Mercurial > octave-antonio
view scripts/polynomial/poly.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 | 4197fc428c7d |
children |
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## Copyright (C) 1994-2015 John W. Eaton ## ## 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} {} poly (@var{A}) ## @deftypefnx {Function File} {} poly (@var{x}) ## If @var{A} is a square @math{N}-by-@math{N} matrix, @code{poly (@var{A})} ## is the row vector of the coefficients of @code{det (z * eye (N) - A)}, ## the characteristic polynomial of @var{A}. ## ## For example, the following code finds the eigenvalues of @var{A} which are ## the roots of @code{poly (@var{A})}. ## ## @example ## @group ## roots (poly (eye (3))) ## @result{} 1.00001 + 0.00001i ## 1.00001 - 0.00001i ## 0.99999 + 0.00000i ## @end group ## @end example ## ## In fact, all three eigenvalues are exactly 1 which emphasizes that for ## numerical performance the @code{eig} function should be used to compute ## eigenvalues. ## ## If @var{x} is a vector, @code{poly (@var{x})} is a vector of the ## coefficients of the polynomial whose roots are the elements of @var{x}. ## That is, if @var{c} is a polynomial, then the elements of ## @code{@var{d} = roots (poly (@var{c}))} are contained in @var{c}. The ## vectors @var{c} and @var{d} are not identical, however, due to sorting and ## numerical errors. ## @seealso{roots, eig} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Created: 24 December 1993 ## Adapted-By: jwe function y = poly (x) if (nargin != 1) print_usage (); endif m = min (size (x)); n = max (size (x)); if (m == 0) y = 1; return; elseif (m == 1) v = x; elseif (m == n) v = eig (x); else print_usage (); endif y = zeros (1, n+1); y(1) = 1; for j = 1:n; y(2:(j+1)) = y(2:(j+1)) - v(j) .* y(1:j); endfor if (all (all (imag (x) == 0))) y = real (y); endif endfunction %!assert (poly ([]), 1) %!assert (poly ([1, 2, 3]), [1, -6, 11, -6]) %!assert (poly ([1, 2; 3, 4]), [1, -5, -2], sqrt (eps)) %!error poly ([1, 2, 3; 4, 5, 6])