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

annotate src/DLD-FUNCTIONS/qr.cc @ 7789:82be108cc558

First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code

author	David Bateman <dbateman@free.fr>
date	Sun, 27 Apr 2008 22:34:17 +0200
parents	efccca5f2ad7
children	87865ed7405f

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
7700 efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	23 // The qrupdate, qrinsert, qrdelete and qrshift functions were written by
7553 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"
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	35 #include "fCmplxQR.h"
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	36 #include "fCmplxQRP.h"
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	37 #include "floatQR.h"
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	38 #include "floatQRP.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	39 #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	40 #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	41
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	42
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	43 #include "defun-dld.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	44 #include "error.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	45 #include "gripes.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	46 #include "oct-obj.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	47 #include "utils.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	48
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	49 // [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	50 // that Q * R = X
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] = 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	53 // 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	54 // computed.
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): form QRP factorization of X where
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	57 // P is a permutation matrix such that
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	58 // A * P = Q * R
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	59 //
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	60 // [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	61 // permutation vector P such that Q * R = X (:, P)
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	62 //
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	63 // 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	64 // that R = triu (qr (X))
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	65
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	66 DEFUN_DLD (qr, args, nargout,
3548 ab7fa5a8f23f [project @ 2000-02-03 01:17:15 by jwe] jwe parents: 3372 diff changeset	67 "-- texinfo --\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	68 @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	69 @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	70 @cindex QR factorization\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	71 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	72 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	73 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	74 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	75 [q, r] = qr (a)\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	76 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	77 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	78 @noindent\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	79 returns\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 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	82 q =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	83 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	84 -0.31623 -0.94868\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	85 -0.94868 0.31623\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	86 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	87 r =\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 -3.16228 -4.42719\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	90 0.00000 -0.63246\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	91 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	92 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	93 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	94 squares problems\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	95 @iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	96 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	97 $$\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	98 \\min_x \\left\\Vert A x - b \\right\\Vert_2\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	99 $$\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	100 @end tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	101 @end iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	102 @ifinfo\n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	103 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	104 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	105 @code{min norm(A x - b)}\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	106 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	107 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	108 @end ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	109 for overdetermined systems of equations (i.e.,\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	110 @iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	111 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	112 $A$\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	113 @end tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	114 @end iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	115 @ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	116 @code{a}\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	117 @end ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	118 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	119 @iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	120 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	121 $QR = A$ 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	122 @end tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	123 @end iftex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	124 @ifinfo\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	125 @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	126 upper triangular.\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	127 @end ifinfo\n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	128 \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	129 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	130 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	131 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	132 \n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	133 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	134 @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	135 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	136 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	137 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	138 @example\n\
3600 c11d138d654a [project @ 2000-02-24 03:55:32 by jwe] jwe parents: 3548 diff changeset	139 [q, r, p] = qr(a)\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	140 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	141 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	142 @noindent\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	143 returns\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 @example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	146 q = \n\
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	147 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	148 -0.44721 -0.89443\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	149 -0.89443 0.44721\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	150 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	151 r =\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	152 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	153 -4.47214 -3.13050\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	154 0.00000 0.44721\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	155 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	156 p =\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 0 1\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	159 1 0\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	160 @end example\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	161 \n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	162 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	163 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	164 @code{span (a)}.\n\
7491 7879ef1042a8 qr doc fix Jaroslav Hajek parents: 7017 diff changeset	165 \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	166 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	167 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	168 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	169 @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	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 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	172 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	173 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	174 \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 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	176 @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	177 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	178 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	179 \n\
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	180 @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	181 [@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	182 @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	183 @end example\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3069 diff changeset	184 @end deftypefn")
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	185 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	186 octave_value_list retval;
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 int nargin = args.length ();
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	189
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	190 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	191 {
5823 080c08b192d8 [project @ 2006-05-19 05:32:17 by jwe] jwe parents: 5307 diff changeset	192 print_usage ();
2928 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 }
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 octave_value arg = args(0);
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	197
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	198 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	199
