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annotate scripts/general/del2.m @ 20266:83792dd9bcc1

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Use in-place operators in m-files where possible. * scripts/audio/@audioplayer/set.m, scripts/audio/@audiorecorder/set.m, scripts/audio/mu2lin.m, scripts/elfun/cosd.m, scripts/general/del2.m, scripts/general/profexplore.m, scripts/general/quadl.m, scripts/general/rat.m, scripts/general/rotdim.m, scripts/help/get_first_help_sentence.m, scripts/help/private/__strip_html_tags__.m, scripts/image/cubehelix.m, scripts/io/textread.m, scripts/linear-algebra/duplication_matrix.m, scripts/linear-algebra/housh.m, scripts/linear-algebra/krylov.m, scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m, scripts/linear-algebra/onenormest.m, scripts/optimization/fminsearch.m, scripts/optimization/lsqnonneg.m, scripts/optimization/qp.m, scripts/plot/appearance/annotation.m, scripts/plot/appearance/axis.m, scripts/plot/appearance/legend.m, scripts/plot/appearance/specular.m, scripts/plot/draw/colorbar.m, scripts/plot/draw/hist.m, scripts/plot/draw/plotmatrix.m, scripts/plot/draw/private/__stem__.m, scripts/plot/util/__actual_axis_position__.m, scripts/plot/util/__gnuplot_drawnow__.m, scripts/plot/util/findobj.m, scripts/plot/util/print.m, scripts/plot/util/private/__go_draw_axes__.m, scripts/plot/util/private/__print_parse_opts__.m, scripts/plot/util/rotate.m, scripts/polynomial/pchip.m, scripts/polynomial/polyaffine.m, scripts/polynomial/polyder.m, scripts/polynomial/private/__splinefit__.m, scripts/polynomial/residue.m, scripts/signal/arch_fit.m, scripts/signal/arch_rnd.m, scripts/signal/bartlett.m, scripts/signal/blackman.m, scripts/signal/freqz.m, scripts/signal/hamming.m, scripts/signal/hanning.m, scripts/signal/spectral_adf.m, scripts/signal/spectral_xdf.m, scripts/signal/stft.m, scripts/sparse/bicgstab.m, scripts/sparse/cgs.m, scripts/sparse/private/__sprand_impl__.m, scripts/sparse/qmr.m, scripts/sparse/sprandsym.m, scripts/sparse/svds.m, scripts/specfun/legendre.m, scripts/special-matrix/gallery.m, scripts/statistics/base/gls.m, scripts/statistics/models/logistic_regression.m, scripts/statistics/tests/kruskal_wallis_test.m, scripts/statistics/tests/manova.m, scripts/statistics/tests/wilcoxon_test.m, scripts/time/datevec.m: Use in-place operators in m-files where possible.
author Rik <rik@octave.org>
date Tue, 26 May 2015 21:07:42 -0700
parents 7503499a252b
children
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4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 2000-2015 Kai Habel
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2 ## Copyright (C) 2007 David Bateman
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {@var{d} =} del2 (@var{M})
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22 ## @deftypefnx {Function File} {@var{d} =} del2 (@var{M}, @var{h})
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23 ## @deftypefnx {Function File} {@var{d} =} del2 (@var{M}, @var{dx}, @var{dy}, @dots{})
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24 ##
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25 ## Calculate the discrete Laplace
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26 ## @tex
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27 ## operator $( \nabla^2 )$.
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28 ## @end tex
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29 ## @ifnottex
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30 ## operator.
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31 ## @end ifnottex
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32 ##
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33 ## For a 2-dimensional matrix @var{M} this is defined as
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34 ## @tex
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35 ## $$d = {1 \over 4} \left( {d^2 \over dx^2} M(x,y) + {d^2 \over dy^2} M(x,y) \right)$$
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36 ## @end tex
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37 ## @ifnottex
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38 ##
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39 ## @example
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40 ## @group
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41 ## 1 / d^2 d^2 \
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42 ## D = --- * | --- M(x,y) + --- M(x,y) |
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43 ## 4 \ dx^2 dy^2 /
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44 ## @end group
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45 ## @end example
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46 ##
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47 ## @end ifnottex
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48 ## For N-dimensional arrays the sum in parentheses is expanded to include second
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49 ## derivatives over the additional higher dimensions.
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50 ##
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51 ## The spacing between evaluation points may be defined by @var{h}, which is a
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52 ## scalar defining the equidistant spacing in all dimensions. Alternatively,
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53 ## the spacing in each dimension may be defined separately by @var{dx},
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54 ## @var{dy}, etc. A scalar spacing argument defines equidistant spacing,
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55 ## whereas a vector argument can be used to specify variable spacing. The
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56 ## length of the spacing vectors must match the respective dimension of
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57 ## @var{M}. The default spacing value is 1.
