Mercurial > octave-nkf
view scripts/polynomial/polyeig.m @ 20651:e54ecb33727e
lo-array-gripes.cc: Remove FIXME's related to buffer size.
* lo-array-gripes.cc: Remove FIXME's related to buffer size. Shorten sprintf
buffers from 100 to 64 characters (still well more than 19 required).
Use 'const' decorator on constant value for clarity. Remove extra space
between variable and array bracket.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 12 Oct 2015 21:13:47 -0700 |
parents | f1d0f506ee78 |
children |
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## Copyright (C) 2012-2015 Fotios Kasolis ## ## This file is part of Octave. ## ## Octave 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 3 of the License, or (at ## your option) any later version. ## ## Octave 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 Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{z} =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl}) ## @deftypefnx {Function File} {[@var{v}, @var{z}] =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl}) ## ## Solve the polynomial eigenvalue problem of degree @var{l}. ## ## Given an @var{n*n} matrix polynomial ## ## @code{@var{C}(s) = @var{C0} + @var{C1} s + @dots{} + @var{Cl} s^l} ## ## @code{polyeig} solves the eigenvalue problem ## ## @code{(@var{C0} + @var{C1} + @dots{} + @var{Cl})v = 0}. ## ## Note that the eigenvalues @var{z} are the zeros of the matrix polynomial. ## @var{z} is a row vector with @var{n*l} elements. @var{v} is a matrix ## (@var{n} x @var{n}*@var{l}) with columns that correspond to the ## eigenvectors. ## ## @seealso{eig, eigs, compan} ## @end deftypefn ## Author: Fotios Kasolis function [z, v] = polyeig (varargin) if (nargin < 1 || nargout > 2) print_usage (); endif nin = numel (varargin); n = rows (varargin{1}); for i = 1 : nin if (! issquare (varargin{i})) error ("polyeig: coefficients must be square matrices"); endif if (rows (varargin{i}) != n) error ("polyeig: coefficients must have the same dimensions"); endif endfor ## matrix polynomial degree l = nin - 1; ## form needed matrices C = [ zeros(n * (l - 1), n), eye(n * (l - 1)); -cell2mat(varargin(1:end-1)) ]; D = [ eye(n * (l - 1)), zeros(n * (l - 1), n); zeros(n, n * (l - 1)), varargin{end} ]; ## solve generalized eigenvalue problem if (nargout == 2) [z, v] = eig (C, D); v = diag (v); ## return n-element eigenvectors normalized so that the infinity-norm = 1 z = z(1:n,:); ## max() takes the abs if complex: t = max (z); z /= diag (t); else z = eig (C, D); endif endfunction %!shared C0, C1 %! C0 = [8, 0; 0, 4]; C1 = [1, 0; 0, 1]; %!test %! z = polyeig (C0, C1); %! assert (z, [-8; -4]); %!test %! [v,z] = polyeig (C0, C1); %! assert (z, [-8; -4]); %! z = diag (z); %! d = C0*v + C1*v*z; %! assert (norm (d), 0.0); ## Test input validation %!error polyeig () %!error [a,b,c] = polyeig (1) %!error <coefficients must be square matrices> polyeig (ones (3,2)) %!error <coefficients must have the same dimensions> polyeig (ones (3,3), ones (2,2))