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	200 if (arg_is_empty < 0)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	201 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	202 else if (arg_is_empty > 0)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	203 return octave_value_list (3, Matrix ());
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	204
7505 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 (arg.is_sparse_type ())
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: 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 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	208 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	209 int have_b = 0;
3068 17e2f90e0d3b [project @ 1997-07-08 02:17:36 by jwe] jwe parents: 3014 diff changeset	210
7505 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 (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	212 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	213 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	214 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	215 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	216 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	217 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	218 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	219 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	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 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	222 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	223 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	224 }
7505 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 (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	226 is_cmplx = true;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	227 }
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	228
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	229 if (!error_state)
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 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	232 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	233 else if (is_cmplx)
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	234 {
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	235 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	236 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	237 {
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 (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	239 {
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(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	241 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	242 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	243 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	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 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	246 {
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(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	248 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	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 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	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 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	254 else
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	255 {
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	256 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	257 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	258 {
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 (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	260 {
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(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	262 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	263 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	264 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	265 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	266 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	267 {
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(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	269 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	270 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	271 else
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	272 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	273 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	274 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	275 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	276 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	277 else
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	278 {
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	279 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	280 : (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	281
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	282 if (arg.is_single_type ())
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	283 {
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	284 if (arg.is_real_type ())
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	285 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	286 FloatMatrix m = arg.float_matrix_value ();
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	287
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	288 if (! error_state)
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	289 {
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	290 switch (nargout)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	291 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	292 case 0:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	293 case 1:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	294 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	295 FloatQR fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	296 retval(0) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	297 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	298 break;
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	299
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	300 case 2:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	301 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	302 FloatQR fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	303 retval(1) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	304 retval(0) = fact.Q ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	305 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	306 break;
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	307
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	308 default:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	309 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	310 FloatQRP fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	311 retval(2) = fact.P ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	312 retval(1) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	313 retval(0) = fact.Q ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	314 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	315 break;
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	316 }
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	317 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	318 }
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	319 else if (arg.is_complex_type ())
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	320 {
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	321 FloatComplexMatrix m = arg.float_complex_matrix_value ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	322
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	323 if (! error_state)
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	324 {
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	325 switch (nargout)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	326 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	327 case 0:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	328 case 1:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	329 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	330 FloatComplexQR fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	331 retval(0) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	332 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	333 break;
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	334
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	335 case 2:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	336 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	337 FloatComplexQR fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	338 retval(1) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	339 retval(0) = fact.Q ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	340 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	341 break;
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	342
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	343 default:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	344 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	345 FloatComplexQRP fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	346 retval(2) = fact.P ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	347 retval(1) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	348 retval(0) = fact.Q ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	349 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	350 break;
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	351 }
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	352 }
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	353 }
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 else
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	356 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	357 if (arg.is_real_type ())
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	358 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	359 Matrix m = arg.matrix_value ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	360
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	361 if (! error_state)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	362 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	363 switch (nargout)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	364 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	365 case 0:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	366 case 1:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	367 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	368 QR fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	369 retval(0) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	370 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	371 break;
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	372
