Q} is in general a full\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	164 matrix, this function returns the @var{Q}-less factorization @var{r} of\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	165 @var{a}, such that @code{@var{r} = chol (@var{a}' * @var{a})}.\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	166 \n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	167 If the final argument is the scalar @code{0} and the number of rows is\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	168 larger than the number of columns, then an economy factorization is\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	169 returned. That is @var{r} will have only @code{size (@var{a},1)} rows.\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	170 \n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	171 If an additional matrix @var{b} is supplied, then @code{qr} returns\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	172 @var{c}, where @code{@var{c} = @var{q}' * @var{b}}. This allows the\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	173 least squares approximation of @code{@var{a} \\ @var{b}} to be calculated\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	174 as\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	175 \n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	176 @example\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	177 [@var{c},@var{r}] = spqr (@var{a},@var{b})\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	178 @var{x} = @var{r} \\ @var{c}\n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	179 @end example\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	180 @end deftypefn")
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	181 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	182 octave_value_list retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	183
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	184 int nargin = args.length ();
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	185
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	186 if (nargin < 1 \|\| nargin > (args(0).is_sparse_type() ? 3 : 2))
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	187 {
5823 080c08b192d8 [project @ 2006-05-19 05:32:17 by jwe] jwe parents: 5307 diff changeset	188 print_usage ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	189 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	190 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	191
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	192 octave_value arg = args(0);
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	193
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	194 int arg_is_empty = empty_arg ("qr", arg.rows (), arg.columns ());
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	195
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	196 if (arg_is_empty < 0)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	197 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	198 else if (arg_is_empty > 0)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	199 return octave_value_list (3, Matrix ());
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	200
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	201 if (arg.is_sparse_type ())
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	202 {
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	203 bool economy = false;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	204 bool is_cmplx = false;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	205 int have_b = 0;
3068 17e2f90e0d3b [project @ 1997-07-08 02:17:36 by jwe] jwe parents: 3014 diff changeset	206
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	207 if (arg.is_complex_type ())
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	208 is_cmplx = true;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	209 if (nargin > 1)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	210 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	211 have_b = 1;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	212 if (args(nargin-1).is_scalar_type ())
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	213 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	214 int val = args(nargin-1).int_value ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	215 if (val == 0)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	216 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	217 economy = true;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	218 have_b = (nargin > 2 ? 2 : 0);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	219 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	220 }
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	221 if (have_b > 0 && args(have_b).is_complex_type ())
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	222 is_cmplx = true;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	223 }
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	224
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	225 if (!error_state)
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	226 {
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	227 if (have_b && nargout < 2)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	228 error ("qr: incorrect number of output arguments");
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	229 else if (is_cmplx)
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	230 {
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	231 SparseComplexQR q (arg.sparse_complex_matrix_value ());
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	232 if (!error_state)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	233 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	234 if (have_b > 0)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	235 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	236 retval(1) = q.R (economy);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	237 retval(0) = q.C (args(have_b).complex_matrix_value ());
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	238 if (arg.rows() < arg.columns())
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	239 warning ("qr: non minimum norm solution for under-determined problem");
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	240 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	241 else if (nargout > 1)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	242 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	243 retval(1) = q.R (economy);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	244 retval(0) = q.Q ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	245 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	246 else
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	247 retval(0) = q.R (economy);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	248 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	249 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	250 else
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	251 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	252 SparseQR q (arg.sparse_matrix_value ());
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	253 if (!error_state)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	254 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	255 if (have_b > 0)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	256 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	257 retval(1) = q.R (economy);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	258 retval(0) = q.C (args(have_b).matrix_value ());
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	259 if (args(0).rows() < args(0).columns())
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	260 warning ("qr: non minimum norm solution for under-determined problem");
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	261 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	262 else if (nargout > 1)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	263 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	264 retval(1) = q.R (economy);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	265 retval(0) = q.Q ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	266 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	267 else
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	268 retval(0) = q.R (economy);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	269 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	270 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	271 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	272 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	273 else
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	274 {
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	275 QR::type type = (nargout == 0 \|\| nargout == 1) ? QR::raw
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	276 : (nargin == 2 ? QR::economy : QR::std);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	277
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	278 if (arg.is_real_type ())
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	279 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	280 Matrix m = arg.matrix_value ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	281
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	282 if (! error_state)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	283 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	284 switch (nargout)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	285 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	286 case 0:
