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

annotate scripts/linear-algebra/condeig.m @ 30564:796f54d4ddbf stable

update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2021. In all .txi and .texi files except gpl.txi and gpl.texi in the doc/liboctave and doc/interpreter directories, change the copyright to "Octave Project Developers", the same as used for other source files. Update copyright notices for 2022 (not done since 2019). For gpl.txi and gpl.texi, change the copyright notice to be "Free Software Foundation, Inc." and leave the date at 2007 only because this file only contains the text of the GPL, not anything created by the Octave Project Developers. Add Paul Thomas to contributors.in.

author	John W. Eaton <jwe@octave.org>
date	Tue, 28 Dec 2021 18:22:40 -0500
parents	7854d5752dd2
children	597f3ee61a48

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 ##
30564 796f54d4ddbf update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	3 ## Copyright (C) 2006-2022 The Octave Project Developers
27918 b442ec6dda5c use centralized file for copyright info for individual contributors John W. Eaton <jwe@octave.org> parents: 27216 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/>.
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	7 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	8 ## This file is part of Octave.
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: 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
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: 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.
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	14 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	15 ## Octave is distributed in the hope that it will be useful, but
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: 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.
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	19 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	20 ## You should have received a copy of the GNU General Public License
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: 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 ########################################################################
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	25
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	26 ## -- texinfo --
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	27 ## @deftypefn {} {@var{c} =} condeig (@var{a})
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	28 ## @deftypefnx {} {[@var{v}, @var{lambda}, @var{c}] =} condeig (@var{a})
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	29 ## Compute condition numbers of a matrix with respect to eigenvalues.
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	30 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	31 ## The condition numbers are the reciprocals of the cosines of the angles
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	32 ## between the left and right eigenvectors; Large values indicate that the
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	33 ## matrix has multiple distinct eigenvalues.
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	34 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	35 ## The input @var{a} must be a square numeric matrix.
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	36 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	37 ## The outputs are:
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	38 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	39 ## @itemize @bullet
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	40 ## @item
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	41 ## @var{c} is a vector of condition numbers for the eigenvalues of
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	42 ## @var{a}.
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	43 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	44 ## @item
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	45 ## @var{v} is the matrix of right eigenvectors of @var{a}. The result is
22195 93ed9396f2c3 * condeig.m: fix Texinfo markup typo in condeig doc string (bug #48672) Mike Miller <mtmiller@octave.org> parents: 22129 diff changeset	46 ## equivalent to calling @code{[@var{v}, @var{lambda}] = eig (@var{a})}.
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	47 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	48 ## @item
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	49 ## @var{lambda} is the diagonal matrix of eigenvalues of @var{a}. The
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	50 ## result is equivalent to calling
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	51 ## @code{[@var{v}, @var{lambda}] = eig (@var{a})}.
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	52 ## @end itemize
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	53 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	54 ## Example
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	55 ##
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	56 ## @example
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	57 ## @group
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	58 ## a = [1, 2; 3, 4];
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	59 ## c = condeig (a)
26600 f6730533820e doc: clean up doc example blocks for accuracy and consistent formatting Mike Miller <mtmiller@octave.org> parents: 26376 diff changeset	60 ## @result{} c =
f6730533820e doc: clean up doc example blocks for accuracy and consistent formatting Mike Miller <mtmiller@octave.org> parents: 26376 diff changeset	61 ## 1.0150
f6730533820e doc: clean up doc example blocks for accuracy and consistent formatting Mike Miller <mtmiller@octave.org> parents: 26376 diff changeset	62 ## 1.0150
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	63 ## @end group
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	64 ## @end example
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	65 ## @seealso{eig, cond, balance}
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	66 ## @end deftypefn
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	67
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	68 function [v, lambda, c] = condeig (a)
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	69
28891 de5f2f9a64ff maint: Use same coding style when checking for a minimum of 1 input. Rik <rik@octave.org> parents: 27923 diff changeset	70 if (nargin < 1)
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	71 print_usage ();
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	72 endif