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	373 case 2:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	374 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	375 QR fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	376 retval(1) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	377 retval(0) = fact.Q ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	378 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	379 break;
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	380
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	381 default:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	382 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	383 QRP fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	384 retval(2) = fact.P ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	385 retval(1) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	386 retval(0) = fact.Q ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	387 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	388 break;
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	389 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	390 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	391 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	392 else if (arg.is_complex_type ())
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	393 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	394 ComplexMatrix m = arg.complex_matrix_value ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	395
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	396 if (! error_state)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	397 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	398 switch (nargout)
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	399 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	400 case 0:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	401 case 1:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	402 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	403 ComplexQR fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	404 retval(0) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	405 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	406 break;
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	407
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	408 case 2:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	409 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	410 ComplexQR fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	411 retval(1) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	412 retval(0) = fact.Q ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	413 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	414 break;
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	415
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	416 default:
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	417 {
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	418 ComplexQRP fact (m, type);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	419 retval(2) = fact.P ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	420 retval(1) = fact.R ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	421 retval(0) = fact.Q ();
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	422 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	423 break;
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	424 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	425 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	426 }
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	427 else
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	428 gripe_wrong_type_arg ("qr", arg);
82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7700 diff changeset	429 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	430 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	431
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	432 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	433 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	434
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	435 /*
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	436
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	437 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	438 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	439
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	440 %!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	441 %! 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	442 %! 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	443 %! 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	444 %! 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	445
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	446 %!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	447 %! 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	448 %! 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	449 %! 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	450 %! 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	451 %! 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	452 %! 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	453
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	454 %!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	455 %! 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	456 %! 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	457 %! [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	458 %! 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	459
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	460 %!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	461 %! 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	462 %! 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	463 %! 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	464 %! [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	465 %! 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	466
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	467 %% 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	468 %!#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	469 %! 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	470 %! 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	471 %! 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	472 %! [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	473 %! 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	474
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	475 %!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	476 %! 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	477 %! 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	478 %! 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	479 %! 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	480
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	481 %!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	482 %! 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	483 %! 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	484 %! 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	485 %! 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	486 %! 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	487 %! 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	488
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	489 %!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	490 %! 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	491 %! 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	492 %! [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	493 %! 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	494
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	495 %!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	496 %! 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	497 %! 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	498 %! 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	499 %! [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	500 %! 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	501
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	502 %% 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	503 %!#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	504 %! 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	505 %! 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	506 %! 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	507 %! [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	508 %! 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	509
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	510 %!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	511
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	512 */
f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	513
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	514 DEFUN_DLD (qrupdate, args, ,
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	515 "-- texinfo --\n\
7650 eb7bdde776f2 Texinfo fixes John W. Eaton <jwe@octave.org> parents: 7560 diff changeset	516 @deftypefn {Loadable Function} {[@var{Q1}, @var{R1}] =} qrupdate (@var{Q}, @var{R}, @var{u}, @var{v})\n\
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	517 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	518 @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	519 @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	520 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	521 column vectors (rank-1 update).\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	522 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	523 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	524 QQ'uv' instead of uv'.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	525 @seealso{qr, qrinsert, qrdelete}\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	526 @end deftypefn")
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	527 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	528 octave_idx_type nargin = args.length ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	529 octave_value_list retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	530
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	531 if (nargin != 4)
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	532 {
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	533 print_usage ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	534 return retval;
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	535 }
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	536
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	537 octave_value argq = args(0);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	538 octave_value argr = args(1);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	539 octave_value argu = args(2);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	540 octave_value argv = args(3);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	541