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	287 case 1:
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	288 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	289 QR fact (m, type);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	290 retval(0) = fact.R ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	291 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	292 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	293
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	294 case 2:
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	295 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	296 QR fact (m, type);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	297 retval(1) = fact.R ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	298 retval(0) = fact.Q ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	299 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	300 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	301
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	302 default:
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	303 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	304 QRP fact (m, type);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	305 retval(2) = fact.P ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	306 retval(1) = fact.R ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	307 retval(0) = fact.Q ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	308 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	309 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	310 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	311 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	312 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	313 else if (arg.is_complex_type ())
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	314 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	315 ComplexMatrix m = arg.complex_matrix_value ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	316
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	317 if (! error_state)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	318 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	319 switch (nargout)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	320 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	321 case 0:
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	322 case 1:
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	323 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	324 ComplexQR fact (m, type);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	325 retval(0) = fact.R ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	326 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	327 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	328
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	329 case 2:
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	330 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	331 ComplexQR fact (m, type);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	332 retval(1) = fact.R ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	333 retval(0) = fact.Q ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	334 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	335 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	336
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	337 default:
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	338 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	339 ComplexQRP fact (m, type);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	340 retval(2) = fact.P ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	341 retval(1) = fact.R ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	342 retval(0) = fact.Q ();
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	343 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	344 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	345 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	346 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	347 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	348 else
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	349 gripe_wrong_type_arg ("qr", arg);
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	350 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	351
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	352 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	353 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	354
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	355 /*
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	356
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	357 The deactivated tests below can't be tested till rectangular back-subs is
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	358 implemented for sparse matrices.
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	359
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	360 %!testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	361 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	362 %! a = sprandn(n,n,d)+speye(n,n);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	363 %! r = qr(a);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	364 %! assert(r'r,a'a,1e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	365
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	366 %!testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	367 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	368 %! a = sprandn(n,n,d)+speye(n,n);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	369 %! q = symamd(a);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	370 %! a = a(q,q);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	371 %! r = qr(a);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	372 %! assert(r'r,a'a,1e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	373
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	374 %!testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	375 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	376 %! a = sprandn(n,n,d)+speye(n,n);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	377 %! [c,r] = qr(a,ones(n,1));
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	378 %! assert (r\c,full(a)\ones(n,1),10e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	379
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	380 %!testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	381 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	382 %! a = sprandn(n,n,d)+speye(n,n);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	383 %! b = randn(n,2);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	384 %! [c,r] = qr(a,b);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	385 %! assert (r\c,full(a)\b,10e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	386
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	387 %% Test under-determined systems!!
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	388 %!#testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	389 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	390 %! a = sprandn(n,n+1,d)+speye(n,n+1);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	391 %! b = randn(n,2);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	392 %! [c,r] = qr(a,b);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	393 %! assert (r\c,full(a)\b,10e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	394
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	395 %!testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	396 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	397 %! a = 1i*sprandn(n,n,d)+speye(n,n);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	398 %! r = qr(a);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	399 %! assert(r'r,a'a,1e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	400
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	401 %!testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	402 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	403 %! a = 1i*sprandn(n,n,d)+speye(n,n);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	404 %! q = symamd(a);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	405 %! a = a(q,q);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	406 %! r = qr(a);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	407 %! assert(r'r,a'a,1e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	408
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	409 %!testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	410 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	411 %! a = 1i*sprandn(n,n,d)+speye(n,n);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	412 %! [c,r] = qr(a,ones(n,1));
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	413 %! assert (r\c,full(a)\ones(n,1),10e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	414
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	415 %!testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	416 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	417 %! a = 1i*sprandn(n,n,d)+speye(n,n);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	418 %! b = randn(n,2);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	419 %! [c,r] = qr(a,b);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	420 %! assert (r\c,full(a)\b,10e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	421
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	422 %% Test under-determined systems!!
