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

annotate src/DLD-FUNCTIONS/qr.cc @ 7505:f5005d9510f4

Remove dispatched sparse functions and treat in the generic versions of the functions

author	David Bateman <dbateman@free.fr>
date	Wed, 20 Feb 2008 15:52:11 -0500
parents	7879ef1042a8
children	56be6f31dd4e

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
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	23 #ifdef HAVE_CONFIG_H
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	24 #include <config.h>
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	25 #endif
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	26
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	27 #include "CmplxQR.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	28 #include "CmplxQRP.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	29 #include "dbleQR.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	30 #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	31 #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	32 #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	33
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	34
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	35 #include "defun-dld.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	36 #include "error.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	37 #include "gripes.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	38 #include "oct-obj.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	39 #include "utils.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	40
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	41 // [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	42 // that Q * R = X
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	43 //
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	44 // [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	45 // 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	46 // computed.
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, P] = qr (X): form QRP factorization of X where
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	49 // P is a permutation matrix such that
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	50 // A * P = Q * R
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, 0): form the economy decomposition with
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	53 // permutation vector P such that Q * R = X (:, P)
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	54 //
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	55 // 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	56 // that R = triu (qr (X))
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	57
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	58 DEFUN_DLD (qr, args, nargout,
3548 ab7fa5a8f23f [project @ 2000-02-03 01:17:15 by jwe] jwe parents: 3372 diff changeset	59 "-- texinfo --\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	60 @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	61 @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	62 @cindex QR factorization\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	63 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	64 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	65 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	66 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	67 [q, r] = qr (a)\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	68 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	69 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	70 @noindent\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	71 returns\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	72 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	73 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	74 q =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	75 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	76 -0.31623 -0.94868\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	77 -0.94868 0.31623\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	78 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	79 r =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	80 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	81 -3.16228 -4.42719\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	82 0.00000 -0.63246\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	83 @end example\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 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	86 squares problems\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	87 @iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	88 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	89 $$\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	90 \\min_x \\left\\Vert A x - b \\right\\Vert_2\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	91 $$\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	92 @end tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	93 @end iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	94 @ifinfo\n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	95 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	96 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	97 @code{min norm(A x - b)}\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	98 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	99 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	100 @end ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	101 for overdetermined systems of equations (i.e.,\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	102 @iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	103 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	104 $A$\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	105 @end tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	106 @end iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	107 @ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	108 @code{a}\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	109 @end ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	110 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	111 @iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	112 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	113 $QR = A$ 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	114 @end tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	115 @end iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	116 @ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	117 @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	118 upper triangular.\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	119 @end ifinfo\n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	120 \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	121 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	122 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	123 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	124 \n\
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 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	126 @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	127 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	128 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	129 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	130 @example\n\
3600 c11d138d654a [project @ 2000-02-24 03:55:32 by jwe] jwe parents: 3548 diff changeset	131 [q, r, p] = qr(a)\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	132 @end example\n\
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 @noindent\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	135 returns\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	136 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	137 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	138 q = \n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	139 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	140 -0.44721 -0.89443\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	141 -0.89443 0.44721\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	142 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	143 r =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	144 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	145 -4.47214 -3.13050\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	146 0.00000 0.44721\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	147 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	148 p =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	149 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	150 0 1\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	151 1 0\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	152 @end example\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 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	155 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	156 @code{span (a)}.\n\
7491 7879ef1042a8 qr doc fix Jaroslav Hajek parents: 7017 diff changeset	157 \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	158 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	159 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	160 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	161 @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	162 \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 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	164 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	165 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	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 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	168 @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	169 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	170 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	171 \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 @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	173 [@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	174 @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	175 @end example\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	176 @end deftypefn")
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	177 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	178 octave_value_list retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	179
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	180 int nargin = args.length ();
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	181
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	182 if (nargin < 1 \|\| nargin > (args(0).is_sparse_type() ? 3 : 2) \|\| nargout > 3)
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	183 {
5823 080c08b192d8 [project @ 2006-05-19 05:32:17 by jwe] jwe parents: 5307 diff changeset	184 print_usage ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	185 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	186 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	187
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	188 octave_value arg = args(0);
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	189
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	190 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	191
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	192 if (arg_is_empty < 0)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	193 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	194 else if (arg_is_empty > 0)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	195 return octave_value_list (3, Matrix ());
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	196
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	197 if (arg.is_sparse_type ())
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	198 {
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	199 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	200 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	201 int have_b = 0;
3068 17e2f90e0d3b [project @ 1997-07-08 02:17:36 by jwe] jwe parents: 3014 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 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	204 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	205 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	206 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	207 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	208 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	209 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	210 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	211 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	212 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	213 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	214 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	215 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	216 }
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	217 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	218 is_cmplx = true;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	219 }
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	220
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 (!error_state)
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	222 {
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	223 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	224 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	225 else if (is_cmplx)
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 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	228 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	229 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	230 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	231 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	232 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	233 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	234 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	235 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	236 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	237 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	238 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	239 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	240 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	241 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	242 else
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(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	244 }
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 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	248 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	249 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	250 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	251 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	252 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	253 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	254 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	255 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	256 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	257 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	258 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	259 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	260 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	261 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	262 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	263 else
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(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	265 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	266 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	267 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	268 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	269 else
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	270 {
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	271 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	272 : (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	273
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	274 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	275 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	276 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	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 (! 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	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 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	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 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	283 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	284 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	285 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	286 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	287 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	288 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	289
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	290 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	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 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	293 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	294 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	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 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	297
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	298 default:
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 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	301 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	302 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	303 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	304 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	305 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	306 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	307 }
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 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	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 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	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 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	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 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	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 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	318 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	319 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	320 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	321 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	322 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	323 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	324
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	325 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	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 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	328 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	329 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	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 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	332
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	333 default:
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 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	336 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	337 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	338 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	339 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	340 break;
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	341 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	342 }
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 else
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 gripe_wrong_type_arg ("qr", arg);
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	347 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	348 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	349
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	350 return retval;
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
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	353 /*
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	354
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	355 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	356 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	357
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	358 %!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	359 %! 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	360 %! 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	361 %! 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	362 %! 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	363
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	364 %!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	365 %! 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	366 %! 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	367 %! 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	368 %! 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	369 %! 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	370 %! 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	371
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	372 %!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	373 %! 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	374 %! 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	375 %! [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	376 %! 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	377
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	378 %!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	379 %! 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	380 %! 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	381 %! 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	382 %! [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	383 %! 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	384
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	385 %% 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	386 %!#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	387 %! 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	388 %! 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	389 %! 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	390 %! [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	391 %! 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	392
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	393 %!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	394 %! 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	395 %! 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	396 %! 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	397 %! 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	398
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	399 %!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	400 %! 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	401 %! 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	402 %! 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	403 %! 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	404 %! 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	405 %! 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	406
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	407 %!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	408 %! 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	409 %! 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	410 %! [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	411 %! 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	412
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	413 %!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	414 %! 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	415 %! 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	416 %! 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	417 %! [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	418 %! 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	419
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	420 %% 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	421 %!#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	422 %! 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	423 %! 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	424 %! 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	425 %! [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	426 %! 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	427
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	428 %!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	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 */
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 /*
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	434 ;;; Local Variables: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	435 ;;; mode: C++ ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	436 ;;; End: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	437 */

Mercurial > octave-antonio

annotate src/DLD-FUNCTIONS/qr.cc @ 7505:f5005d9510f4