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% POLY POLY Convert Roots To Polynomial Coefficients
%
% Usage
%
% This function calculates the polynomial coefficients for given roots
%
% p = poly(r)
%
% when r is a vector, is a vector whose elements are the coefficients
% of the polynomial whose roots are the elements of r. Alternately,
% you can provide a matrix
%
% p = poly(A)
%
% when A is an N x N square matrix, is a row vector with
% N+1 elements which are the coefficients of the
% characteristic polynomial, det(lambda*eye(size(A))-A).
%
% Contributed by Paulo Xavier Candeias under GPL.
function p = poly(r)
if (nargin < 1) | (nargout > 1)
error('wrong use (see help poly)')
end
% Identify arguments
if issquare(r)
r = eig(r);
else
r = r(:).';
end
% Strip out infinities
r = r( ~isinf(r) );
% Expand recursion formula
n = length(r);
p = [1,zeros(1,n)];
for v = 1:n
p(2:v+1) = p(2:v+1)-r(v)*p(1:v);
end
% The result should be real if the roots are complex conjugates.
r_neg_comp_roots = r(imag(r)<0);
r_pos_comp_roots = r(imag(r)>0);
if (numel(r_neg_comp_roots) == numel(r_pos_comp_roots))
if sort(r(imag(r)>0))-sort(conj(r(imag(r)<0)))<teps(r)
p = real(p);
end
end
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