annotate scripts/general/divergence.m @ 14363:f3d52523cde1

Use Octave coding conventions in all m-file %!test blocks * wavread.m, acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m, asec.m, asecd.m, asech.m, asind.m, atand.m, cosd.m, cot.m, cotd.m, coth.m, csc.m, cscd.m, csch.m, sec.m, secd.m, sech.m, sind.m, tand.m, accumarray.m, accumdim.m, bitcmp.m, bitget.m, bitset.m, blkdiag.m, cart2pol.m, cart2sph.m, celldisp.m, chop.m, circshift.m, colon.m, common_size.m, cplxpair.m, cumtrapz.m, curl.m, dblquad.m, deal.m, divergence.m, flipdim.m, fliplr.m, flipud.m, genvarname.m, gradient.m, idivide.m, int2str.m, interp1.m, interp1q.m, interp2.m, interp3.m, interpft.m, interpn.m, isa.m, isdir.m, isequal.m, isequalwithequalnans.m, issquare.m, logspace.m, nargchk.m, narginchk.m, nargoutchk.m, nextpow2.m, nthargout.m, num2str.m, pol2cart.m, polyarea.m, postpad.m, prepad.m, profile.m, profshow.m, quadgk.m, quadv.m, randi.m, rat.m, repmat.m, rot90.m, rotdim.m, shift.m, shiftdim.m, sph2cart.m, structfun.m, trapz.m, triplequad.m, convhull.m, dsearch.m, dsearchn.m, griddata3.m, griddatan.m, rectint.m, tsearchn.m, __makeinfo__.m, doc.m, get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m, imwrite.m, dlmwrite.m, fileread.m, is_valid_file_id.m, strread.m, textread.m, textscan.m, commutation_matrix.m, cond.m, condest.m, cross.m, duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m, issymmetric.m, logm.m, normest.m, null.m, onenormest.m, orth.m, planerot.m, qzhess.m, rank.m, rref.m, trace.m, vech.m, ans.m, bincoeff.m, bug_report.m, bzip2.m, comma.m, compare_versions.m, computer.m, edit.m, fileparts.m, fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m, ismac.m, ispc.m, isunix.m, list_primes.m, ls.m, mexext.m, namelengthmax.m, news.m, orderfields.m, paren.m, recycle.m, rmappdata.m, semicolon.m, setappdata.m, setfield.m, substruct.m, symvar.m, ver.m, version.m, warning_ids.m, xor.m, fminbnd.m, fsolve.m, fzero.m, lsqnonneg.m, optimset.m, pqpnonneg.m, sqp.m, matlabroot.m, __gnuplot_drawnow__.m, __plt_get_axis_arg__.m, ancestor.m, cla.m, clf.m, close.m, colorbar.m, colstyle.m, comet3.m, contourc.m, figure.m, gca.m, gcbf.m, gcbo.m, gcf.m, ginput.m, graphics_toolkit.m, gtext.m, hggroup.m, hist.m, hold.m, isfigure.m, ishghandle.m, ishold.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m, line.m, loglog.m, loglogerr.m, meshgrid.m, ndgrid.m, newplot.m, orient.m, patch.m, plot3.m, plotyy.m, __print_parse_opts__.m, quiver3.m, refreshdata.m, ribbon.m, semilogx.m, semilogxerr.m, semilogy.m, stem.m, stem3.m, subplot.m, title.m, uigetfile.m, view.m, whitebg.m, compan.m, conv.m, deconv.m, mkpp.m, mpoles.m, pchip.m, poly.m, polyaffine.m, polyder.m, polyfit.m, polygcd.m, polyint.m, polyout.m, polyval.m, polyvalm.m, ppder.m, ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, intersect.m, ismember.m, powerset.m, setdiff.m, setxor.m, union.m, unique.m, autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, fftconv.m, fftfilt.m, fftshift.m, freqz.m, hamming.m, hanning.m, ifftshift.m, sinc.m, sinetone.m, sinewave.m, unwrap.m, bicg.m, bicgstab.m, gmres.m, gplot.m, nonzeros.m, pcg.m, pcr.m, spaugment.m, spconvert.m, spdiags.m, speye.m, spfun.m, spones.m, sprand.m, sprandsym.m, spstats.m, spy.m, svds.m, treelayout.m, bessel.m, beta.m, betaln.m, factor.m, factorial.m, isprime.m, lcm.m, legendre.m, nchoosek.m, nthroot.m, perms.m, pow2.m, primes.m, reallog.m, realpow.m, realsqrt.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, rosser.m, vander.m, __finish__.m, center.m, cloglog.m, corr.m, cov.m, gls.m, histc.m, iqr.m, kendall.m, kurtosis.m, logit.m, mahalanobis.m, mean.m, meansq.m, median.m, mode.m, moment.m, ols.m, ppplot.m, prctile.m, probit.m, quantile.m, range.m, ranks.m, run_count.m, runlength.m, skewness.m, spearman.m, statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m, betarnd.m, binocdf.m, binoinv.m, binopdf.m, binornd.m, cauchy_cdf.m, cauchy_inv.m, cauchy_pdf.m, cauchy_rnd.m, chi2cdf.m, chi2inv.m, chi2pdf.m, chi2rnd.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m, empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, expcdf.m, expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m, gaminv.m, gampdf.m, gamrnd.m, geocdf.m, geoinv.m, geopdf.m, geornd.m, hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m, laplace_cdf.m, laplace_inv.m, laplace_pdf.m, laplace_rnd.m, logistic_cdf.m, logistic_inv.m, logistic_pdf.m, logistic_rnd.m, logncdf.m, logninv.m, lognpdf.m, lognrnd.m, nbincdf.m, nbininv.m, nbinpdf.m, nbinrnd.m, normcdf.m, norminv.m, normpdf.m, normrnd.m, poisscdf.m, poissinv.m, poisspdf.m, poissrnd.m, stdnormal_cdf.m, stdnormal_inv.m, stdnormal_pdf.m, stdnormal_rnd.m, tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m, unifcdf.m, unifinv.m, unifpdf.m, unifrnd.m, wblcdf.m, wblinv.m, wblpdf.m, wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m, bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m, findstr.m, hex2dec.m, index.m, isletter.m, mat2str.m, rindex.m, str2num.m, strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m, substr.m, validatestring.m, demo.m, example.m, fail.m, speed.m, addtodate.m, asctime.m, clock.m, ctime.m, date.m, datenum.m, datetick.m, datevec.m, eomday.m, etime.m, is_leap_year.m, now.m: Use Octave coding conventions in all m-file %!test blocks
author Rik <octave@nomad.inbox5.com>
date Mon, 13 Feb 2012 07:29:44 -0800
parents 72c96de7a403
children 460a3c6d8bf1
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1 ## Copyright (C) 2009-2012 Kai Habel
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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{div} =} divergence (@var{x}, @var{y}, @var{z}, @var{fx}, @var{fy}, @var{fz})
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21 ## @deftypefnx {Function File} {@var{div} =} divergence (@var{fx}, @var{fy}, @var{fz})
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22 ## @deftypefnx {Function File} {@var{div} =} divergence (@var{x}, @var{y}, @var{fx}, @var{fy})
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23 ## @deftypefnx {Function File} {@var{div} =} divergence (@var{fx}, @var{fy})
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24 ## Calculate divergence of a vector field given by the arrays @var{fx},
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25 ## @var{fy}, and @var{fz} or @var{fx}, @var{fy} respectively.
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26 ## @tex
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27 ## $$
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28 ## div F(x,y,z) = \partial_x{F} + \partial_y{F} + \partial_z{F}
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29 ## $$
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30 ## @end tex
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31 ## @ifnottex
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32 ##
