Mercurial > octave
annotate scripts/polynomial/mpoles.m @ 27919:1891570abac8
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> |
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date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
children | bd51beb6205e |
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27919
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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 ## |
6964 | 6 ## |
7 ## This file is part of Octave. | |
8 ## | |
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9 ## Octave is free software: you can redistribute it and/or modify it |
6964 | 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. |
6964 | 13 ## |
14 ## Octave is distributed in the hope that it will be useful, but | |
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. |
6964 | 18 ## |
19 ## You should have received a copy of the GNU General Public License | |
7016 | 20 ## along with Octave; see the file COPYING. If not, see |
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21 ## <https://www.gnu.org/licenses/>. |
6964 | 22 |
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. |
6964 | 33 ## |
34 ## If the optional parameter @var{reorder} is zero, poles are not sorted. | |
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))}. |
6964 | 39 ## |
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40 ## For example: |
6964 | 41 ## |
42 ## @example | |
43 ## @group | |
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] |
6964 | 49 ## @end group |
50 ## @end example | |
51 ## | |
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52 ## @seealso{residue, poly, roots, conv, deconv} |
6964 | 53 ## @end deftypefn |
54 | |
55 ## Author: Ben Abbott <bpabbott@mac.com> | |
56 ## Created: Sept 30, 2007 | |
57 | |
58 function [multp, indx] = mpoles (p, tol, reorder) | |
59 | |
60 if (nargin < 1 || nargin > 3) | |
61 print_usage (); | |
62 endif | |
63 | |
64 if (nargin < 2 || isempty (tol)) | |
65 tol = 0.001; | |
66 endif | |
67 | |
68 if (nargin < 3 || isempty (reorder)) | |
69 reorder = true; | |
70 endif | |
71 | |
72 Np = numel (p); | |
73 | |
74 ## Force the poles to be a column vector. | |
75 | |
76 p = p(:); | |
77 | |
78 ## Sort the poles according to their magnitidues, largest first. | |
79 | |
80 if (reorder) | |
81 ## Sort with smallest magnitude first. | |
82 [p, ordr] = sort (p); | |
83 ## Reverse order, largest maginitude first. | |
84 n = Np:-1:1; | |
85 p = p(n); | |
86 ordr = ordr(n); | |
87 else | |
88 ordr = 1:Np; | |
89 endif | |
90 | |
91 ## Find pole multiplicty by comparing the relative differnce in the | |
92 ## poles. | |
93 | |
94 multp = zeros (Np, 1); | |
95 indx = []; | |
96 n = find (multp == 0, 1); | |
97 while (n) | |
98 dp = abs (p-p(n)); | |
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 |
6964 | 103 p0 = 1; |
7151 | 104 endif |
6964 | 105 else |
106 p0 = abs (p(n)); | |
107 endif | |
108 k = find (dp < tol * p0); | |
7360 | 109 ## Poles can only be members of one multiplicity group. |
110 if (numel (indx)) | |
111 k = k(! ismember (k, indx)); | |
112 endif | |
6964 | 113 m = 1:numel (k); |
114 multp(k) = m; | |
115 indx = [indx; k]; | |
116 n = find (multp == 0, 1); | |
117 endwhile | |
118 multp = multp(indx); | |
6998 | 119 indx = ordr(indx); |
6964 | 120 |
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]); |