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view scripts/polynomial/poly.m @ 14327:4d917a6a858b stable
doc: Use Octave coding conventions in @example blocks of docstrings.
* accumarray.m, accumdim.m, bar.m, base2dec.m, bincoeff.m, bitcmp.m, bitset.m,
celldisp.m, chop.m, clabel.m, cloglog.m, colon.m, compass.m, computer.m,
contour3.m, contourc.m, corr.m, cstrcat.m, ctime.m, cylinder.m, date.m,
dec2base.m, demo.m, dir.m, dlmwrite.m, expm.m, ezcontourf.m, ezcontour.m,
ezmeshc.m, ezmesh.m, ezplot.m, ezsurfc.m, ezsurf.m, feather.m, findobj.m,
flipdim.m, fplot.m, genvarname.m, getfield.m, hankel.m, hilb.m, hist.m,
idivide.m, index.m, int2str.m, interp1.m, is_leap_year.m, ismember.m,
isocolors.m, isonormals.m, isosurface.m, kurtosis.m, legendre.m, linkprop.m,
logit.m, logm.m, __makeinfo__.m, __marching_cube__.m, median.m, mkoctfile.m,
moment.m, mpoles.m, orderfields.m, pcg.m, pcr.m, plot3.m, plotmatrix.m,
polyaffine.m, polygcd.m, poly.m, polyout.m, print.m, qp.m, quadgk.m, qzhess.m,
randi.m, rat.m, refreshdata.m, residue.m, rose.m, rot90.m, saveas.m, saveobj.m,
shiftdim.m, skewness.m, spaugment.m, spdiags.m, sqp.m, stem.m, str2num.m,
strcat.m, strjust.m, strread.m, strsplit.m, structfun.m, subplot.m,
subsindex.m, substruct.m, surfl.m, surfnorm.m, svds.m, uimenu.m, union.m,
voronoi.m, warning_ids.m, wblpdf.m: Use Octave coding conventions in
@example blocks of docstrings.
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Sat, 04 Feb 2012 22:12:50 -0800 |
parents | 72c96de7a403 |
children | f3d52523cde1 |
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## Copyright (C) 1994-2012 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(all (all (poly ([1, 2, 3]) == [1, -6, 11, -6]))); %!assert(all (all (abs (poly ([1, 2; 3, 4]) - [1, -5, -2]) < sqrt (eps)))); %!error poly ([1, 2, 3; 4, 5, 6]); %!assert(poly ([]),1);