Mercurial > octave-antonio
view scripts/polynomial/compan.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} {} compan (@var{c}) ## Compute the companion matrix corresponding to polynomial coefficient vector ## @var{c}. ## ## The companion matrix is ## @tex ## $$ ## A = \left[\matrix{ ## -c_2/c_1 & -c_3/c_1 & \cdots & -c_N/c_1 & -c_{N+1}/c_1\cr ## 1 & 0 & \cdots & 0 & 0 \cr ## 0 & 1 & \cdots & 0 & 0 \cr ## \vdots & \vdots & \ddots & \vdots & \vdots \cr ## 0 & 0 & \cdots & 1 & 0}\right]. ## $$ ## @end tex ## @ifnottex ## @c Set example in small font to prevent overfull line ## ## @smallexample ## @group ## _ _ ## | -c(2)/c(1) -c(3)/c(1) @dots{} -c(N)/c(1) -c(N+1)/c(1) | ## | 1 0 @dots{} 0 0 | ## | 0 1 @dots{} 0 0 | ## A = | . . . . . | ## | . . . . . | ## | . . . . . | ## |_ 0 0 @dots{} 1 0 _| ## @end group ## @end smallexample ## ## @end ifnottex ## The eigenvalues of the companion matrix are equal to the roots of the ## polynomial. ## @seealso{roots, poly, eig} ## @end deftypefn ## Author: Tony Richardson <arichard@stark.cc.oh.us> ## Created: June 1994 ## Adapted-By: jwe function A = compan (c) if (nargin != 1) print_usage (); endif if (! isvector (c)) error ("compan: expecting a vector argument"); endif n = length (c); if (n == 1) A = []; else A = diag (ones (n-2, 1), -1); A(1,:) = -c(2:n) / c(1); endif endfunction %!assert (compan ([1, 2, 3]), [-2, -3; 1, 0]) %!assert (compan ([1; 2; 3]), [-2, -3; 1, 0]) %!assert (isempty (compan (4))) %!assert (compan ([3, 2, 1]), [-2/3, -1/3; 1, 0]) %!error compan ([1,2;3,4]) %!error compan ([])