Mercurial > octave
annotate scripts/general/del2.m @ 31253:a40c0b7aa376
maint: changes to follow Octave coding conventions.
* NEWS.8.md: Wrap lines to 72 chars.
* LSODE-opts.in: Use two spaces after sentence ending period.
* LSODE.cc: Use minimum of two spaces between code and start of comment.
* MemoizedFunction.m: Change copyright date to 2022 since this is the year it
was accepted into core. Don't wrap error() lines to 80 chars. Use newlines
to improve readability of switch statements. Use minimum of two spaces between
code and start of comment.
* del2.m, integral.m, interp1.m, interp2.m, griddata.m, inpolygon.m, waitbar.m,
cubehelix.m, ind2x.m, importdata.m, textread.m, logm.m, lighting.m, shading.m,
xticklabels.m, yticklabels.m, zticklabels.m, colorbar.m, meshc.m, print.m,
__gnuplot_draw_axes__.m, struct2hdl.m, ppval.m, ismember.m, iqr.m: Use a space
between comment character '#' and start of comment. Use hyphen for adjectives
describing dimensions such as "1-D".
* vectorize.m, ode23s.m: Use is_function_handle() instead of "isa (x, "function_handle")"
for clarity and performance.
* clearAllMemoizedCaches.m: Change copyright date to 2022 since this is the
year it was accepted into core. Remove input validation which is done by
interpreter. Use two newlines between end of code and start of BIST tests.
* memoize.m: Change copyright date to 2022 since this is the year it was
accepted into core. Re-wrap documentation to 80 chars. Use
is_function_handle() instead of "isa (x, "function_handle")" for clarity and
performance. Use two newlines between end of code and start of BIST tests.
Use semicolon for assert statements within %!test block. Re-write BIST tests
for input validation.
* __memoize__.m: Change copyright date to 2022 since this is the year it was
accepted into core. Use spaces in for statements to improve readability.
* unique.m: Add FIXME note to commented BIST test
* dec2bin.m: Remove stray newline at end of file.
* triplequad.m: Reduce doubly-commented BIST syntax using "#%!#" to "#%!".
* delaunayn.m: Use input variable names in error() statements. Use minimum of
two spaces between code and start of comment. Use hyphen for describing
dimensions. Use two newlines between end of code and start of BIST tests.
Update BIST tests to pass.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 03 Oct 2022 18:06:55 -0700 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2000-2022 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
6788 | 7 ## |
8 ## This file is part of Octave. | |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
6788 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
6788 | 14 ## |
15 ## Octave is distributed in the hope that it will be useful, but | |
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
6788 | 19 ## |
20 ## You should have received a copy of the GNU General Public License | |
7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
6788 | 25 |
26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {@var{L} =} del2 (@var{M}) |
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28 ## @deftypefnx {} {@var{L} =} del2 (@var{M}, @var{h}) |
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29 ## @deftypefnx {} {@var{L} =} del2 (@var{M}, @var{dx}, @var{dy}, @dots{}) |
6788 | 30 ## |
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31 ## Calculate the discrete Laplace |
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32 ## @tex |
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33 ## operator $( \nabla^2 )$. |
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34 ## @end tex |
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35 ## @ifnottex |
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36 ## operator. |
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37 ## @end ifnottex |
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38 ## |
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39 ## For a 2-dimensional matrix @var{M} this is defined as |
6788 | 40 ## @tex |
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41 ## $$L = {1 \over 4} \left( {d^2 \over dx^2} M(x,y) + {d^2 \over dy^2} M(x,y) \right)$$ |
6788 | 42 ## @end tex |
43 ## @ifnottex | |
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44 ## |
6788 | 45 ## @example |
46 ## @group | |
47 ## 1 / d^2 d^2 \ | |
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48 ## L = --- * | --- M(x,y) + --- M(x,y) | |
6788 | 49 ## 4 \ dx^2 dy^2 / |
50 ## @end group | |
51 ## @end example | |
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52 ## |
6788 | 53 ## @end ifnottex |
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54 ## For N-dimensional arrays the sum in parentheses is expanded to include |
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55 ## second derivatives over the additional higher dimensions. |
6788 | 56 ## |
57 ## The spacing between evaluation points may be defined by @var{h}, which is a | |
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58 ## scalar defining the equidistant spacing in all dimensions. Alternatively, |
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59 ## the spacing in each dimension may be defined separately by @var{dx}, |
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60 ## @var{dy}, etc. A scalar spacing argument defines equidistant spacing, |
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61 ## whereas a vector argument can be used to specify variable spacing. The |
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62 ## length of the spacing vectors must match the respective dimension of |
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63 ## @var{M}. The default spacing value is 1. |
6788 | 64 ## |
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65 ## Dimensions with fewer than 3 data points are skipped. Boundary points are |
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66 ## calculated from the linear extrapolation of interior points. |
6788 | 67 ## |
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68 ## Example: Second derivative of 2*x^3 |
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69 ## |
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70 ## @example |
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71 ## @group |
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72 ## f = @@(x) 2*x.^3; |
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73 ## dd = @@(x) 12*x; |
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74 ## x = 1:6; |
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75 ## L = 4*del2 (f(x)); |
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76 ## assert (L, dd (x)); |
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77 ## @end group |
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78 ## @end example |
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79 ## |
6788 | 80 ## @seealso{gradient, diff} |
81 ## @end deftypefn | |
82 | |
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83 function L = del2 (M, varargin) |
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84 |
6788 | 85 if (nargin < 1) |
86 print_usage (); | |
87 endif | |
88 | |
89 nd = ndims (M); | |
90 sz = size (M); | |
91 dx = cell (1, nd); | |
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92 if (nargin == 1) |