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33 ## @example
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34 ## @group
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35 ## d d d
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36 ## div F(x,y,z) = -- F(x,y,z) + -- F(x,y,z) + -- F(x,y,z)
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37 ## dx dy dz
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38 ## @end group
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39 ## @end example
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40 ##
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41 ## @end ifnottex
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42 ## The coordinates of the vector field can be given by the arguments @var{x},
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43 ## @var{y}, @var{z} or @var{x}, @var{y} respectively.
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44 ##
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45 ## @seealso{curl, gradient, del2, dot}
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46 ## @end deftypefn
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47
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48 ## Author: Kai Habel <kai.habel@gmx.de>
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49
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50 function retval = divergence (varargin)
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51
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52 fidx = 1;
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53 if (nargin == 2)
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54 sz = size (varargin{fidx});
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55 dx = (1:sz(2))(:);
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56 dy = (1:sz(1))(:);
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57 elseif (nargin == 3)
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58 sz = size (varargin{fidx});
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59 dx = 1:sz(2);
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60 dy = 1:sz(1);
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61 dz = 1:sz(3);
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62 elseif (nargin == 4)
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63 fidx = 3;
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64 dx = varargin{1}(1,:);
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65 dy = varargin{2}(:,1);
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66 elseif (nargin == 6)
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67 fidx = 4;
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68 dx = varargin{1}(1,:,1)(:);
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69 dy = varargin{2}(:,1,1)(:);
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70 dz = varargin{3}(1,1,:)(:);
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71 else
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72 print_usage();
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73 endif
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74
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75 if ((nargin == 4) || (nargin == 2))
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76 if (!size_equal (varargin{fidx},varargin{fidx + 1}))
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77 error ("divergence: size of X and Y must match");
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78 elseif (ndims (varargin{fidx}) != 2)
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79 error ("divergence: expected two-dimensional matrices X and Y");
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80 elseif ((length (dx) != columns (varargin{fidx})) || (length (dy) != rows (varargin{fidx})))
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81 error ("divergence: size of dx and dy must match the respective dimension of X and Y");
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82 endif
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83
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84 retval = gradient(varargin{fidx}, dx, dy);
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85 retval += gradient(varargin{fidx + 1}.', dy, dx).';
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86
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87 elseif ((nargin == 6) || (nargin == 3))
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88 if (!size_equal (varargin{fidx},varargin{fidx + 1},varargin{fidx + 2}))
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89 error ("divergence: size of X, Y, and Z must match");
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90 elseif (ndims (varargin{fidx}) != 3)
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91 error ("divergence: expected two-dimensional matrices X, Y, and Z");
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92 elseif ((length (dx) != size (varargin{fidx}, 2))
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93 || (length (dy) != size (varargin{fidx}, 1))
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94 || (length (dz) != size (varargin{fidx}, 3)))
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95 error ("divergence: size of dx, dy, and dz must match the respective dimesion of X, Y, and Z");
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96 endif
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97
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98 ## x-direction
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99 retval = gradient (varargin{fidx}, dx, dy, dz);
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100 ## y-direction
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101 retval += shiftdim (gradient (shiftdim (varargin{fidx + 1}, 2), dy), 1);
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102 ## z-direction
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103 retval += shiftdim (gradient (shiftdim (varargin{fidx + 2}, 1), dz), 2);
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104 endif
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105
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106 endfunction
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107
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108
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109 %!test
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110 %! [X,Y] = meshgrid (-20:20,-22:22);
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111 %! div = divergence (X-Y,Y);
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112 %! assert (all (div(:) == 2));
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113 %! assert (size_equal (X,Y,div));
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114