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

annotate scripts/linear-algebra/cond.m @ 33625:d213a148b3f1 default tip @

ensure exp. terminal widget has focus at startup * main-window.cc (main_window): call focus_command_window only if event loop is idle by using a single shot timer * main-window.h: make focus_command_window a public slot

author	Torsten Lilge <ttl-octave@mailbox.org>
date	Sun, 26 May 2024 02:29:44 +0200
parents	2e484f9f1f18
children

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ########################################################################
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 ##
32632 2e484f9f1f18 maint: update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 31706 diff changeset	3 ## Copyright (C) 1993-2024 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 27898 diff changeset	4 ##
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 ## See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 ## distribution or <https://octave.org/copyright/>.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	7 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	8 ## This file is part of Octave.
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	9 ##
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	10 ## Octave is free software: you can redistribute it and/or modify it
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	11 ## under the terms of the GNU General Public License as published by
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	12 ## the Free Software Foundation, either version 3 of the License, or
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	13 ## (at your option) any later version.
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 ## 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	16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
22755 3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
3a2b891d0b33 maint: Standardize Copyright formatting. Rik <rik@octave.org> parents: 22323 diff changeset	18 ## GNU General Public License for more details.
2313 5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	19 ##
5ca126254d15 [project @ 1996-07-11 21:25:22 by jwe] jwe parents: 2311 diff changeset	20 ## 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	21 ## along with Octave; see the file COPYING. If not, see
24534 194eb4bd202b maint: Update punctuation for GPL v3 license text. Rik <rik@octave.org> parents: 23220 diff changeset	22 ## <https://www.gnu.org/licenses/>.
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 ##
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ########################################################################
245 16a24e76d6e0 [project @ 1993-12-03 02:00:15 by jwe] jwe parents: 4 diff changeset	25
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3265 diff changeset	26 ## -- texinfo --
30875 5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files. Rik <rik@octave.org> parents: 30564 diff changeset	27 ## @deftypefn {} {@var{c} =} cond (@var{A})
5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files. Rik <rik@octave.org> parents: 30564 diff changeset	28 ## @deftypefnx {} {@var{c} =} 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	29 ## 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	30 ## inversion.
12642 f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation. Rik <octave@nomad.inbox5.com> parents: 12584 diff changeset	31 ##
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	32 ## @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	33 ## @tex
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	34 ## $ {\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	35 ## @end tex
38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	36 ## @ifnottex
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	37 ## @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	38 ## @end ifnottex
38eae0c3a003 Add TeX equation to cond.m documentation Rik <octave@nomad.inbox5.com> parents: 9307 diff changeset	39 ##
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	40 ## 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	41 ## singular value decomposition. Other possible selections are
28958 6fd6ad758b10 doc: Use @xref, @pxref rather than "see @code{}" in TexInfo. Rik <rik@octave.org> parents: 28886 diff changeset	42 ## @code{@var{p} = 1, Inf, "fro"} which are generally faster. For a full
6fd6ad758b10 doc: Use @xref, @pxref rather than "see @code{}" in TexInfo. Rik <rik@octave.org> parents: 28886 diff changeset	43 ## discussion of possible @var{p} values, @pxref{XREFnorm,,@code{norm}}.
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	44 ##
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	45 ## 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	46 ## 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	47 ## 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	48 ## 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	49 ## 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	50 ## 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	51 ## @seealso{condest, rcond, condeig, norm, svd}
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3265 diff changeset	52 ## @end deftypefn
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	53
30875 5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files. Rik <rik@octave.org> parents: 30564 diff changeset	54 function c = cond (A, p = 2)
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	55
28789 28de41192f3c Eliminate unneeded verification of nargin, nargout in m-files. Rik <rik@octave.org> parents: 27923 diff changeset	56 if (nargin < 1)
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	57 print_usage ();
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	58 endif
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	59
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	60 if (ndims (A) > 2)
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	61 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	62 endif
4890 e7da90a1cc11 [project @ 2004-05-06 20:36:29 by jwe] jwe parents: 4478 diff changeset	63
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	64 if (p == 2)
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	65 if (isempty (A))
30875 5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files. Rik <rik@octave.org> parents: 30564 diff changeset	66 c = 0.0;
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	67 else
31357 303bbdc3c536 Avoid out-of-memory errors for sparse matrices and ! isfinite usage. Rik <rik@octave.org> parents: 30875 diff changeset	68 try
303bbdc3c536 Avoid out-of-memory errors for sparse matrices and ! isfinite usage. Rik <rik@octave.org> parents: 30875 diff changeset	69 sigma = svd (A);
303bbdc3c536 Avoid out-of-memory errors for sparse matrices and ! isfinite usage. Rik <rik@octave.org> parents: 30875 diff changeset	70 catch
303bbdc3c536 Avoid out-of-memory errors for sparse matrices and ! isfinite usage. Rik <rik@octave.org> parents: 30875 diff changeset	71 error ("cond: A must not contain Inf or NaN values");
303bbdc3c536 Avoid out-of-memory errors for sparse matrices and ! isfinite usage. Rik <rik@octave.org> parents: 30875 diff changeset	72 end_try_catch
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	73 sigma_1 = sigma(1);
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	74 sigma_n = sigma(end);
9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	75 if (sigma_1 == 0 \|\| sigma_n == 0)
30875 5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files. Rik <rik@octave.org> parents: 30564 diff changeset	76 c = Inf;
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	77 else
30875 5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files. Rik <rik@octave.org> parents: 30564 diff changeset	78 c = sigma_1 / sigma_n;
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	79 endif
3250 ae3bdfd82f91 [project @ 1999-07-13 03:49:22 by jwe] jwe parents: 2847 diff changeset	80 endif
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	81 else
30875 5d3faba0342e doc: Ensure documentation lists output argument when it exists for all m-files. Rik <rik@octave.org> parents: 30564 diff changeset	82 c = norm (A, p) * norm (inv (A), p);
4 b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	83 endif
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	84
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe] jwe parents: diff changeset	85 endfunction
7411 83a8781b529d [project @ 2008-01-22 21:52:25 by jwe] jwe parents: 7017 diff changeset	86
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	87
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	88 %!test
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	89 %! 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	90 %! tol = 1e-6;
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	91 %! 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	92 %! for n = 1:numel (type)
7484 e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	93 %! rcondition(n) = 1 / cond (y, type{n});
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	94 %! endfor
e7485946272b new norm arg for cond John W. Eaton <jwe@octave.org> parents: 7411 diff changeset	95 %! 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	96
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	97 %!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	98 %!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	99
28886 d8318c12d903 test: remove unnecessary BIST tests in m-files checking for excessive number of inputs. Rik <rik@octave.org> parents: 28789 diff changeset	100 %!error <Invalid call> cond ()
16957 9f50dd7ece60 cond.m: Update documentation and coding style. Rik <rik@octave.org> parents: 14363 diff changeset	101 %!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	102 %!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	103 %!error <A must not contain Inf or NaN value> cond ([1, 2;NaN 4])

Mercurial > octave

annotate scripts/linear-algebra/cond.m @ 33625:d213a148b3f1 default tip @