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cplxreal.m

%% Copyright (C) 2005 Julius O. Smith III
%%
%% This program 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 2 of the License, or
%% (at your option) any later version.
%%
%% This program 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 this program; If not, see <http://www.gnu.org/licenses/>.

%% -*- texinfo -*-
%% @deftypefn {Function File} { =} cplxreal (@var{z}, @var{thresh})
%% Split the vector z into its complex (@var{zc}) and real (@var{zr}) elements,
%% eliminating one of each complex-conjugate pair.
%%
%% INPUTS:@*
%%   @itemize
%%   @item
%%   @var{z}      = row- or column-vector of complex numbers@*
%%   @item
%%   @var{thresh} = tolerance threshold for numerical comparisons (default = 100*eps)
%%   @end itemize
%%
%% RETURNED:@*
%%   @itemize
%%   @item
%% @var{zc} = elements of @var{z} having positive imaginary parts@*
%%   @item
%% @var{zr} = elements of @var{z} having zero imaginary part@*
%%   @end itemize
%%
%% Each complex element of @var{z} is assumed to have a complex-conjugate
%% counterpart elsewhere in @var{z} as well.  Elements are declared real
%% if their imaginary parts have magnitude less than @var{thresh}.
%%
%% @seealso{cplxpair}
%% @end deftypefn

function [zc,zr] = cplxreal(z,thresh)

if nargin<2, thresh=100*eps; end
% interesting for testing: if nargin<2, thresh=1E-3; end

if isempty(z)
  zc=[];
  zr=[];
else
  zcp = cplxpair(z); % sort complex pairs, real roots at end
  nz = length(z);
  nzrsec = 0;
  i=nz;
  while i && abs(imag(zcp(i)))<thresh % determine no. of real values
    zcp(i) = real(zcp(i));
    nzrsec = nzrsec+1;
    i=i-1;
  end
  nzsect2 = nz-nzrsec;
  if mod(nzsect2,2)~=0
    error('cplxreal: Odd number of complex values!'); 
  end
  nzsec = nzsect2/2;
  zc = zcp(2:2:nzsect2);
  zr = zcp(nzsect2+1:nz);
end
%!test 
%! [zc,zr] = cplxreal(roots([1 0 0 1]));
%! assert({zc,zr},{0.5+i*sin(pi/3),-1},10*eps);

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