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	423 %!#testif HAVE_CXSPARSE
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	424 %! n = 20; d= 0.2;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	425 %! a = 1i*sprandn(n,n+1,d)+speye(n,n+1);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	426 %! b = randn(n,2);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	427 %! [c,r] = qr(a,b);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	428 %! assert (r\c,full(a)\b,10e-10)
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	429
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	430 %!error qr(sprandn(10,10,0.2),ones(10,1));
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	431
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	432 */
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	433
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	434 DEFUN_DLD (qrupdate, args, ,
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	435 "-- texinfo --\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	436 @deftypefn{Loadable Function} {[@var{Q1}, @var{R1}]} = qrupdate (@var{Q}, @var{R}, @var{u}, @var{v})\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	437 Given a QR@tie{}factorization of a real or complex matrix\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	438 @w{@var{A} = @var{Q}*@var{R}}, @var{Q}@tie{}unitary and\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	439 @var{R}@tie{}upper trapezoidal, return the QR@tie{}factorization\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	440 of @w{@var{A} + @var{u}*@var{v}'}, where @var{u} and @var{v} are\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	441 column vectors (rank-1 update).\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	442 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	443 If the matrix @var{Q} is not square, the matrix @var{A} is updated by\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	444 QQ'uv' instead of uv'.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	445 @seealso{qr, qrinsert, qrdelete}\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	446 @end deftypefn")
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	447 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	448 octave_idx_type nargin = args.length ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	449 octave_value_list retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	450
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	451 octave_value argQ,argR,argu,argv;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	452
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	453 if (nargin == 4
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	454 && (argQ = args(0),argQ.is_matrix_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	455 && (argR = args(1),argR.is_matrix_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	456 && (argu = args(2),argu.is_matrix_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	457 && (argv = args(3),argv.is_matrix_type ()))
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	458 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	459 octave_idx_type m = argQ.rows ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	460 octave_idx_type n = argR.columns ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	461 octave_idx_type k = argQ.columns ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	462
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	463 if (argR.rows () == k
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	464 && argu.rows () == m && argu.columns () == 1
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	465 && argv.rows () == n && argv.columns () == 1)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	466 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	467 if (argQ.is_real_matrix ()
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	468 && argR.is_real_matrix ()
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	469 && argu.is_real_matrix ()
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	470 && argv.is_real_matrix ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	471 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	472 // all real case
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	473 Matrix Q = argQ.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	474 Matrix R = argR.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	475 Matrix u = argu.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	476 Matrix v = argv.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	477
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	478 QR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	479 fact.update (u, v);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	480
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	481 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	482 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	483 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	484 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	485 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	486 // complex case
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	487 ComplexMatrix Q = argQ.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	488 ComplexMatrix R = argR.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	489 ComplexMatrix u = argu.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	490 ComplexMatrix v = argv.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	491
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	492 ComplexQR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	493 fact.update (u, v);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	494
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	495 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	496 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	497 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	498 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	499 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	500 error ("qrupdate: dimensions mismatch");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	501 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	502 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	503 print_usage ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	504
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	505 return retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	506 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	507 /*