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	542 if (argq.is_matrix_type () && argr.is_matrix_type ()
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	543 && argu.is_matrix_type () && argv.is_matrix_type ())
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	544 {
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	545 octave_idx_type m = argq.rows ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	546 octave_idx_type n = argr.columns ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	547 octave_idx_type k = argq.columns ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	548
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	549 if (argr.rows () == k
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	550 && argu.rows () == m && argu.columns () == 1
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	551 && argv.rows () == n && argv.columns () == 1)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	552 {
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	553 if (argq.is_real_matrix ()
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	554 && argr.is_real_matrix ()
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	555 && argu.is_real_matrix ()
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	556 && argv.is_real_matrix ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	557 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	558 // all real case
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	559 Matrix Q = argq.matrix_value ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	560 Matrix R = argr.matrix_value ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	561 Matrix u = argu.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	562 Matrix v = argv.matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	563
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	564 QR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	565 fact.update (u, v);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	566
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	567 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	568 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	569 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	570 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	571 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	572 // complex case
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	573 ComplexMatrix Q = argq.complex_matrix_value ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	574 ComplexMatrix R = argr.complex_matrix_value ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	575 ComplexMatrix u = argu.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	576 ComplexMatrix v = argv.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	577
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	578 ComplexQR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	579 fact.update (u, v);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	580
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	581 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	582 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	583 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	584 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	585 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	586 error ("qrupdate: dimensions mismatch");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	587 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	588 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	589 print_usage ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	590
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	591 return retval;
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 /*
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	594 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	595 %! A = [0.091364 0.613038 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	596 %! 0.594638 0.425302 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	597 %! 0.383594 0.291238 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	598 %! 0.265712 0.268003 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	599 %! 0.669966 0.743851 0.445057 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	600 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	601 %! u = [0.85082;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	602 %! 0.76426;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	603 %! 0.42883;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	604 %! 0.53010;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	605 %! 0.80683 ];
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 %! v = [0.98810;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	608 %! 0.24295;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	609 %! 0.43167 ];
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 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	612 %! [Q,R] = qrupdate(Q,R,u,v);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	613 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	614 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	615 %! 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	616 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	617 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	618 %! 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	619 %! 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	620 %! 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	621 %! 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	622 %! 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	623 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	624 %! u = [0.20351 + 0.05401i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	625 %! 0.13141 + 0.43708i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	626 %! 0.29808 + 0.08789i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	627 %! 0.69821 + 0.38844i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	628 %! 0.74871 + 0.25821i ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	629 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	630 %! v = [0.85839 + 0.29468i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	631 %! 0.20820 + 0.93090i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	632 %! 0.86184 + 0.34689i ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	633 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	634 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	635 %! [Q,R] = qrupdate(Q,R,u,v);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	636 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	637 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	638 %! 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	639 */
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	640
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	641 DEFUN_DLD (qrinsert, args, ,
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	642 "-- texinfo --\n\
7650 eb7bdde776f2 Texinfo fixes John W. Eaton <jwe@octave.org> parents: 7560 diff changeset	643 @deftypefn {Loadable Function} {[@var{Q1}, @var{R1}] =} qrinsert (@var{Q}, @var{R}, @var{j}, @var{x}, @var{orient})\n\
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	644 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	645 @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	646 @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	647 @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	648 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	649 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	650 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	651 @code{\"row\"}).\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	652 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	653 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	654 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	655 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	656 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	657 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	658 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	659 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	660 @seealso{qr, qrupdate, qrdelete}\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	661 @end deftypefn")
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	662 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	663 octave_idx_type nargin = args.length ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	664 octave_value_list retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	665
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	666 if (nargin < 4 \|\| nargin > 5)
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	667 {
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	668 print_usage ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	669 return retval;
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	670 }
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	671
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	672 octave_value argq = args(0);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	673 octave_value argr = args(1);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	674 octave_value argj = args(2);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	675 octave_value argx = args(3);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	676
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	677 if (argq.is_matrix_type () && argr.is_matrix_type ()
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	678 && argj.is_scalar_type () && argx.is_matrix_type ()
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	679 && (nargin < 5 \|\| args(4).is_string ()))
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	680 {
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	681 octave_idx_type m = argq.rows ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	682 octave_idx_type n = argr.columns ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	683 octave_idx_type k = argq.columns ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	684
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	685 std::string orient = (nargin < 5) ? "col" : args(4).string_value ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	686
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	687 bool row = orient == "row";
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	688
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	689 if (row \|\| orient == "col")
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	690 if (argr.rows () == k
