update packages

[CreaPhase.git] / octave_packages / m / polynomial / mpoles.m

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+## Copyright (C) 2007-2012 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])
+