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58 ##
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59 ## At least 3 data points are needed for each dimension. Boundary points are
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60 ## calculated from the linear extrapolation of interior points.
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61 ##
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62 ## @seealso{gradient, diff}
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63 ## @end deftypefn
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64
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65 ## Author: Kai Habel <kai.habel@gmx.de>
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66
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67 function D = del2 (M, varargin)
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68
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69 if (nargin < 1)
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70 print_usage ();
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71 endif
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72
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73 nd = ndims (M);
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74 sz = size (M);
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75 dx = cell (1, nd);
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76 if (nargin == 2 || nargin == 1)
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77 if (nargin == 1)
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78 h = 1;
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79 else
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80 h = varargin{1};
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81 endif
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82 for i = 1 : nd
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83 if (isscalar (h))
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84 dx{i} = h * ones (sz (i), 1);
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85 else
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86 if (length (h) == sz (i))
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87 dx{i} = diff (h)(:);
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88 else
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89 error ("del2: dimensionality mismatch in %d-th spacing vector", i);
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90 endif
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91 endif
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92 endfor
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93 elseif (nargin - 1 == nd)
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94 ## Reverse dx{1} and dx{2} as the X-dim is the 2nd dim of the ND array
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95 tmp = varargin{1};
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96 varargin{1} = varargin{2};
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97 varargin{2} = tmp;
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98
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99 for i = 1 : nd
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100 if (isscalar (varargin{i}))
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101 dx{i} = varargin{i} * ones (sz (i), 1);
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102 else
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103 if (length (varargin{i}) == sz (i))
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104 dx{i} = diff (varargin{i})(:);
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105 else
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106 error ("del2: dimensionality mismatch in %d-th spacing vector", i);
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107 endif
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108 endif
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109 endfor
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110 else
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111 print_usage ();
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112 endif
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113
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114 idx = cell (1, nd);
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115 for i = 1: nd
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116 idx{i} = ":";
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117 endfor
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118
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119 D = zeros (sz);
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120 for i = 1: nd
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121 if (sz(i) >= 3)
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122 DD = zeros (sz);
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123 idx1 = idx2 = idx3 = idx;
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124
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125 ## interior points
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126 idx1{i} = 1 : sz(i) - 2;
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parents:
diff changeset
127 idx2{i} = 2 : sz(i) - 1;
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dbateman
parents:
diff changeset
128 idx3{i} = 3 : sz(i);
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
129 szi = sz;
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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diff changeset
130 szi (i) = 1;
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parents:
diff changeset
131
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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diff changeset
132 h1 = repmat (shiftdim (dx{i}(1 : sz(i) - 2), 1 - i), szi);
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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diff changeset
133 h2 = repmat (shiftdim (dx{i}(2 : sz(i) - 1), 1 - i), szi);
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diff changeset
134 DD(idx2{:}) = ((M(idx1{:}) - M(idx2{:})) ./ h1 + ...
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9167
diff changeset
135 (M(idx3{:}) - M(idx2{:})) ./ h2) ./ (h1 + h2);
6788
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parents:
diff changeset
136
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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137 ## left and right boundary
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diff changeset
138 if (sz(i) == 3)
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
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diff changeset
139 DD(idx1{:}) = DD(idx3{:}) = DD(idx2{:});
6788
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diff changeset
140 else
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9167
diff changeset
141 idx1{i} = 1;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9167
diff changeset
142 idx2{i} = 2;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9167
diff changeset
143 idx3{i} = 3;
19867
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19731
diff changeset
144 DD(idx1{:}) = (dx{i}(1) + dx{i}(2)) / dx{i}(2) * DD(idx2{:}) - ...
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
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diff changeset
145 dx{i}(1) / dx{i}(2) * DD(idx3{:});
6788
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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parents:
diff changeset
146
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9167
diff changeset
147 idx1{i} = sz(i);
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9167
diff changeset
148 idx2{i} = sz(i) - 1;
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 9167
diff changeset
149 idx3{i} = sz(i) - 2;
19867
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
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parents: 19731
diff changeset
150 DD(idx1{:}) = (dx{i}(sz(i) - 1) + dx{i}(sz(i) - 2)) / ...
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19731
diff changeset
151 dx{i}(sz(i) - 2) * DD(idx2{:}) - ...
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
Rik <rik@octave.org>
parents: 19731
diff changeset
152 dx{i}(sz(i) - 1) / dx{i}(sz(i) - 2) * DD(idx3{:});
6788
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parents:
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153 endif
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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parents:
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154
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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parents:
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155 D += DD;
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
156 endif
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
157 endfor
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
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parents:
diff changeset
158
20266
83792dd9bcc1 Use in-place operators in m-files where possible.