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	691 && (! row \|\| m == k)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	692 && argx.rows () == (row ? 1 : m)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	693 && argx.columns () == (row ? n : 1))
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	694 {
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	695 octave_idx_type j = argj.int_value ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	696
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	697 if (j >= 1 && j <= (row ? n : m)+1)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	698 {
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	699 if (argq.is_real_matrix ()
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	700 && argr.is_real_matrix ()
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	701 && argx.is_real_matrix ())
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	702 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	703 // real case
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	704 Matrix Q = argq.matrix_value ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	705 Matrix R = argr.matrix_value ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	706 Matrix x = argx.matrix_value ();
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 QR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	709
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	710 if (row)
7560 0ef0f9802a37 modify QR updating methods to use 0-based indexing Jaroslav Hajek <highegg@gmail.com> parents: 7559 diff changeset	711 fact.insert_row (x, j-1);
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	712 else
7560 0ef0f9802a37 modify QR updating methods to use 0-based indexing Jaroslav Hajek <highegg@gmail.com> parents: 7559 diff changeset	713 fact.insert_col (x, j-1);
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	714
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	715 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	716 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	717 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	718 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	719 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	720 // complex case
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	721 ComplexMatrix Q = argq.complex_matrix_value ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	722 ComplexMatrix R = argr.complex_matrix_value ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	723 ComplexMatrix x = argx.complex_matrix_value ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	724
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	725 ComplexQR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	726
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	727 if (row)
7560 0ef0f9802a37 modify QR updating methods to use 0-based indexing Jaroslav Hajek <highegg@gmail.com> parents: 7559 diff changeset	728 fact.insert_row (x, j-1);
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	729 else
7560 0ef0f9802a37 modify QR updating methods to use 0-based indexing Jaroslav Hajek <highegg@gmail.com> parents: 7559 diff changeset	730 fact.insert_col (x, j-1);
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	731
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	732 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	733 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	734 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	735
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	736 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	737 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	738 error ("qrinsert: index j out of range");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	739 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	740 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	741 error ("qrinsert: dimension mismatch");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	742
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	743 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	744 error ("qrinsert: orient must be \"col\" or \"row\"");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	745 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	746 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	747 print_usage ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	748
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	749 return retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	750 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	751
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	752 /*
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	753 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	754 %! A = [0.091364 0.613038 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	755 %! 0.594638 0.425302 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	756 %! 0.383594 0.291238 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	757 %! 0.265712 0.268003 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	758 %! 0.669966 0.743851 0.445057 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	759 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	760 %! x = [0.85082;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	761 %! 0.76426;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	762 %! 0.42883;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	763 %! 0.53010;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	764 %! 0.80683 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	765 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	766 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	767 %! [Q,R] = qrinsert(Q,R,3,x);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	768 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	769 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	770 %! 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	771 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	772 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	773 %! 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	774 %! 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	775 %! 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	776 %! 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	777 %! 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	778 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	779 %! x = [0.20351 + 0.05401i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	780 %! 0.13141 + 0.43708i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	781 %! 0.29808 + 0.08789i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	782 %! 0.69821 + 0.38844i;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	783 %! 0.74871 + 0.25821i ];
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 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	786 %! [Q,R] = qrinsert(Q,R,3,x);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	787 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	788 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	789 %! 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	790 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	791 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	792 %! A = [0.091364 0.613038 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	793 %! 0.594638 0.425302 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	794 %! 0.383594 0.291238 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	795 %! 0.265712 0.268003 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	796 %! 0.669966 0.743851 0.445057 ];
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 %! x = [0.85082 0.76426 0.42883 ];
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 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	801 %! [Q,R] = qrinsert(Q,R,3,x,'row');
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	802 %! assert(norm(vec(Q'Q - eye(6)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	803 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	804 %! 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	805 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	806 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	807 %! 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	808 %! 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	809 %! 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	810 %! 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	811 %! 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	812 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	813 %! 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	814 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	815 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	816 %! [Q,R] = qrinsert(Q,R,3,x,'row');
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	817 %! assert(norm(vec(Q'Q - eye(6)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	818 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	819 %! 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	820 */
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	821
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	822 DEFUN_DLD (qrdelete, args, ,
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	823 "-- texinfo --\n\
7650 eb7bdde776f2 Texinfo fixes John W. Eaton <jwe@octave.org> parents: 7560 diff changeset	824 @deftypefn {Loadable Function} {[@var{Q1}, @var{R1}] =} qrdelete (@var{Q}, @var{R}, @var{j}, @var{orient})\n\
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	825 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	826 @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	827 @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	828 @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	829 (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	830 @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	831 @var{orient} is \"row\").\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	832 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	833 The default value of @var{orient} is \"col\".\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	834 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	835 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	836 be square.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	837 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	838 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	839 updated factorization is always stripped to the economical form, i.e.\n\
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	840 @code{columns (Q) == rows (R) <= columns (R)}.\n\
