octave-nkf: scripts/linear-algebra/cond.m annotate

annotate scripts/linear-algebra/cond.m @ 14138:72c96de7a403 stable

maint: update copyright notices for 2012

author	John W. Eaton <jwe@octave.org>
date	Mon, 02 Jan 2012 14:25:41 -0500
parents	f96b9b9f141b
children	f3d52523cde1

rev	line source
14138 72c96de7a403 maint: update copyright notices for 2012 John W. Eaton <jwe@octave.org> parents: 12642 diff changeset	1 ## Copyright (C) 1993-2012 John W. Eaton
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	2 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	3 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	4 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	6 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	8 ## your option) any later version.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	9 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	13 ## General Public License for more details.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	14 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	15 ## 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: 6046 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	17 ## <http://www.gnu.org/licenses/>.
245 16a24e76d6e0 [project @ 1993-12-03 02:00:15 by jwe] jwe parents: 4 diff changeset	18
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3265 diff changeset	19 ## -- texinfo --
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	20 ## @deftypefn {Function File} {} cond (@var{A})
11563 3c6e8aaa9555 Grammarcheck m-files before 3.4 release. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	21 ## @deftypefnx {Function File} {} cond (@var{A}, @var{p})
12584 7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	22 ## Compute the @var{p}-norm condition number of a matrix.
12642 f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation. Rik <octave@nomad.inbox5.com> parents: 12584 diff changeset	23 ##
12584 7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	24 ## @code{cond (@var{A})} is ## defined as
10602 38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	25 ## @tex
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	26 ## $ {\parallel A \parallel_p * \parallel A^{-1} \parallel_p .} $
10602 38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	27 ## @end tex
38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	28 ## @ifnottex
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	29 ## @code{norm (@var{A}, @var{p}) * norm (inv (@var{A}), @var{p})}.
10602 38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	30 ## @end ifnottex
38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	31 ##
38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	32 ## By default @code{@var{p} = 2} is used which implies a (relatively slow)
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	33 ## singular value decomposition. Other possible selections are
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10602 diff changeset	34 ## @code{@var{p} = 1, Inf, "fro"} which are generally faster. See
10602 38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	35 ## @code{norm} for a full discussion of possible @var{p} values.
9307 c2923c27c877 Various documentation improvements Rik <rdrider0-list@yahoo.com> parents: 9051 diff changeset	36 ## @seealso{condest, rcond, norm, svd}
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3265 diff changeset	37 ## @end deftypefn
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	38
2314 949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	39 ## Author: jwe
949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	40
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	41 function retval = cond (A, p)
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	42
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	43 if (nargin && nargin < 3)
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	44 if (ndims (A) > 2)
8664 e07e93c04080 style fixes John W. Eaton <jwe@octave.org> parents: 7768 diff changeset	45 error ("cond: only valid on 2-D objects");
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	46 endif
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	47
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	48 if (nargin <2)
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	49 p = 2;
4890 e7da90a1cc11 [project @ 2004-05-06 20:36:29 by jwe] jwe parents: 4478 diff changeset	50 endif
e7da90a1cc11 [project @ 2004-05-06 20:36:29 by jwe] jwe parents: 4478 diff changeset	51
7768 a2d9f325b65a Use isschar instead of deprecated isstr Rafael Laboissiere <rafael@debian.org> parents: 7484 diff changeset	52 if (! ischar (p) && p == 2)
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	53 [nr, nc] = size (A);
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	54 if (nr == 0 \|\| nc == 0)
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	55 retval = 0.0;
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	56 elseif (any (any (isinf (A) \| isnan (A))))
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	57 error ("cond: argument must not contain Inf or NaN values");
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	58 else
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	59 sigma = svd (A);
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	60 sigma_1 = sigma(1);
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	61 sigma_n = sigma(end);
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	62 if (sigma_1 == 0 \|\| sigma_n == 0)
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	63 retval = Inf;
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	64 else
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	65 retval = sigma_1 / sigma_n;
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	66 endif
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	67 endif
3250 ae3bdfd82f91 [project @ 1999-07-13 03:49:22 by jwe] jwe parents: 2847 diff changeset	68 else
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11563 diff changeset	69 retval = norm (A, p) * norm (inv (A), p);
3250 ae3bdfd82f91 [project @ 1999-07-13 03:49:22 by jwe] jwe parents: 2847 diff changeset	70 endif
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	71 else
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5642 diff changeset	72 print_usage ();
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	73 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	74
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	75 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	76
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	77 %!test
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	78 %! y= [7, 2, 3; 1, 3, 4; 6, 4, 5];
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	79 %! tol = 1e-6;
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	80 %! type = {1, 2, 'fro', 'inf', inf};
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	81 %! for n = 1:numel(type)
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	82 %! rcondition(n) = 1 / cond (y, type{n});
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	83 %! endfor
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	84 %! assert (rcondition, [0.017460, 0.019597, 0.018714, 0.012022, 0.012022], tol);
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	85
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	86 %!assert (abs (cond ([1, 2; 2, 1]) - 3) < sqrt (eps));
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	87
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	88 %!assert (cond ([1, 2, 3; 4, 5, 6; 7, 8, 9]) > 1.0e+16);
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	89
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	90 %!error cond ();
83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	91
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	92 %!error cond (1, 2, 3);
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	93

Mercurial > octave-nkf

annotate scripts/linear-algebra/cond.m @ 14138:72c96de7a403 stable