Rik <rik@octave.org>
parents: 20193
diff changeset
159 D ./= nd;
6788
c81a0f3f5a82 [project @ 2007-07-23 22:05:29 by dbateman]
dbateman
parents:
diff changeset
160 endfunction
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 14138
diff changeset
161
18651
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
162
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
163 ## 3x3 constant test
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
164 %!test
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
165 %! a = ones (3,3);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
166 %! b = del2 (a);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
167 %! assert (b(:,1), [0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
168 %! assert (b(:,2), [0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
169 %! assert (b(:,3), [0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
170
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
171 ## 3x3 planar test
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
172 %!test
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
173 %! a = [1,2,3;2,3,4;3,4,5];
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
174 %! b = del2 (a);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
175 %! assert (b(:,1), [0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
176 %! assert (b(:,2), [0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
177 %! assert (b(:,3), [0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
178
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
179 ## 3x3 corner test
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
180 %!test
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
181 %! a = zeros (3,3);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
182 %! a(1,1) = 1.0;
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
183 %! b = 2*del2 (a);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
184 %! assert (b(:,1), [1.00;0.50;0.50]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
185 %! assert (b(:,2), [0.50;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
186 %! assert (b(:,3), [0.50;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
187 %! assert (b, flipud (2*del2 (flipud (a))));
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
188 %! assert (b, fliplr (2*del2 (fliplr (a))));
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
189 %! assert (b, flipud (fliplr (2*del2 (fliplr (flipud (a))))));
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
190
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
191 ## 3x3 boundary test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
192 %!test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
193 %! a = zeros (3,3);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
194 %! a(2,1)=1.0;
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
195 %! b = 2*del2 (a);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
196 %! assert (b(:,1), [-1.00;-0.50;-1.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
197 %! assert (b(:,2), [0.00;0.50;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
198 %! assert (b(:,3), [0.00;0.50;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
199 %! assert (b, flipud (2*del2 (flipud (a))));
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
200 %! assert (b, fliplr (2*del2 (fliplr (a))));
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
201 %! assert (b, flipud (fliplr (2*del2 (fliplr (flipud (a))))));
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
202
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
203 ## 3x3 center test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
204 %!test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
205 %! a = zeros (3,3);
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
206 %! a(2,2) = 1.0;
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
207 %! b = del2 (a);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
208 %! assert (b(:,1), [0.00;-0.50;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
209 %! assert (b(:,2), [-0.50;-1.00;-0.50]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
210 %! assert (b(:,3), [0.00;-0.50;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
211
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
212 ## 4x4 constant test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
213 %!test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
214 %! a = ones (4,4);
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
215 %! b = del2 (a);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
216 %! assert (b(:,1), [0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
217 %! assert (b(:,2), [0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
218 %! assert (b(:,3), [0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
219 %! assert (b(:,4), [0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
220
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
221 ## 4x4 planar test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
222 %!test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
223 %! a = [1,2,3,4;2,3,4,5;3,4,5,6;4,5,6,7];
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
224 %! b = del2 (a);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
225 %! assert (b(:,1), [0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
226 %! assert (b(:,2), [0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
227 %! assert (b(:,3), [0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
228 %! assert (b(:,4), [0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
229
21e5205679d0 del2.m: Add %!tests (bug #42005).
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230 ## 4x4 corner test
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
231 %!test
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
232 %! a = zeros (4,4);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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233 %! a(1,1) = 1.0;
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
234 %! b = 2*del2 (a);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
235 %! assert (b(:,1), [2.00;0.50;0.00;-0.50]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
236 %! assert (b(:,2), [0.50;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
237 %! assert (b(:,3), [0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
238 %! assert (b(:,4), [-0.50;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
239 %! assert (b, flipud (2*del2 (flipud (a))));
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
240 %! assert (b, fliplr (2*del2 (fliplr (a))));
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
241 %! assert (b, flipud (fliplr (2*del2 (fliplr (flipud (a))))));
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
242
21e5205679d0 del2.m: Add %!tests (bug #42005).
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243 ## 9x9 center test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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diff changeset
244 %!test
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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245 %! a = zeros (9,9);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
246 %! a(5,5) = 1.0;
21e5205679d0 del2.m: Add %!tests (bug #42005).
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247 %! b = 2*del2 (a);
21e5205679d0 del2.m: Add %!tests (bug #42005).
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diff changeset
248 %! assert (b(:,1), [0.00;0.00;0.00;0.00;0.00;0.00;0.00;0.00;0.00]);
21e5205679d0 del2.m: Add %!tests (bug #42005).
