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## Copyright (C) 2007-2013 Ben Abbott
##
## 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} {[@var{multp}, @var{idxp}] =} mpoles (@var{p})
## @deftypefnx {Function File} {[@var{multp}, @var{idxp}] =} mpoles (@var{p}, @var{tol})
## @deftypefnx {Function File} {[@var{multp}, @var{idxp}] =} mpoles (@var{p}, @var{tol}, @var{reorder})
## Identify unique poles in @var{p} and their associated multiplicity. The
## output is ordered from largest pole to smallest pole.
##
## If the relative difference of two poles is less than @var{tol} then
## they are considered to be multiples. The default value for @var{tol}
## is 0.001.
##
## If the optional parameter @var{reorder} is zero, poles are not sorted.
##
## The output @var{multp} is a vector specifying the multiplicity of the
## poles. @code{@var{multp}(n)} refers to the multiplicity of the Nth pole
## @code{@var{p}(@var{idxp}(n))}.
##
## For example:
##
## @example
## @group
## p = [2 3 1 1 2];
## [m, n] = mpoles (p)
## @result{} m = [1; 1; 2; 1; 2]
## @result{} n = [2; 5; 1; 4; 3]
## @result{} p(n) = [3, 2, 2, 1, 1]
## @end group
## @end example
##
## @seealso{residue, poly, roots, conv, deconv}
## @end deftypefn
## Author: Ben Abbott <bpabbott@mac.com>
## Created: Sept 30, 2007
function [multp, indx] = mpoles (p, tol, reorder)
if (nargin < 1 || nargin > 3)
print_usage ();
endif
if (nargin < 2 || isempty (tol))
tol = 0.001;
endif
if (nargin < 3 || isempty (reorder))
reorder = true;
endif
Np = numel (p);
## Force the poles to be a column vector.
p = p(:);
## Sort the poles according to their magnitidues, largest first.
if (reorder)
## Sort with smallest magnitude first.
[p, ordr] = sort (p);
## Reverse order, largest maginitude first.
n = Np:-1:1;
p = p(n);
ordr = ordr(n);
else
ordr = 1:Np;
endif
## Find pole multiplicty by comparing the relative differnce in the
## poles.
multp = zeros (Np, 1);
indx = [];
n = find (multp == 0, 1);
while (n)
dp = abs (p-p(n));
if (p(n) == 0.0)
if (any (abs (p) > 0 & isfinite (p)))
p0 = mean (abs (p(abs (p) > 0 & isfinite (p))));
else
p0 = 1;
endif
else
p0 = abs (p(n));
endif
k = find (dp < tol * p0);
## Poles can only be members of one multiplicity group.
if (numel (indx))
k = k(! ismember (k, indx));
endif
m = 1:numel (k);
multp(k) = m;
indx = [indx; k];
n = find (multp == 0, 1);
endwhile
multp = multp(indx);
indx = ordr(indx);
endfunction
%!test
%! [mp, n] = mpoles ([0 0], 0.01);
%! assert (mp, [1; 2]);
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