Mercurial > jwe > octave
view scripts/polynomial/polyeig.m @ 20165:f1d0f506ee78 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed optimization, polynomial, signal script directories.
* scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m,
scripts/optimization/fminunc.m, scripts/optimization/fsolve.m,
scripts/optimization/fzero.m, scripts/optimization/glpk.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/pqpnonneg.m,
scripts/optimization/qp.m, scripts/optimization/sqp.m,
scripts/polynomial/compan.m, scripts/polynomial/mkpp.m,
scripts/polynomial/mpoles.m, scripts/polynomial/pchip.m,
scripts/polynomial/poly.m, scripts/polynomial/polyaffine.m,
scripts/polynomial/polyder.m, scripts/polynomial/polyeig.m,
scripts/polynomial/polyfit.m, scripts/polynomial/polygcd.m,
scripts/polynomial/polyint.m, scripts/polynomial/polyout.m,
scripts/polynomial/polyval.m, scripts/polynomial/ppder.m,
scripts/polynomial/ppint.m, scripts/polynomial/ppjumps.m,
scripts/polynomial/ppval.m, scripts/polynomial/residue.m,
scripts/polynomial/roots.m, scripts/polynomial/spline.m,
scripts/polynomial/splinefit.m, scripts/polynomial/unmkpp.m,
scripts/signal/arch_fit.m, scripts/signal/arch_rnd.m,
scripts/signal/arma_rnd.m, scripts/signal/autoreg_matrix.m,
scripts/signal/bartlett.m, scripts/signal/blackman.m, scripts/signal/detrend.m,
scripts/signal/diffpara.m, scripts/signal/durbinlevinson.m,
scripts/signal/fftconv.m, scripts/signal/fftfilt.m, scripts/signal/fftshift.m,
scripts/signal/filter2.m, scripts/signal/freqz.m, scripts/signal/hamming.m,
scripts/signal/hanning.m, scripts/signal/hurst.m, scripts/signal/ifftshift.m,
scripts/signal/periodogram.m, scripts/signal/sinc.m, scripts/signal/sinetone.m,
scripts/signal/sinewave.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/signal/spencer.m, scripts/signal/stft.m,
scripts/signal/synthesis.m, scripts/signal/unwrap.m,
scripts/signal/yulewalker.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 04 May 2015 21:50:57 -0700 |
parents | 9fc020886ae9 |
children | 516bb87ea72e |
line wrap: on
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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))