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annotate scripts/polynomial/mpoles.m @ 10821:693e22af08ae
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| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Mon, 26 Jul 2010 21:25:36 -0700 |
| parents | be55736a0783 |
| children | fd0a3ac60b0e |
| rev | line source |
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| 9245 | 1 ## Copyright (C) 2007, 2008, 2009 Ben Abbott |
| 6964 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 6964 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 6964 | 18 |
| 19 ## -*- texinfo -*- | |
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20 ## @deftypefn {Function File} {[@var{multp}, @var{indx}] =} mpoles (@var{p}) |
| 6964 | 21 ## @deftypefnx {Function File} {[@var{multp}, @var{indx}] =} mpoles (@var{p}, @var{tol}) |
| 22 ## @deftypefnx {Function File} {[@var{multp}, @var{indx}] =} mpoles (@var{p}, @var{tol}, @var{reorder}) | |
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23 ## Identify unique poles in @var{p} and associates their multiplicity, |
| 6964 | 24 ## ordering them from largest to smallest. |
| 25 ## | |
| 26 ## If the relative difference of the poles is less than @var{tol}, then | |
| 27 ## they are considered to be multiples. The default value for @var{tol} | |
| 28 ## is 0.001. | |
| 29 ## | |
| 30 ## If the optional parameter @var{reorder} is zero, poles are not sorted. | |
| 31 ## | |
| 32 ## The value @var{multp} is a vector specifying the multiplicity of the | |
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Cleanup documentation for poly.texi, interp.texi, geometry.texi
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parents:
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33 ## poles. @var{multp}(:) refers to multiplicity of @var{p}(@var{indx}(:)). |
| 6964 | 34 ## |
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35 ## For example: |
| 6964 | 36 ## |
| 37 ## @example | |
| 38 ## @group | |
| 39 ## p = [2 3 1 1 2]; | |
| 40 ## [m, n] = mpoles(p); | |
| 41 ## @result{} m = [1; 1; 2; 1; 2] | |
| 42 ## @result{} n = [2; 5; 1; 4; 3] | |
| 43 ## @result{} p(n) = [3, 2, 2, 1, 1] | |
| 44 ## @end group | |
| 45 ## @end example | |
| 46 ## | |
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47 ## @seealso{poly, roots, conv, deconv, polyval, polyderiv, polyint, residue} |
| 6964 | 48 ## @end deftypefn |
| 49 | |
| 50 ## Author: Ben Abbott <bpabbott@mac.com> | |
| 51 ## Created: Sept 30, 2007 | |
| 52 | |
| 53 function [multp, indx] = mpoles (p, tol, reorder) | |
| 54 | |
| 55 if (nargin < 1 || nargin > 3) | |
| 56 print_usage (); | |
| 57 endif | |
| 58 | |
| 59 if (nargin < 2 || isempty (tol)) | |
| 60 tol = 0.001; | |
| 61 endif | |
| 62 | |
| 63 if (nargin < 3 || isempty (reorder)) | |
| 64 reorder = true; | |
| 65 endif | |
| 66 | |
| 67 Np = numel (p); | |
| 68 | |
| 69 ## Force the poles to be a column vector. | |
| 70 | |
| 71 p = p(:); | |
| 72 | |
| 73 ## Sort the poles according to their magnitidues, largest first. | |
| 74 | |
| 75 if (reorder) | |
| 76 ## Sort with smallest magnitude first. | |
| 77 [p, ordr] = sort (p); | |
| 78 ## Reverse order, largest maginitude first. | |
| 79 n = Np:-1:1; | |
| 80 p = p(n); | |
| 81 ordr = ordr(n); | |
| 82 else | |
| 83 ordr = 1:Np; | |
| 84 endif | |
| 85 | |
| 86 ## Find pole multiplicty by comparing the relative differnce in the | |
| 87 ## poles. | |
| 88 | |
| 89 multp = zeros (Np, 1); | |
| 90 indx = []; | |
| 91 n = find (multp == 0, 1); | |
| 92 while (n) | |
| 93 dp = abs (p-p(n)); | |
| 94 if (p(n) == 0.0) | |
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95 if (any (abs (p) > 0 & isfinite (p))) |
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96 p0 = mean (abs (p(abs (p) > 0 & isfinite (p)))); |
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97 else |
| 6964 | 98 p0 = 1; |
| 7151 | 99 endif |
| 6964 | 100 else |
| 101 p0 = abs (p(n)); | |
| 102 endif | |
| 103 k = find (dp < tol * p0); | |
| 7360 | 104 ## Poles can only be members of one multiplicity group. |
| 105 if (numel (indx)) | |
| 106 k = k(! ismember (k, indx)); | |
| 107 endif | |
| 6964 | 108 m = 1:numel (k); |
| 109 multp(k) = m; | |
| 110 indx = [indx; k]; | |
| 111 n = find (multp == 0, 1); | |
| 112 endwhile | |
| 113 multp = multp(indx); | |
| 6998 | 114 indx = ordr(indx); |
| 6964 | 115 |
| 116 endfunction | |
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117 |
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mpoles.m: Fix infinite loop for a multiplicity of poles at zero. Test added.
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118 %!test |
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mpoles.m: Fix infinite loop for a multiplicity of poles at zero. Test added.
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119 %! [mp, n] = mpoles ([0 0], 0.01); |
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mpoles.m: Fix infinite loop for a multiplicity of poles at zero. Test added.
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parents:
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120 %! assert (mp, [1; 2]) |
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121 |