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	841 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	842 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	843 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	844 \"col+\" instead.\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	845 \n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	846 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	847 @seealso{qr, qrinsert, qrupdate}\n\
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	848 @end deftypefn")
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	849 {
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	850 octave_idx_type nargin = args.length ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	851 octave_value_list retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	852
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	853 if (nargin < 3 \|\| nargin > 4)
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	854 {
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	855 print_usage ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	856 return retval;
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	857 }
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	858
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	859 octave_value argq = args(0);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	860 octave_value argr = args(1);
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	861 octave_value argj = args(2);
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	862
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	863 if (argq.is_matrix_type () && argr.is_matrix_type () && argj.is_scalar_type ()
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	864 && (nargin < 4 \|\| args(3).is_string ()))
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	865 {
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	866 octave_idx_type m = argq.rows ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	867 octave_idx_type k = argq.columns ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	868 octave_idx_type n = argr.columns ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	869
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	870 std::string orient = (nargin < 4) ? "col" : args(3).string_value ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	871
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	872 bool row = orient == "row";
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	873 bool colp = orient == "col+";
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	874
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	875 if (row \|\| colp \|\| orient == "col")
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	876 if (argr.rows () == k
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	877 && (! row \|\| m == k))
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	878 {
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	879 octave_idx_type j = argj.scalar_value ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	880 if (j >= 1 && j <= (row ? n : m))
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	881 {
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	882 if (argq.is_real_matrix ()
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	883 && argr.is_real_matrix ())
7553 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 // real case
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	886 Matrix Q = argq.matrix_value ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	887 Matrix R = argr.matrix_value ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	888
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	889 QR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	890
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	891 if (row)
7560 0ef0f9802a37 modify QR updating methods to use 0-based indexing Jaroslav Hajek <highegg@gmail.com> parents: 7559 diff changeset	892 fact.delete_row (j-1);
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	893 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	894 {
7560 0ef0f9802a37 modify QR updating methods to use 0-based indexing Jaroslav Hajek <highegg@gmail.com> parents: 7559 diff changeset	895 fact.delete_col (j-1);
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	896
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	897 if (! colp && k < m)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	898 fact.economize ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	899 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	900
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	901 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	902 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	903 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	904 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	905 {
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	906 // complex case
7559 07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	907 ComplexMatrix Q = argq.complex_matrix_value ();
07522d7dcdf8 fixes to QR and Cholesky updating code Jaroslav Hajek <highegg@gmail.com> parents: 7554 diff changeset	908 ComplexMatrix R = argr.complex_matrix_value ();
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	909
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	910 ComplexQR fact (Q, R);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	911
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	912 if (row)
7560 0ef0f9802a37 modify QR updating methods to use 0-based indexing Jaroslav Hajek <highegg@gmail.com> parents: 7559 diff changeset	913 fact.delete_row (j-1);
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	914 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	915 {
7560 0ef0f9802a37 modify QR updating methods to use 0-based indexing Jaroslav Hajek <highegg@gmail.com> parents: 7559 diff changeset	916 fact.delete_col (j-1);
7553 56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	917
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	918 if (! colp && k < m)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	919 fact.economize ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	920 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	921
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	922 retval(1) = fact.R ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	923 retval(0) = fact.Q ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	924 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	925
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	926 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	927 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	928 error ("qrdelete: index j out of range");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	929 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	930 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	931 error ("qrdelete: dimension mismatch");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	932
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	933 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	934 error ("qrdelete: orient must be \"col\" or \"row\"");
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	935 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	936 else
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	937 print_usage ();
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	938
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	939 return retval;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	940 }
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	941
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	942 /*
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	943 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	944 %! A = [0.091364 0.613038 0.027504 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	945 %! 0.594638 0.425302 0.562834 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	946 %! 0.383594 0.291238 0.742073 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	947 %! 0.265712 0.268003 0.783553 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	948 %! 0.669966 0.743851 0.457255 0.445057 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	949 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	950 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	951 %! [Q,R] = qrdelete(Q,R,3);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	952 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	953 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	954 %! 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	955 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	956 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	957 %! 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	958 %! 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	959 %! 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	960 %! 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	961 %! 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	962 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	963 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	964 %! [Q,R] = qrdelete(Q,R,3);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	965 %! assert(norm(vec(Q'Q - eye(5)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	966 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	967 %! 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	968 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	969 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	970 %! A = [0.091364 0.613038 0.027504 0.999083;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	971 %! 0.594638 0.425302 0.562834 0.603537;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	972 %! 0.383594 0.291238 0.742073 0.085574;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	973 %! 0.265712 0.268003 0.783553 0.238409;
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	974 %! 0.669966 0.743851 0.457255 0.445057 ];
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	975 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	976 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	977 %! [Q,R] = qrdelete(Q,R,3,'row');
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	978 %! assert(norm(vec(Q'Q - eye(4)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	979 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	980 %! 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	981 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	982 %!test
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	983 %! 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	984 %! 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	985 %! 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	986 %! 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	987 %! 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	988 %!
