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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2020.
author John W. Eaton <jwe@octave.org>
date Mon, 06 Jan 2020 22:29:51 -0500
parents b442ec6dda5c
children bd51beb6205e
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27919
1891570abac8 update Octave Project Developers copyright for the new year
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1 ## Copyright (C) 2007-2020 The Octave Project Developers
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2 ##
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution
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4 ## or <https://octave.org/COPYRIGHT.html/>.
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5 ##
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6 ##
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7 ## This file is part of Octave.
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8 ##
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9 ## Octave is free software: you can redistribute it and/or modify it
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10 ## under the terms of the GNU General Public License as published by
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11 ## the Free Software Foundation, either version 3 of the License, or
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12 ## (at your option) any later version.
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13 ##
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14 ## Octave is distributed in the hope that it will be useful, but
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15 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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17 ## GNU General Public License for more details.
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18 ##
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19 ## You should have received a copy of the GNU General Public License
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20 ## along with Octave; see the file COPYING. If not, see
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21 ## <https://www.gnu.org/licenses/>.
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22
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23 ## -*- texinfo -*-
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24 ## @deftypefn {} {[@var{multp}, @var{idxp}] =} mpoles (@var{p})
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25 ## @deftypefnx {} {[@var{multp}, @var{idxp}] =} mpoles (@var{p}, @var{tol})
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26 ## @deftypefnx {} {[@var{multp}, @var{idxp}] =} mpoles (@var{p}, @var{tol}, @var{reorder})
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27 ## Identify unique poles in @var{p} and their associated multiplicity.
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28 ##
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29 ## The output is ordered from largest pole to smallest pole.
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30 ##
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31 ## If the relative difference of two poles is less than @var{tol} then they are
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32 ## considered to be multiples. The default value for @var{tol} is 0.001.
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33 ##
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34 ## If the optional parameter @var{reorder} is zero, poles are not sorted.
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35 ##
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36 ## The output @var{multp} is a vector specifying the multiplicity of the poles.
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37 ## @code{@var{multp}(n)} refers to the multiplicity of the Nth pole
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38 ## @code{@var{p}(@var{idxp}(n))}.
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39 ##
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40 ## For example:
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41 ##
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42 ## @example
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43 ## @group
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44 ## p = [2 3 1 1 2];
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45 ## [m, n] = mpoles (p)
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46 ## @result{} m = [1; 1; 2; 1; 2]
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47 ## @result{} n = [2; 5; 1; 4; 3]
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48 ## @result{} p(n) = [3, 2, 2, 1, 1]
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49 ## @end group
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50 ## @end example
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51 ##
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52 ## @seealso{residue, poly, roots, conv, deconv}
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53 ## @end deftypefn
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54
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55 ## Author: Ben Abbott <bpabbott@mac.com>
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56 ## Created: Sept 30, 2007
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57
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58 function [multp, indx] = mpoles (p, tol, reorder)
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59
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60 if (nargin < 1 || nargin > 3)
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61 print_usage ();
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62 endif
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63
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64 if (nargin < 2 || isempty (tol))
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65 tol = 0.001;
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66 endif
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67
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68 if (nargin < 3 || isempty (reorder))
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69 reorder = true;
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70 endif
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71
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72 Np = numel (p);
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73
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74 ## Force the poles to be a column vector.
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75
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76 p = p(:);
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77
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78 ## Sort the poles according to their magnitidues, largest first.
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79
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80 if (reorder)
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81 ## Sort with smallest magnitude first.
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82 [p, ordr] = sort (p);
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83 ## Reverse order, largest maginitude first.
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84 n = Np:-1:1;
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85 p = p(n);
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86 ordr = ordr(n);
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87 else
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88 ordr = 1:Np;
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89 endif
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90
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91 ## Find pole multiplicty by comparing the relative differnce in the
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92 ## poles.
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93
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94 multp = zeros (Np, 1);
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95 indx = [];
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96 n = find (multp == 0, 1);
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97 while (n)
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98 dp = abs (p-p(n));
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99 if (p(n) == 0.0)
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100 if (any (abs (p) > 0 & isfinite (p)))
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101 p0 = mean (abs (p(abs (p) > 0 & isfinite (p))));
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102 else
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103 p0 = 1;
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104 endif
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105 else
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106 p0 = abs (p(n));
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107 endif
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108 k = find (dp < tol * p0);
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109 ## Poles can only be members of one multiplicity group.
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110 if (numel (indx))
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111 k = k(! ismember (k, indx));
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112 endif
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113 m = 1:numel (k);
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114 multp(k) = m;
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115 indx = [indx; k];
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116 n = find (multp == 0, 1);
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117 endwhile
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118 multp = multp(indx);
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119 indx = ordr(indx);
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120
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121 endfunction
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122
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123
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124 %!test
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125 %! [mp, n] = mpoles ([0 0], 0.01);
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126 %! assert (mp, [1; 2]);