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	508 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	509 %! A = [0.091364 0.613038 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	510 %! 0.594638 0.425302 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	511 %! 0.383594 0.291238 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	512 %! 0.265712 0.268003 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	513 %! 0.669966 0.743851 0.445057 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	514 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	515 %! u = [0.85082;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	516 %! 0.76426;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	517 %! 0.42883;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	518 %! 0.53010;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	519 %! 0.80683 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	520 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	521 %! v = [0.98810;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	522 %! 0.24295;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	523 %! 0.43167 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	524 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	525 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	526 %! [Q,R] = qrupdate(Q,R,u,v);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	527 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	528 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	529 %! assert(norm(vec(QR - A - uv'),Inf) < norm(A)1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	530 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	531 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	532 %! A = [0.620405 + 0.956953i 0.480013 + 0.048806i 0.402627 + 0.338171i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	533 %! 0.589077 + 0.658457i 0.013205 + 0.279323i 0.229284 + 0.721929i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	534 %! 0.092758 + 0.345687i 0.928679 + 0.241052i 0.764536 + 0.832406i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	535 %! 0.912098 + 0.721024i 0.049018 + 0.269452i 0.730029 + 0.796517i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	536 %! 0.112849 + 0.603871i 0.486352 + 0.142337i 0.355646 + 0.151496i ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	537 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	538 %! u = [0.20351 + 0.05401i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	539 %! 0.13141 + 0.43708i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	540 %! 0.29808 + 0.08789i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	541 %! 0.69821 + 0.38844i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	542 %! 0.74871 + 0.25821i ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	543 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	544 %! v = [0.85839 + 0.29468i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	545 %! 0.20820 + 0.93090i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	546 %! 0.86184 + 0.34689i ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	547 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	548 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	549 %! [Q,R] = qrupdate(Q,R,u,v);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	550 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	551 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	552 %! assert(norm(vec(QR - A - uv'),Inf) < norm(A)1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	553 */
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	554
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	555 DEFUN_DLD (qrinsert, args, ,
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	556 "-- texinfo --\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	557 @deftypefn{Loadable Function} {[@var{Q1}, @var{R1}]} = qrinsert (@var{Q}, @var{R}, @var{j}, @var{x}, @var{orient})\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	558 Given a QR@tie{}factorization of a real or complex matrix\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	559 @w{@var{A} = @var{Q}*@var{R}}, @var{Q}@tie{}unitary and\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	560 @var{R}@tie{}upper trapezoidal, return the QR@tie{}factorization of\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	561 @w{[A(:,1:j-1) x A(:,j:n)]}, where @var{u} is a column vector to be\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	562 inserted into @var{A} (if @var{orient} is @code{\"col\"}), or the\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	563 QR@tie{}factorization of @w{[A(1:j-1,:);x;A(:,j:n)]}, where @var{x}\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	564 is a row vector to be inserted into @var{A} (if @var{orient} is\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	565 @code{\"row\"}).\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	566 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	567 The default value of @var{orient} is @code{\"col\"}.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	568 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	569 If @var{orient} is @code{\"col\"} and the matrix @var{Q} is not square,\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	570 then what gets inserted is the projection of @var{u} onto the space\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	571 spanned by columns of @var{Q}, i.e. QQ'u.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	572 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	573 If @var{orient} is @code{\"row\"}, @var{Q} must be square.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	574 @seealso{qr, qrupdate, qrdelete}\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	575 @end deftypefn")
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	576 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	577 octave_idx_type nargin = args.length ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	578 octave_value_list retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	579
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	580 octave_value argQ,argR,argj,argx,argor;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	581
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	582 if ((nargin == 4 \|\| nargin == 5)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	583 && (argQ = args(0), argQ.is_matrix_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	584 && (argR = args(1), argR.is_matrix_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	585 && (argj = args(2), argj.is_scalar_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	586 && (argx = args(3), argx.is_matrix_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	587 && (nargin < 5 \|\| (argor = args (4), argor.is_string ())))
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	588 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	589 octave_idx_type m = argQ.rows ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	590 octave_idx_type n = argR.columns ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	591 octave_idx_type k = argQ.columns();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	592
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	593 bool row = false;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	594
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	595 std::string orient = (nargin < 5) ? "col" : argor.string_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	596
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	597 if (nargin < 5 \|\| (row = orient == "row") \|\| (orient == "col"))
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	598 if (argR.rows () == k
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	599 && (! row \|\| m == k)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	600 && argx.rows () == (row ? 1 : m)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	601 && argx.columns () == (row ? n : 1))
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	602 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	603 int j = argj.int_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	604
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	605 if (j >= 1 && j <= (row ? n : m)+1)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	606 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	607 if (argQ.is_real_matrix ()
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	608 && argR.is_real_matrix ()
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	609 && argx.is_real_matrix ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	610 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	611 // real case