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	989 %! [Q,R] = qr(A);
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	990 %! [Q,R] = qrdelete(Q,R,3,'row');
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	991 %! assert(norm(vec(Q'Q - eye(4)),Inf) < 1e1eps)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	992 %! assert(norm(vec(triu(R)-R),Inf) == 0)
56be6f31dd4e implementation of QR factorization updating Jaroslav Hajek <highegg@gmail.com> parents: 7505 diff changeset	993 %! 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	994 */
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	995
7700 efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	996 DEFUN_DLD (qrshift, args, ,
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	997 "-- texinfo --\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	998 @deftypefn {Loadable Function} {[@var{Q1}, @var{R1}] =} qrshift (@var{Q}, @var{R}, @var{i}, @var{j})\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	999 Given a QR@tie{}factorization of a real or complex matrix\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1000 @w{@var{A} = @var{Q}*@var{R}}, @var{Q}@tie{}unitary and\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1001 @var{R}@tie{}upper trapezoidal, return the QR@tie{}factorization\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1002 of @w{@var{A}(:,p)}, where @w{p} is the permutation @*\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1003 @code{p = [1:i-1, shift(i:j, 1), j+1:n]} if @w{@var{i} < @var{j}} @*\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1004 or @*\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1005 @code{p = [1:j-1, shift(j:i,-1), i+1:n]} if @w{@var{j} < @var{i}}. @*\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1006 \n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1007 @seealso{qr, qrinsert, qrdelete}\n\
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1008 @end deftypefn")
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1009 {
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1010 octave_idx_type nargin = args.length ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1011 octave_value_list retval;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1012
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1013 if (nargin != 4)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1014 {
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1015 print_usage ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1016 return retval;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1017 }
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1018
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1019 octave_value argq = args(0);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1020 octave_value argr = args(1);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1021 octave_value argi = args(2);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1022 octave_value argj = args(3);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1023
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1024 if (argq.is_matrix_type () && argr.is_matrix_type ()
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1025 && argi.is_real_scalar () && argj.is_real_scalar ())
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1026 {
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1027 octave_idx_type m = argq.rows ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1028 octave_idx_type n = argr.columns ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1029 octave_idx_type k = argq.columns ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1030
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1031 if (argr.rows () == k)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1032 {
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1033 octave_idx_type i = argi.scalar_value ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1034 octave_idx_type j = argj.scalar_value ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1035 if (i > 1 && i <= n && j > 1 && j <= n)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1036 {
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1037 if (argq.is_real_matrix ()
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1038 && argr.is_real_matrix ())
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1039 {
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1040 // all real case
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1041 Matrix Q = argq.matrix_value ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1042 Matrix R = argr.matrix_value ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1043
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1044 QR fact (Q, R);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1045 fact.shift_cols (i-1, j-1);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1046
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1047 retval(1) = fact.R ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1048 retval(0) = fact.Q ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1049 }
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1050 else
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1051 {
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1052 // complex case
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1053 ComplexMatrix Q = argq.complex_matrix_value ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1054 ComplexMatrix R = argr.complex_matrix_value ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1055
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1056 ComplexQR fact (Q, R);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1057 fact.shift_cols (i-1, j-1);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1058
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1059 retval(1) = fact.R ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1060 retval(0) = fact.Q ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1061 }
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1062 }
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1063 else
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1064 error ("qrshift: index out of range");
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1065 }
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1066 else
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1067 error ("qrshift: dimensions mismatch");
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1068 }
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1069 else
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1070 print_usage ();
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1071
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1072 return retval;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1073 }
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1074 /*
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1075 %!test
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1076 %! A = [0.091364 0.613038 0.999083;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1077 %! 0.594638 0.425302 0.603537;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1078 %! 0.383594 0.291238 0.085574;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1079 %! 0.265712 0.268003 0.238409;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1080 %! 0.669966 0.743851 0.445057 ].';
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1081 %!
