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

annotate scripts/linear-algebra/cond.m @ 23220:092078913d54

maint: Merge stable to default.

author	John W. Eaton <jwe@octave.org>
date	Wed, 22 Feb 2017 12:58:07 -0500
parents	ef4d915df748 3ac9f9ecfae5
children	194eb4bd202b

rev	line source
23219 3ac9f9ecfae5 maint: Update copyright dates. John W. Eaton <jwe@octave.org> parents: 23083 diff changeset	1 ## Copyright (C) 1993-2017 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
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	8 ## (at 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
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## GNU General Public License for more details.
2313 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 --
20852 516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20160 diff changeset	20 ## @deftypefn {} {} cond (@var{A})
516bb87ea72e 2015 Code Sprint: remove class of function from docstring for all m-files. Rik <rik@octave.org> parents: 20160 diff changeset	21 ## @deftypefnx {} {} cond (@var{A}, @var{p})
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: 20852 diff changeset	22 ## Compute the @var{p}-norm condition number of a matrix with respect to
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: 20852 diff changeset	23 ## inversion.
12642 f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation. Rik <octave@nomad.inbox5.com> parents: 12584 diff changeset	24 ##
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	25 ## @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	26 ## @tex
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	27 ## $ {\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	28 ## @end tex
38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	29 ## @ifnottex
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	30 ## @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	31 ## @end ifnottex
38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	32 ##
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	33 ## 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	34 ## singular value decomposition. Other possible selections are
20160 03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	35 ## @code{@var{p} = 1, Inf, "fro"} which are generally faster. See @code{norm}
03b9d17a2d95 doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19697 diff changeset	36 ## for a full discussion of possible @var{p} values.
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	37 ##
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	38 ## The condition number of a matrix quantifies the sensitivity of the matrix
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	39 ## inversion operation when small changes are made to matrix elements. Ideally
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	40 ## the condition number will be close to 1. When the number is large this
17171 c3bd7314643c doc: Periodic spellcheck of documentation. Rik <rik@octave.org> parents: 16969 diff changeset	41 ## indicates small changes (such as underflow or round-off error) will produce
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	42 ## large changes in the resulting output. In such cases the solution results
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	43 ## from numerical computing are not likely to be accurate.
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: 20852 diff changeset	44 ## @seealso{condest, rcond, condeig, norm, svd}
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3265 diff changeset	45 ## @end deftypefn
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	46
2314 949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	47 ## Author: jwe
949ab8eba8bc [project @ 1996-07-12 03:58:02 by jwe] jwe parents: 2313 diff changeset	48
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	49 function retval = cond (A, p = 2)
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	50
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	51 if (nargin < 1 \|\| nargin > 2)
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	52 print_usage ();
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	53 endif
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	54
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	55 if (ndims (A) > 2)
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	56 error ("cond: A must be a 2-D matrix");
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	57 endif
4890 e7da90a1cc11 [project @ 2004-05-06 20:36:29 by jwe] jwe parents: 4478 diff changeset	58
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	59 if (p == 2)
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	60 if (isempty (A))
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	61 retval = 0.0;
16969 58188d5a2587 Use isfinite() to replace isinf() \| isnan() combination for 30% speed-up. Rik <rik@octave.org> parents: 16957 diff changeset	62 elseif (any (! isfinite (A(:))))
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	63 error ("cond: A must not contain Inf or NaN values");
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	64 else
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	65 sigma = svd (A);
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	66 sigma_1 = sigma(1);
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	67 sigma_n = sigma(end);
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	68 if (sigma_1 == 0 \|\| sigma_n == 0)
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	69 retval = Inf;
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	70 else
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	71 retval = sigma_1 / sigma_n;
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	72 endif
3250 ae3bdfd82f91 [project @ 1999-07-13 03:49:22 by jwe] jwe parents: 2847 diff changeset	73 endif
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	74 else
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	75 retval = norm (A, p) * norm (inv (A), p);
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	76 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	77
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	78 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	79
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	80
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	81 %!test
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	82 %! y = [7, 2, 3; 1, 3, 4; 6, 4, 5];
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	83 %! tol = 1e-6;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	84 %! type = {1, 2, "fro", "inf", inf};
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	85 %! for n = 1:numel (type)
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	86 %! rcondition(n) = 1 / cond (y, type{n});
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	87 %! endfor
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	88 %! 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	89
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	90 %!assert (cond ([1, 2; 2, 1]), 3, sqrt (eps))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	91 %!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	92
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	93 %!error cond ()
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	94 %!error cond (1, 2, 3)
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	95 %!error <A must be a 2-D matrix> cond (ones (1,3,3))
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	96 %!error <A must not contain Inf or NaN value> cond ([1, 2;Inf 4])
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	97 %!error <A must not contain Inf or NaN value> cond ([1, 2;NaN 4])

Mercurial > octave

annotate scripts/linear-algebra/cond.m @ 23220:092078913d54