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	612 Matrix Q = argQ.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	613 Matrix R = argR.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	614 Matrix x = argx.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	615
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	616 QR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	617
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	618 if (row)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	619 fact.insert_row(x, j);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	620 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	621 fact.insert_col(x, j);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	622
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	623 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	624 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	625 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	626 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	627 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	628 // complex case
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	629 ComplexMatrix Q = argQ.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	630 ComplexMatrix R = argR.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	631 ComplexMatrix x = argx.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	632
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	633 ComplexQR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	634
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	635 if (row)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	636 fact.insert_row (x, j);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	637 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	638 fact.insert_col (x, j);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	639
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	640 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	641 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	642 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	643
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	644 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	645 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	646 error ("qrinsert: index j out of range");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	647 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	648 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	649 error ("qrinsert: dimension mismatch");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	650
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	651 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	652 error ("qrinsert: orient must be \"col\" or \"row\"");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	653 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	654 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	655 print_usage ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	656
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	657 return retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	658 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	659
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	660 /*
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	661 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	662 %! A = [0.091364 0.613038 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	663 %! 0.594638 0.425302 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	664 %! 0.383594 0.291238 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	665 %! 0.265712 0.268003 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	666 %! 0.669966 0.743851 0.445057 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	667 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	668 %! x = [0.85082;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	669 %! 0.76426;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	670 %! 0.42883;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	671 %! 0.53010;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	672 %! 0.80683 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	673 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	674 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	675 %! [Q,R] = qrinsert(Q,R,3,x);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	676 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	677 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	678 %! assert(norm(vec(QR - [A(:,1:2) x A(:,3)]),Inf) < norm(A)1e1*eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	679 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	680 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	681 %! A = [0.620405 + 0.956953i 0.480013 + 0.048806i 0.402627 + 0.338171i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	682 %! 0.589077 + 0.658457i 0.013205 + 0.279323i 0.229284 + 0.721929i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	683 %! 0.092758 + 0.345687i 0.928679 + 0.241052i 0.764536 + 0.832406i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	684 %! 0.912098 + 0.721024i 0.049018 + 0.269452i 0.730029 + 0.796517i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	685 %! 0.112849 + 0.603871i 0.486352 + 0.142337i 0.355646 + 0.151496i ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	686 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	687 %! x = [0.20351 + 0.05401i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	688 %! 0.13141 + 0.43708i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	689 %! 0.29808 + 0.08789i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	690 %! 0.69821 + 0.38844i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	691 %! 0.74871 + 0.25821i ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	692 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	693 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	694 %! [Q,R] = qrinsert(Q,R,3,x);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	695 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	696 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	697 %! assert(norm(vec(QR - [A(:,1:2) x A(:,3)]),Inf) < norm(A)1e1*eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	698 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	699 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	700 %! A = [0.091364 0.613038 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	701 %! 0.594638 0.425302 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	702 %! 0.383594 0.291238 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	703 %! 0.265712 0.268003 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	704 %! 0.669966 0.743851 0.445057 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	705 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	706 %! x = [0.85082 0.76426 0.42883 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	707 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	708 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	709 %! [Q,R] = qrinsert(Q,R,3,x,'row');
