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annotate scripts/polynomial/mpoles.m @ 14327:4d917a6a858b stable
doc: Use Octave coding conventions in @example blocks of docstrings.
* accumarray.m, accumdim.m, bar.m, base2dec.m, bincoeff.m, bitcmp.m, bitset.m,
celldisp.m, chop.m, clabel.m, cloglog.m, colon.m, compass.m, computer.m,
contour3.m, contourc.m, corr.m, cstrcat.m, ctime.m, cylinder.m, date.m,
dec2base.m, demo.m, dir.m, dlmwrite.m, expm.m, ezcontourf.m, ezcontour.m,
ezmeshc.m, ezmesh.m, ezplot.m, ezsurfc.m, ezsurf.m, feather.m, findobj.m,
flipdim.m, fplot.m, genvarname.m, getfield.m, hankel.m, hilb.m, hist.m,
idivide.m, index.m, int2str.m, interp1.m, is_leap_year.m, ismember.m,
isocolors.m, isonormals.m, isosurface.m, kurtosis.m, legendre.m, linkprop.m,
logit.m, logm.m, __makeinfo__.m, __marching_cube__.m, median.m, mkoctfile.m,
moment.m, mpoles.m, orderfields.m, pcg.m, pcr.m, plot3.m, plotmatrix.m,
polyaffine.m, polygcd.m, poly.m, polyout.m, print.m, qp.m, quadgk.m, qzhess.m,
randi.m, rat.m, refreshdata.m, residue.m, rose.m, rot90.m, saveas.m, saveobj.m,
shiftdim.m, skewness.m, spaugment.m, spdiags.m, sqp.m, stem.m, str2num.m,
strcat.m, strjust.m, strread.m, strsplit.m, structfun.m, subplot.m,
subsindex.m, substruct.m, surfl.m, surfnorm.m, svds.m, uimenu.m, union.m,
voronoi.m, warning_ids.m, wblpdf.m: Use Octave coding conventions in
@example blocks of docstrings.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sat, 04 Feb 2012 22:12:50 -0800 |
| parents | 72c96de7a403 |
| children | f3d52523cde1 |
| rev | line source |
|---|---|
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1 ## Copyright (C) 2007-2012 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{idxp}] =} mpoles (@var{p}) |
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21 ## @deftypefnx {Function File} {[@var{multp}, @var{idxp}] =} mpoles (@var{p}, @var{tol}) |
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22 ## @deftypefnx {Function File} {[@var{multp}, @var{idxp}] =} mpoles (@var{p}, @var{tol}, @var{reorder}) |
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23 ## Identify unique poles in @var{p} and their associated multiplicity. The |
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24 ## output is ordered from largest pole to smallest pole. |
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25 ## |
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26 ## If the relative difference of two poles is less than @var{tol} then |
| 6964 | 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 ## | |
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32 ## The output @var{multp} is a vector specifying the multiplicity of the |
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33 ## poles. @code{@var{multp}(n)} refers to the multiplicity of the Nth pole |
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34 ## @code{@var{p}(@var{idxp}(n))}. |
| 6964 | 35 ## |
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36 ## For example: |
| 6964 | 37 ## |
| 38 ## @example | |
| 39 ## @group | |
| 40 ## p = [2 3 1 1 2]; | |
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41 ## [m, n] = mpoles (p) |
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42 ## @result{} m = [1; 1; 2; 1; 2] |
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43 ## @result{} n = [2; 5; 1; 4; 3] |
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44 ## @result{} p(n) = [3, 2, 2, 1, 1] |
| 6964 | 45 ## @end group |
| 46 ## @end example | |
| 47 ## | |
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48 ## @seealso{residue, poly, roots, conv, deconv} |
| 6964 | 49 ## @end deftypefn |
| 50 | |
| 51 ## Author: Ben Abbott <bpabbott@mac.com> | |
| 52 ## Created: Sept 30, 2007 | |
| 53 | |
| 54 function [multp, indx] = mpoles (p, tol, reorder) | |
| 55 | |
| 56 if (nargin < 1 || nargin > 3) | |
| 57 print_usage (); | |
| 58 endif | |
| 59 | |
| 60 if (nargin < 2 || isempty (tol)) | |
| 61 tol = 0.001; | |
| 62 endif | |
| 63 | |
| 64 if (nargin < 3 || isempty (reorder)) | |
| 65 reorder = true; | |
| 66 endif | |
| 67 | |
| 68 Np = numel (p); | |
| 69 | |
| 70 ## Force the poles to be a column vector. | |
| 71 | |
| 72 p = p(:); | |
| 73 | |
| 74 ## Sort the poles according to their magnitidues, largest first. | |
| 75 | |
| 76 if (reorder) | |
| 77 ## Sort with smallest magnitude first. | |
| 78 [p, ordr] = sort (p); | |
| 79 ## Reverse order, largest maginitude first. | |
| 80 n = Np:-1:1; | |
| 81 p = p(n); | |
| 82 ordr = ordr(n); | |
| 83 else | |
| 84 ordr = 1:Np; | |
| 85 endif | |
| 86 | |
| 87 ## Find pole multiplicty by comparing the relative differnce in the | |
| 88 ## poles. | |
| 89 | |
| 90 multp = zeros (Np, 1); | |
| 91 indx = []; | |
| 92 n = find (multp == 0, 1); | |
| 93 while (n) | |
| 94 dp = abs (p-p(n)); | |
| 95 if (p(n) == 0.0) | |
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96 if (any (abs (p) > 0 & isfinite (p))) |
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97 p0 = mean (abs (p(abs (p) > 0 & isfinite (p)))); |
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98 else |
| 6964 | 99 p0 = 1; |
| 7151 | 100 endif |
| 6964 | 101 else |
| 102 p0 = abs (p(n)); | |
| 103 endif | |
| 104 k = find (dp < tol * p0); | |
| 7360 | 105 ## Poles can only be members of one multiplicity group. |
| 106 if (numel (indx)) | |
| 107 k = k(! ismember (k, indx)); | |
| 108 endif | |
| 6964 | 109 m = 1:numel (k); |
| 110 multp(k) = m; | |
| 111 indx = [indx; k]; | |
| 112 n = find (multp == 0, 1); | |
| 113 endwhile | |
| 114 multp = multp(indx); | |
| 6998 | 115 indx = ordr(indx); |
| 6964 | 116 |
| 117 endfunction | |
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118 |
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119 %!test |
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120 %! [mp, n] = mpoles ([0 0], 0.01); |
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121 %! assert (mp, [1; 2]) |
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122 |