Mercurial > octave-antonio
view scripts/polynomial/roots.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 |
line wrap: on
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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} {} roots (@var{c}) ## ## Compute the roots of the polynomial @var{c}. ## ## For a vector @var{c} with @math{N} components, return the roots of the ## polynomial ## @tex ## $$ ## c_1 x^{N-1} + \cdots + c_{N-1} x + c_N. ## $$ ## @end tex ## @ifnottex ## ## @example ## c(1) * x^(N-1) + @dots{} + c(N-1) * x + c(N) ## @end example ## ## @end ifnottex ## ## As an example, the following code finds the roots of the quadratic ## polynomial ## @tex ## $$ p(x) = x^2 - 5. $$ ## @end tex ## @ifnottex ## ## @example ## p(x) = x^2 - 5. ## @end example ## ## @end ifnottex ## ## @example ## @group ## c = [1, 0, -5]; ## roots (c) ## @result{} 2.2361 ## @result{} -2.2361 ## @end group ## @end example ## ## Note that the true result is ## @tex ## $\pm \sqrt{5}$ ## @end tex ## @ifnottex ## @math{+/- sqrt(5)} ## @end ifnottex ## which is roughly ## @tex ## $\pm 2.2361$. ## @end tex ## @ifnottex ## @math{+/- 2.2361}. ## @end ifnottex ## @seealso{poly, compan, fzero} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Created: 24 December 1993 ## Adapted-By: jwe function r = roots (v) if (nargin != 1 || (! isvector (v) && ! isempty (v))) print_usage (); elseif (any (! isfinite (v))) error ("roots: inputs must not contain Inf or NaN"); endif v = v(:); n = numel (v); ## If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], ## we can remove the leading k zeros, ## and n - k - l roots of the polynomial are zero. v_max = max (abs (v)); if (isempty (v) || v_max == 0) r = []; return; endif f = find (v ./ v_max); m = numel (f); v = v(f(1):f(m)); l = numel (v); if (l > 1) A = diag (ones (1, l-2), -1); A(1,:) = -v(2:l) ./ v(1); r = eig (A); if (f(m) < n) r = [r; zeros(n - f(m), 1)]; endif else r = zeros (n - f(m), 1); endif endfunction %!test %! p = [poly([3 3 3 3]), 0 0 0 0]; %! r = sort (roots (p)); %! assert (r, [0; 0; 0; 0; 3; 3; 3; 3], 0.001); %!assert (isempty (roots ([]))) %!assert (isempty (roots ([0 0]))) %!assert (isempty (roots (1))) %!assert (roots ([1, -6, 11, -6]), [3; 2; 1], sqrt (eps)) %!assert (roots ([1e-200, -1e200, 1]), 1e-200) %!assert (roots ([1e-200, -1e200 * 1i, 1]), -1e-200 * 1i) %!error roots () %!error roots (1,2) %!error roots ([1, 2; 3, 4]) %!error <inputs must not contain Inf or NaN> roots ([1 Inf 1]) %!error <inputs must not contain Inf or NaN> roots ([1 NaN 1])