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1 ## Copyright (C) 2007, 2008 Ben Abbott |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {[@var{multp}, @var{indx}] =} mpoles (@var{p}) |
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21 ## @deftypefnx {Function File} {[@var{multp}, @var{indx}] =} mpoles (@var{p}, @var{tol}) |
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22 ## @deftypefnx {Function File} {[@var{multp}, @var{indx}] =} mpoles (@var{p}, @var{tol}, @var{reorder}) |
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23 ## Identifiy unique poles in @var{p} and associates their multiplicity, |
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24 ## ordering them from largest to smallest. |
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25 ## |
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26 ## If the relative difference of the poles is less than @var{tol}, then |
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27 ## they are considered to be multiples. The default value for @var{tol} |
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28 ## is 0.001. |
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29 ## |
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30 ## If the optional parameter @var{reorder} is zero, poles are not sorted. |
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31 ## |
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32 ## The value @var{multp} is a vector specifying the multiplicity of the |
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33 ## poles. @var{multp}(:) refers to mulitplicity of @var{p}(@var{indx}(:)). |
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34 ## |
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35 ## For example, |
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36 ## |
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37 ## @example |
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38 ## @group |
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39 ## p = [2 3 1 1 2]; |
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40 ## [m, n] = mpoles(p); |
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41 ## @result{} m = [1; 1; 2; 1; 2] |
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42 ## @result{} n = [2; 5; 1; 4; 3] |
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43 ## @result{} p(n) = [3, 2, 2, 1, 1] |
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44 ## @end group |
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45 ## @end example |
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46 ## |
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47 ## @seealso{poly, roots, conv, deconv, polyval, polyderiv, polyinteg, residue} |
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48 ## @end deftypefn |
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49 |
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50 ## Author: Ben Abbott <bpabbott@mac.com> |
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51 ## Created: Sept 30, 2007 |
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52 |
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53 function [multp, indx] = mpoles (p, tol, reorder) |
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54 |
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55 if (nargin < 1 || nargin > 3) |
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56 print_usage (); |
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57 endif |
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58 |
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59 if (nargin < 2 || isempty (tol)) |
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60 tol = 0.001; |
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61 endif |
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62 |
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63 if (nargin < 3 || isempty (reorder)) |
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64 reorder = true; |
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65 endif |
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66 |
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67 Np = numel (p); |
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68 |
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69 ## Force the poles to be a column vector. |
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70 |
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71 p = p(:); |
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72 |
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73 ## Sort the poles according to their magnitidues, largest first. |
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74 |
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75 if (reorder) |
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76 ## Sort with smallest magnitude first. |
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77 [p, ordr] = sort (p); |
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78 ## Reverse order, largest maginitude first. |
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79 n = Np:-1:1; |
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80 p = p(n); |
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81 ordr = ordr(n); |
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82 else |
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83 ordr = 1:Np; |
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84 endif |
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85 |
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86 ## Find pole multiplicty by comparing the relative differnce in the |
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87 ## poles. |
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88 |
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89 multp = zeros (Np, 1); |
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90 indx = []; |
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91 n = find (multp == 0, 1); |
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92 while (n) |
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93 dp = abs (p-p(n)); |
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94 if (p(n) == 0.0) |
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95 p0 = mean (abs (p(find (abs (p) > 0)))); |
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96 if (isempty (p0)) |
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97 p0 = 1; |
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98 endif |
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99 else |
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100 p0 = abs (p(n)); |
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101 endif |
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102 k = find (dp < tol * p0); |
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103 ## Poles can only be members of one multiplicity group. |
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104 if (numel (indx)) |
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105 k = k(! ismember (k, indx)); |
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106 endif |
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107 m = 1:numel (k); |
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108 multp(k) = m; |
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109 indx = [indx; k]; |
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110 n = find (multp == 0, 1); |
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111 endwhile |
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112 multp = multp(indx); |
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113 indx = ordr(indx); |
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114 |
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115 endfunction |