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	73
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	74 if (! (isnumeric (a) && issquare (a)))
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	75 error ("condeig: A must be a square numeric matrix");
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	76 endif
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	77
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	78 if (issparse (a) && nargout <= 1)
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	79 ## Try to use svds to calculate the condition number as it will typically
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	80 ## be much faster than calling eig as only the smallest and largest
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	81 ## eigenvalue are calculated.
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	82
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	83 ## FIXME: This calculates one condition number for the entire matrix.
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	84 ## In the full case, separate condition numbers are calculated for every
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	85 ## eigenvalue.
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	86 try
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	87 s0 = svds (a, 1, 0); # min eigenvalue
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	88 v = svds (a, 1) / s0; # max eigenvalue
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	89 catch
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	90 ## Caught an error as there is a singular value exactly at zero!!
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	91 v = Inf;
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	92 end_try_catch
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	93 return;
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	94 endif
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	95
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	96 ## Right eigenvectors
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	97 [v, lambda] = eig (a);
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	98
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	99 if (isempty (a))
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	100 c = [];
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	101 else
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	102 ## Corresponding left eigenvectors
26272 aa47b1287d7e condeig.m: Suppress warning about internal intermediate matrix being singular. Rik <rik@octave.org> parents: 25054 diff changeset	103 ## Use 2-argument form to suppress possible singular matrix warning.
aa47b1287d7e condeig.m: Suppress warning about internal intermediate matrix being singular. Rik <rik@octave.org> parents: 25054 diff changeset	104 [vl, ~] = inv (v);
aa47b1287d7e condeig.m: Suppress warning about internal intermediate matrix being singular. Rik <rik@octave.org> parents: 25054 diff changeset	105 vl = vl';
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	106 ## Normalize vectors
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	107 vl ./= repmat (sqrt (sum (abs (vl .^ 2))), rows (vl), 1);
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	108
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	109 ## Condition numbers
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	110 ## Definition: cos (angle) = (norm (v1) * norm (v2)) / dot (v1, v2)
27216 823b4bcf79fc unless necessary for formatting or code, use ' instead of ` John W. Eaton <jwe@octave.org> parents: 26600 diff changeset	111 ## Eigenvectors have been normalized so 'norm (v1) * norm (v2)' = 1
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	112 c = abs (1 ./ dot (vl, v)');
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	113 endif
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	114
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	115 if (nargout <= 1)
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	116 v = c;
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	117 endif
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	118
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	119 endfunction
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	120
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	121
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	122 %!test
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	123 %! a = [1, 2; 3, 4];
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	124 %! c = condeig (a);
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	125 %! expected_c = [1.0150; 1.0150];
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	126 %! assert (c, expected_c, 0.001);
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	127
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	128 %!test
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	129 %! a = [1, 3; 5, 8];
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	130 %! [v, lambda, c] = condeig (a);
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	131 %! [expected_v, expected_lambda] = eig (a);
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	132 %! expected_c = [1.0182; 1.0182];
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	133 %! assert (v, expected_v, 0.001);
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	134 %! assert (lambda, expected_lambda, 0.001);
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	135 %! assert (c, expected_c, 0.001);
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	136
28942 fc4bb4bd1d5e maint: Use '##' as lead-in for full-line comments. Rik <rik@octave.org> parents: 28896 diff changeset	137 ## Test empty input
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	138 %!assert (condeig ([]), [])
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	139
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	140 ## Test input validation
28896 90fea9cc9caa test: Add expected error message <Invalid call> to BIST tests for nargin. Rik <rik@octave.org> parents: 28891 diff changeset	141 %!error <Invalid call> condeig ()
22129 e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	142 %!error <A must be a square numeric matrix> condeig ({1})
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	143 %!error <A must be a square numeric matrix> condeig (ones (3,2))
e859caa53399 condeig.m: New function imported from Octave-Forge linear-algebra package. Rik <rik@octave.org> parents: diff changeset	144 %!error <A must be a square numeric matrix> condeig (ones (2,2,2))

Mercurial > octave

annotate scripts/linear-algebra/condeig.m @ 30564:796f54d4ddbf stable