Allan Jacobs <jacobsallanster@gmail.com>
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249 %! assert (b(:,2), [0.00;0.00;0.00;0.00;0.00;0.00;0.00;0.00;0.00]);
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250 %! assert (b(:,3), [0.00;0.00;0.00;0.00;0.00;0.00;0.00;0.00;0.00]);
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251 %! assert (b(:,4), [0.00;0.00;0.00;0.00;0.50;0.00;0.00;0.00;0.00]);
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252 %! assert (b(:,5), [0.00;0.00;0.00;0.50;-2.00;0.50;0.00;0.00;0.00]);
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253 %! assert (b(:,6), b(:,4));
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254 %! assert (b(:,7), b(:,3));
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255 %! assert (b(:,8), b(:,2));
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256 %! assert (b(:,9), b(:,1));
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257
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258 ## 9x9 boundary test
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259 %!test
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260 %! a = zeros (9,9);
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261 %! a(1,5) = 1.0;
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262 %! b = 2*del2 (a);
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263 %! assert (b(1,:), [0.00,0.00,0.00,0.50,0.00,0.50,0.00,0.00,0.00]);
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264 %! assert (b(2,:), [0.00,0.00,0.00,0.00,0.50,0.00,0.00,0.00,0.00]);
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265 %! assert (b(3:9,:), zeros (7,9));
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266 %! a(1,5) = 0.0;
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267 %! a(5,1) = 1.0;
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268 %! b = 2*del2 (a);
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269 %! assert (b(:,1), [0.00;0.00;0.00;0.50;0.00;0.50;0.00;0.00;0.00]);
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270 %! assert (b(:,2), [0.00;0.00;0.00;0.00;0.50;0.00;0.00;0.00;0.00]);
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271 %! assert (b(:,3:9), zeros (9,7));
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272
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273 ## 9x9 dh center test
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274 %!test
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275 %! a = zeros (9,9);
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276 %! a(5,5) = 1.0;
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277 %! b = 8*del2 (a,2);
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278 %! assert (b(:,1:3), zeros (9,3));
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279 %! assert (b(:,4), [0.00;0.00;0.00;0.00;0.50;0.00;0.00;0.00;0.00]);
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280 %! assert (b(:,5), [0.00;0.00;0.00;0.50;-2.00;0.50;0.00;0.00;0.00]);
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281 %! assert (b(:,6), b(:,4));
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282 %! assert (b(:,7:9), zeros (9,3));
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283
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284 ## 9x9 dx test
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285 %!test
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286 %! a = zeros (9,9);
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287 %! a(5,5) = 1.0;
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288 %! b = 4*del2 (a,2,1);
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289 %! assert (b(1:3,:), zeros (3,9));
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290 %! assert (b(4,:), [0.00;0.00;0.00;0.00;1.00;0.00;0.00;0.00;0.00]');
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291 %! assert (b(5,:), [0.00;0.00;0.00;0.25;-2.5;0.25;0.00;0.00;0.00]');
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292 %! assert (b(6,:), b(4,:));
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293 %! assert (b(7:9,:), zeros (3,9));
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294
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295 ## 9x9 dy test
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296 %!test
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297 %! a = zeros (9,9);
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298 %! a(5,5) = 1.0;
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299 %! b = 4*del2 (a,1,2);
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300 %! assert (b(:,1:3), zeros (9,3));
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301 %! assert (b(:,4), [0.00;0.00;0.00;0.00;1.00;0.00;0.00;0.00;0.00]);
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302 %! assert (b(:,5), [0.00;0.00;0.00;0.25;-2.5;0.25;0.00;0.00;0.00]);
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303 %! assert (b(:,6), b(:,4));
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304 %! assert (b(:,7:9), zeros (9,3));
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305
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306 ## 3D test
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307 %!test
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308 %! a = zeros (9,9,9);
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309 %! a(5,5,5) = 1.0;
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310 %! b = 8*3*del2 (a,2);
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311 %! assert (b(:,:,1:3), zeros (9,9,3));
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312 %! assert (b(:,1:3,:), zeros (9,3,9));
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313 %! assert (b(1:3,:,:), zeros (3,9,9));
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314 %! assert (b(4:5,4,4), [0.0,0.0]');
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315 %! assert (b(5,5,4), 1.00);
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316 %! assert (b(4,4,5), 0.00);
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317 %! assert (b(5,4,5), 1.00);
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318 %! assert (b(5,5,5),-6.00);
19160
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319 %! assert (b, flip (b,1));
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320 %! assert (b, flip (b,2));
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321 %! assert (b, flip (b,3));
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322