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1082 %! i = 2; j = 4; p = [1:i-1, shift(i:j,-1), j+1:5];
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1083 %!
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1084 %! [Q,R] = qr(A);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1085 %! [Q,R] = qrshift(Q,R,i,j);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1086 %! assert(norm(vec(Q'Q - eye(3)),Inf) < 1e1eps)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1087 %! assert(norm(vec(triu(R)-R),Inf) == 0)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1088 %! assert(norm(vec(QR - A(:,p)),Inf) < norm(A)1e1*eps)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1089 %!
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1090 %! j = 2; i = 4; p = [1:j-1, shift(j:i,+1), i+1:5];
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1091 %!
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1092 %! [Q,R] = qr(A);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1093 %! [Q,R] = qrshift(Q,R,i,j);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1094 %! assert(norm(vec(Q'Q - eye(3)),Inf) < 1e1eps)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1095 %! assert(norm(vec(triu(R)-R),Inf) == 0)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1096 %! assert(norm(vec(QR - A(:,p)),Inf) < norm(A)1e1*eps)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1097 %!
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1098 %!test
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1099 %! A = [0.620405 + 0.956953i 0.480013 + 0.048806i 0.402627 + 0.338171i;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1100 %! 0.589077 + 0.658457i 0.013205 + 0.279323i 0.229284 + 0.721929i;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1101 %! 0.092758 + 0.345687i 0.928679 + 0.241052i 0.764536 + 0.832406i;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1102 %! 0.912098 + 0.721024i 0.049018 + 0.269452i 0.730029 + 0.796517i;
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1103 %! 0.112849 + 0.603871i 0.486352 + 0.142337i 0.355646 + 0.151496i ].';
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1104 %!
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1105 %! i = 2; j = 4; p = [1:i-1, shift(i:j,-1), j+1:5];
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1106 %!
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1107 %! [Q,R] = qr(A);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1108 %! [Q,R] = qrshift(Q,R,i,j);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1109 %! assert(norm(vec(Q'Q - eye(3)),Inf) < 1e1eps)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1110 %! assert(norm(vec(triu(R)-R),Inf) == 0)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1111 %! assert(norm(vec(QR - A(:,p)),Inf) < norm(A)1e1*eps)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1112 %!
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1113 %! j = 2; i = 4; p = [1:j-1, shift(j:i,+1), i+1:5];
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1114 %!
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1115 %! [Q,R] = qr(A);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1116 %! [Q,R] = qrshift(Q,R,i,j);
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1117 %! assert(norm(vec(Q'Q - eye(3)),Inf) < 1e1eps)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1118 %! assert(norm(vec(triu(R)-R),Inf) == 0)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1119 %! assert(norm(vec(QR - A(:,p)),Inf) < norm(A)1e1*eps)
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1120 */
efccca5f2ad7 more QR & Cholesky updating functions Jaroslav Hajek <highegg@gmail.com> parents: 7650 diff changeset	1121
7505 f5005d9510f4 Remove dispatched sparse functions and treat in the generic versions of the functions David Bateman <dbateman@free.fr> parents: 7491 diff changeset	1122 /*
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	1123 ;;; Local Variables: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	1124 ;;; mode: C++ ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	1125 ;;; End: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	1126 */

Mercurial > hg > octave-nkf

annotate src/DLD-FUNCTIONS/qr.cc @ 7789:82be108cc558