Mercurial > forge
view main/linear-algebra/inst/condeig.m @ 2719:4e0bad669780 octave-forge
Initial commit into CVS.
author | whyly |
---|---|
date | Tue, 17 Oct 2006 22:18:07 +0000 |
parents | |
children | a33bfad6a8d9 |
line wrap: on
line source
## Copyright (C) 2006 Arno Onken ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, write to the Free Software ## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} =} condeig (@var{a}) ## @deftypefnx {Function File} {[@var{v}, @var{lambda}, @var{c}] =} condeig (@var{a}) ## Computes condition numbers for the eigenvalues of a matrix. The ## condition numbers are the reciprocals of the cosines of the angles ## between the left and right eigenvectors. ## ## Arguments are ## ## @itemize @bullet ## @item ## @var{a} must be a square numeric matrix. ## @end itemize ## ## Return values are ## ## @itemize @bullet ## @item ## @var{c} is a vector of condition numbers for the eigenvalue of ## @var{a}. ## ## @item ## @var{v} is the matrix of right eigenvectors of @var{a}. The result is ## the same as for @code{[v, lambda] = eig (a)}. ## ## @item ## @var{lambda} is the diagonal matrix of eigenvalues of @var{a}. The ## result is the same as for @code{[v, lambda] = eig (a)}. ## @end itemize ## ## Example: ## ## @example ## @group ## a = [1, 2; 3, 4]; ## c = condeig (a) ## @result{} [1.0150; 1.0150] ## @end group ## @end example ## @end deftypefn ## Author: Arno Onken <whyly@gmx.net> ## Description: Condition numbers for eigenvalues function [v, lambda, c] = condeig (a) # Check arguments if (nargin != 1 || nargout > 3) usage ("[v, lambda, c] = condeig (a)"); endif if (! isempty (a) && ! ismatrix (a)) error ("condeig: a must be a numeric matrix"); endif if (columns (a) != rows (a)) error ("condeig: a must be a square matrix"); endif # Right eigenvectors [v, lambda] = eig (a); if (isempty (a)) c = lambda; else # Corresponding left eigenvectors vl = inv (v)'; # Normalize vectors vl = vl ./ repmat (sqrt (sum (abs (vl .^ 2))), rows (vl), 1); # Condition numbers # cos (angle) = (norm (v1) * norm (v2)) / dot (v1, v2) # Norm of the eigenvectors is 1 => norm (v1) * norm (v2) = 1 c = abs (1 ./ dot (vl, v)'); endif if (nargout == 0 || nargout == 1) v = c; endif endfunction %!test %! a = [1, 2; 3, 4]; %! c = condeig (a); %! expected_c = [1.0150; 1.0150]; %! assert (c, expected_c, 0.001); %!test %! a = [1, 3; 5, 8]; %! [v, lambda, c] = condeig (a); %! [expected_v, expected_lambda] = eig (a); %! expected_c = [1.0182; 1.0182]; %! assert (v, expected_v, 0.001); %! assert (lambda, expected_lambda, 0.001); %! assert (c, expected_c, 0.001);