Mercurial > hg > octave-nkf
annotate scripts/general/divergence.m @ 14868:5d3a684236b0
maint: Use Octave coding conventions for cuddling parentheses in scripts directory
* lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m,
colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m,
int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m,
__isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m,
rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m,
inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m,
gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m,
ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m,
compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m,
getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m,
__xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m,
fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m,
copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m,
installed_packages.m, is_architecture_dependent.m, load_package_dirs.m,
print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m,
allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m,
comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m,
fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m,
mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m,
polar.m, print.m, __add_datasource__.m, __add_default_menu__.m,
__axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m,
__errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m,
__ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m,
__go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m,
__pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m,
__stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m,
__uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m,
ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m,
surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m,
mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m,
ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m,
addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m,
arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m,
hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m,
stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m,
__sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m,
treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m,
magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m,
quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m,
bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m,
kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m,
z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m,
strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m,
test.m, now.m: Use Octave coding conventions for cuddling parentheses in
scripts directory.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Tue, 17 Jul 2012 07:08:39 -0700 |
| parents | 460a3c6d8bf1 |
| children | d63878346099 |
| rev | line source |
|---|---|
|
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1 ## Copyright (C) 2009-2012 Kai Habel |
| 11428 | 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 | |
| 7 ## the Free Software Foundation; either version 3 of the License, or (at | |
| 8 ## your option) any later version. | |
| 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 | |
| 16 ## along with Octave; see the file COPYING. If not, see | |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 18 | |
| 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}) |
| 11428 | 21 ## @deftypefnx {Function File} {@var{div} =} divergence (@var{fx}, @var{fy}, @var{fz}) |
| 22 ## @deftypefnx {Function File} {@var{div} =} divergence (@var{x}, @var{y}, @var{fx}, @var{fy}) | |
| 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. |
| 11428 | 26 ## @tex |
| 27 ## $$ | |
| 28 ## div F(x,y,z) = \partial_x{F} + \partial_y{F} + \partial_z{F} | |
| 29 ## $$ | |
| 30 ## @end tex | |
| 31 ## @ifnottex | |
|
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32 ## |
| 11428 | 33 ## @example |
| 34 ## @group | |
| 35 ## d d d | |
| 36 ## div F(x,y,z) = -- F(x,y,z) + -- F(x,y,z) + -- F(x,y,z) | |
| 37 ## dx dy dz | |
| 38 ## @end group | |
| 39 ## @end example | |
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40 ## |
| 11428 | 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. |
| 11428 | 44 ## |
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45 ## @seealso{curl, gradient, del2, dot} |
| 11428 | 46 ## @end deftypefn |
| 47 | |
| 48 ## Author: Kai Habel <kai.habel@gmx.de> | |
| 49 | |
| 50 function retval = divergence (varargin) | |
| 51 | |
| 52 fidx = 1; | |
| 53 if (nargin == 2) | |
| 54 sz = size (varargin{fidx}); | |
| 55 dx = (1:sz(2))(:); | |
| 56 dy = (1:sz(1))(:); | |
| 57 elseif (nargin == 3) | |
| 58 sz = size (varargin{fidx}); | |
| 59 dx = 1:sz(2); | |
| 60 dy = 1:sz(1); | |
| 61 dz = 1:sz(3); | |
| 62 elseif (nargin == 4) | |
| 63 fidx = 3; | |
| 64 dx = varargin{1}(1,:); | |
| 65 dy = varargin{2}(:,1); | |
| 66 elseif (nargin == 6) | |
| 67 fidx = 4; | |
| 68 dx = varargin{1}(1,:,1)(:); | |
| 69 dy = varargin{2}(:,1,1)(:); | |
| 70 dz = varargin{3}(1,1,:)(:); | |
| 71 else | |
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72 print_usage (); |
| 11428 | 73 endif |
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74 |
| 11428 | 75 if ((nargin == 4) || (nargin == 2)) |
| 76 if (!size_equal (varargin{fidx},varargin{fidx + 1})) | |
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77 error ("divergence: size of X and Y must match"); |
| 11428 | 78 elseif (ndims (varargin{fidx}) != 2) |
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79 error ("divergence: expected two-dimensional matrices X and Y"); |
| 11428 | 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"); |
| 11428 | 82 endif |
| 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 |
| 11428 | 87 elseif ((nargin == 6) || (nargin == 3)) |
| 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"); |
| 11428 | 90 elseif (ndims (varargin{fidx}) != 3) |
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91 error ("divergence: expected two-dimensional matrices X, Y, and Z"); |
| 11428 | 92 elseif ((length (dx) != size (varargin{fidx}, 2)) |
| 93 || (length (dy) != size (varargin{fidx}, 1)) | |
| 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"); |
| 11428 | 96 endif |
| 97 | |
| 98 ## x-direction | |
| 99 retval = gradient (varargin{fidx}, dx, dy, dz); | |
| 100 ## y-direction | |
| 101 retval += shiftdim (gradient (shiftdim (varargin{fidx + 1}, 2), dy), 1); | |
| 102 ## z-direction | |
| 103 retval += shiftdim (gradient (shiftdim (varargin{fidx + 2}, 1), dz), 2); | |
| 104 endif | |
| 105 | |
| 106 endfunction | |
| 107 | |
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108 |
| 11428 | 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 |