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	710 %! assert(norm(vec(Q'Q - eye(6)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	711 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	712 %! assert(norm(vec(QR - [A(1:2,:);x;A(3:5,:)]),Inf) < norm(A)1e1*eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	713 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	714 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	715 %! A = [0.620405 + 0.956953i 0.480013 + 0.048806i 0.402627 + 0.338171i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	716 %! 0.589077 + 0.658457i 0.013205 + 0.279323i 0.229284 + 0.721929i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	717 %! 0.092758 + 0.345687i 0.928679 + 0.241052i 0.764536 + 0.832406i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	718 %! 0.912098 + 0.721024i 0.049018 + 0.269452i 0.730029 + 0.796517i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	719 %! 0.112849 + 0.603871i 0.486352 + 0.142337i 0.355646 + 0.151496i ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	720 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	721 %! x = [0.20351 + 0.05401i 0.13141 + 0.43708i 0.29808 + 0.08789i ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	722 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	723 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	724 %! [Q,R] = qrinsert(Q,R,3,x,'row');
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	725 %! assert(norm(vec(Q'Q - eye(6)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	726 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	727 %! assert(norm(vec(QR - [A(1:2,:);x;A(3:5,:)]),Inf) < norm(A)1e1*eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	728 */
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	729
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	730 DEFUN_DLD (qrdelete, args, ,
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	731 "-- texinfo --\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	732 @deftypefn{Loadable Function} {[@var{Q1}, @var{R1}]} = qrdelete (@var{Q}, @var{R}, @var{j}, @var{orient})\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	733 Given a QR@tie{}factorization of a real or complex matrix\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	734 @w{@var{A} = @var{Q}*@var{R}}, @var{Q}@tie{}unitary and\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	735 @var{R}@tie{}upper trapezoidal, return the QR@tie{}factorization of\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	736 @w{[A(:,1:j-1) A(:,j+1:n)]}, i.e. @var{A} with one column deleted\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	737 (if @var{orient} is \"col\"), or the QR@tie{}factorization of\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	738 @w{[A(1:j-1,:);A(:,j+1:n)]}, i.e. @var{A} with one row deleted (if\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	739 @var{orient} is \"row\").\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	740 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	741 The default value of @var{orient} is \"col\".\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	742 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	743 If @var{orient} is \"col\", the matrix @var{Q} is not required to\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	744 be square.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	745 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	746 For @sc{Matlab} compatibility, if @var{Q} is nonsquare on input, the\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	747 updated factorization is always stripped to the economical form, i.e.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	748 @code{columns (Q) == rows (R) = columns (R)}.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	749 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	750 To get the less intelligent but more natural behaviour when @var{Q}\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	751 retains it shape and @var{R} loses one column, set @var{orient} to\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	752 \"col+\" instead.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	753 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	754 If @var{orient} is \"row\", @var{Q} must be square.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	755 @seealso{qr, qrinsert, qrupdate}\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	756 @end deftypefn")
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	757 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	758 int nargin = args.length ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	759 octave_value_list retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	760
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	761 octave_value argQ,argR,argj,argor;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	762
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	763 if ((nargin == 3 \|\| nargin == 4)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	764 && (argQ = args(0), argQ.is_matrix_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	765 && (argR = args(1), argR.is_matrix_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	766 && (argj = args(2), argj.is_scalar_type ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	767 && (nargin < 4 \|\| (argor = args (3), argor.is_string ())))
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	768 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	769 octave_idx_type m = argQ.rows ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	770 octave_idx_type k = argQ.columns ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	771 octave_idx_type n = argR.columns ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	772
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	773 bool row = false;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	774 bool colp = false;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	775
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	776 std::string orient = (nargin < 4) ? "col" : argor.string_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	777
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	778 if (nargin < 4 \|\| (row = orient == "row")
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	779 \|\| (orient == "col") \|\| (colp = orient == "col+"))
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	780 if (argR.rows() == k)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	781 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	782 int j = argj.scalar_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	783 if (j >= 1 && j <= (row ? n : m)+1)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	784 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	785 if (argQ.is_real_matrix ()
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	786 && argR.is_real_matrix ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	787 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	788 // real case
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	789 Matrix Q = argQ.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	790 Matrix R = argR.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	791
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	792 QR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	793
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	794 if (row)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	795 fact.delete_row (j);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	796 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	797 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	798 fact.delete_col (j);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	799
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	800 if (! colp && k < m)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	801 fact.economize ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	802 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	803
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	804 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	805 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	806 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	807 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	808 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	809 // complex case
