Mercurial > octave
view scripts/polynomial/polyeig.m @ 31214:19bd1953fc1d stable
GitHub-CI: Remove ubuntu-18.04 runners from build matrix.
* .github/workflow/make.yaml (ubuntu): GitHub-hosted runners for ubuntu-18.04
are being deprecated. Remove them from build matrix. See also:
https://github.com/actions/runner-images/issues/6002
author | Markus Mützel <markus.muetzel@gmx.de> |
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date | Tue, 30 Aug 2022 11:16:27 +0200 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2012-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{z} =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl}) ## @deftypefnx {} {[@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}x@var{n} matrix polynomial ## ## @code{@var{C}(@var{s}) = @var{C0} + @var{C1} @var{s} + @dots{} + @var{Cl} ## @var{s}^@var{l}} ## ## @code{polyeig} solves the eigenvalue problem ## ## @code{(@var{C0} + @var{C1} @var{z} + @dots{} + @var{Cl} @var{z}^@var{l}) ## @var{v} = 0}. ## ## Note that the eigenvalues @var{z} are the zeros of the matrix polynomial. ## @var{z} is a row vector with @code{@var{n}*@var{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 function [z, v] = polyeig (varargin) if (nargin < 1) print_usage (); endif n = rows (varargin{1}); for i = 1 : nargin 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 = nargin - 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 = eig (C, D); else [z, v] = eig (C, D); v = diag (v); ## return n-element eigenvectors normalized so that the infinity-norm = 1 z = z(1:n,:); t = max (z); # max() takes the abs if complex. z ./= t; 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 <Invalid call> polyeig () %!error <coefficients must be square matrices> polyeig (ones (3,2)) %!error <coefficients must have the same dimensions> %! polyeig (ones (3,3), ones (2,2))