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	810 ComplexMatrix Q = argQ.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	811 ComplexMatrix R = argR.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	812
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	813 ComplexQR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	814
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	815 if (row)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	816 fact.delete_row (j);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	817 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	818 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	819 fact.delete_col (j);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	820
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	821 if (! colp && k < m)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	822 fact.economize ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	823 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	824
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	825 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	826 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	827 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	828
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	829 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	830 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	831 error ("qrdelete: index j out of range");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	832 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	833 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	834 error ("qrdelete: dimension mismatch");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	835
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	836 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	837 error ("qrdelete: orient must be \"col\" or \"row\"");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	838 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	839 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	840 print_usage ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	841
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	842 return retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	843 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	844
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	845 /*
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	846 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	847 %! A = [0.091364 0.613038 0.027504 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	848 %! 0.594638 0.425302 0.562834 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	849 %! 0.383594 0.291238 0.742073 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	850 %! 0.265712 0.268003 0.783553 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	851 %! 0.669966 0.743851 0.457255 0.445057 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	852 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	853 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	854 %! [Q,R] = qrdelete(Q,R,3);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	855 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	856 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	857 %! assert(norm(vec(QR - [A(:,1:2) A(:,4)]),Inf) < norm(A)1e1*eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	858 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	859 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	860 %! A = [0.364554 + 0.993117i 0.669818 + 0.510234i 0.426568 + 0.041337i 0.847051 + 0.233291i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	861 %! 0.049600 + 0.242783i 0.448946 + 0.484022i 0.141155 + 0.074420i 0.446746 + 0.392706i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	862 %! 0.581922 + 0.657416i 0.581460 + 0.030016i 0.219909 + 0.447288i 0.201144 + 0.069132i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	863 %! 0.694986 + 0.000571i 0.682327 + 0.841712i 0.807537 + 0.166086i 0.192767 + 0.358098i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	864 %! 0.945002 + 0.066788i 0.350492 + 0.642638i 0.579629 + 0.048102i 0.600170 + 0.636938i ] * I;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	865 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	866 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	867 %! [Q,R] = qrdelete(Q,R,3);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	868 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	869 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	870 %! assert(norm(vec(QR - [A(:,1:2) A(:,4)]),Inf) < norm(A)1e1*eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	871 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	872 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	873 %! A = [0.091364 0.613038 0.027504 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	874 %! 0.594638 0.425302 0.562834 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	875 %! 0.383594 0.291238 0.742073 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	876 %! 0.265712 0.268003 0.783553 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	877 %! 0.669966 0.743851 0.457255 0.445057 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	878 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	879 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	880 %! [Q,R] = qrdelete(Q,R,3,'row');
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	881 %! assert(norm(vec(Q'Q - eye(4)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	882 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	883 %! assert(norm(vec(QR - [A(1:2,:);A(4:5,:)]),Inf) < norm(A)1e1*eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	884 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	885 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	886 %! A = [0.364554 + 0.993117i 0.669818 + 0.510234i 0.426568 + 0.041337i 0.847051 + 0.233291i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	887 %! 0.049600 + 0.242783i 0.448946 + 0.484022i 0.141155 + 0.074420i 0.446746 + 0.392706i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	888 %! 0.581922 + 0.657416i 0.581460 + 0.030016i 0.219909 + 0.447288i 0.201144 + 0.069132i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	889 %! 0.694986 + 0.000571i 0.682327 + 0.841712i 0.807537 + 0.166086i 0.192767 + 0.358098i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	890 %! 0.945002 + 0.066788i 0.350492 + 0.642638i 0.579629 + 0.048102i 0.600170 + 0.636938i ] * I;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	891 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	892 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	893 %! [Q,R] = qrdelete(Q,R,3,'row');
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	894 %! assert(norm(vec(Q'Q - eye(4)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	895 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	896 %! assert(norm(vec(QR - [A(1:2,:);A(4:5,:)]),Inf) < norm(A)1e1*eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	897 */
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	898
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	899 /*
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	900 ;;; Local Variables: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	901 ;;; mode: C++ ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	902 ;;; End: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	903 */

Mercurial > octave-antonio

annotate src/DLD-FUNCTIONS/qr.cc @ 7553:56be6f31dd4e