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93 for i = 1 : nd |
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94 dx(i) = ones (sz(i), 1); |
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95 endfor |
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96 elseif (nargin == 2 && isscalar (varargin{1})) |
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97 h = varargin{1}; |
6788 | 98 for i = 1 : nd |
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99 dx(i) = h * ones (sz(i), 1); |
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100 endfor |
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101 elseif (numel (varargin) <= nd) |
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102 ndx = numel (varargin); |
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103 varargin(ndx+1:nd) = 1; # Fill missing dims with 1. |
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104 ## Reverse dx{1} and dx{2} as the X-dim is the 2nd dim of a meshgrid array |
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105 varargin([1, 2]) = varargin([2, 1]); |
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106 for i = 1 : nd |
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107 arg = varargin{i}; |
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108 if (isscalar (arg)) |
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109 dx(i) = arg * ones (sz(i), 1); |
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110 elseif (isvector (arg)) |
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111 if (length (arg) != sz(i)) |
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112 error ("del2: number of elements in spacing vector %d does not match dimension %d of M", i, i); |
10549 | 113 endif |
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114 dx(i) = diff (varargin{i})(:); |
6788 | 115 else |
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116 error ("del2: spacing element %d must be a scalar or vector", i); |
6788 | 117 endif |
118 endfor | |
119 else | |
120 print_usage (); | |
121 endif | |
122 | |
123 idx = cell (1, nd); | |
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124 idx(:) = ":"; |
6788 | 125 |
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126 L = zeros (sz); |
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127 for i = 1 : nd |
6788 | 128 if (sz(i) >= 3) |
129 DD = zeros (sz); | |
130 idx1 = idx2 = idx3 = idx; | |
131 | |
132 ## interior points | |
133 idx1{i} = 1 : sz(i) - 2; | |
134 idx2{i} = 2 : sz(i) - 1; | |
135 idx3{i} = 3 : sz(i); | |
136 szi = sz; | |
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137 szi(i) = 1; |
6788 | 138 |
139 h1 = repmat (shiftdim (dx{i}(1 : sz(i) - 2), 1 - i), szi); | |
140 h2 = repmat (shiftdim (dx{i}(2 : sz(i) - 1), 1 - i), szi); | |
141 DD(idx2{:}) = ((M(idx1{:}) - M(idx2{:})) ./ h1 + ... | |
10549 | 142 (M(idx3{:}) - M(idx2{:})) ./ h2) ./ (h1 + h2); |
6788 | 143 |
144 ## left and right boundary | |
145 if (sz(i) == 3) | |
10549 | 146 DD(idx1{:}) = DD(idx3{:}) = DD(idx2{:}); |
6788 | 147 else |
10549 | 148 idx1{i} = 1; |
149 idx2{i} = 2; | |
150 idx3{i} = 3; | |
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151 DD(idx1{:}) = (dx{i}(1) + dx{i}(2)) / dx{i}(2) * DD(idx2{:}) - ... |
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152 dx{i}(1) / dx{i}(2) * DD(idx3{:}); |
6788 | 153 |
10549 | 154 idx1{i} = sz(i); |
155 idx2{i} = sz(i) - 1; | |
156 idx3{i} = sz(i) - 2; | |
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157 DD(idx1{:}) = (dx{i}(sz(i) - 1) + dx{i}(sz(i) - 2)) / ... |
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158 dx{i}(sz(i) - 2) * DD(idx2{:}) - ... |
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159 dx{i}(sz(i) - 1) / dx{i}(sz(i) - 2) * DD(idx3{:}); |
6788 | 160 endif |
161 | |
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162 L += DD; |
6788 | 163 endif |
164 endfor | |
165 | |
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166 L ./= nd; |
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167 |
6788 | 168 endfunction |
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169 |
18617
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170 |
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171 ## 3x3 constant test |
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172 %!test |
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173 %! a = ones (3,3); |
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174 %! b = del2 (a); |
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175 %! assert (b(:,1), [0.00;0.00;0.00]); |
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176 %! assert (b(:,2), [0.00;0.00;0.00]); |
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177 %! assert (b(:,3), [0.00;0.00;0.00]); |
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178 |
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179 ## 3x3 planar test |
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180 %!test |
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181 %! a = [1,2,3;2,3,4;3,4,5]; |
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182 %! b = del2 (a); |
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183 %! assert (b(:,1), [0.00;0.00;0.00]); |
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184 %! assert (b(:,2), [0.00;0.00;0.00]); |
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185 %! assert (b(:,3), [0.00;0.00;0.00]); |
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186 |
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187 ## 3x3 corner test |
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188 %!test |
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189 %! a = zeros (3,3); |
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190 %! a(1,1) = 1.0; |
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191 %! b = 2*del2 (a); |
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192 %! assert (b(:,1), [1.00;0.50;0.50]); |
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193 %! assert (b(:,2), [0.50;0.00;0.00]); |
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194 %! assert (b(:,3), [0.50;0.00;0.00]); |
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195 %! assert (b, flipud (2*del2 (flipud (a)))); |
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196 %! assert (b, fliplr (2*del2 (fliplr (a)))); |
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197 %! assert (b, flipud (fliplr (2*del2 (fliplr (flipud (a)))))); |
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198 |
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199 ## 3x3 boundary test |
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200 %!test |
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201 %! a = zeros (3,3); |
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202 %! a(2,1)=1.0; |
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203 %! b = 2*del2 (a); |
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204 %! assert (b(:,1), [-1.00;-0.50;-1.00]); |
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205 %! assert (b(:,2), [0.00;0.50;0.00]); |
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206 %! assert (b(:,3), [0.00;0.50;0.00]); |
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207 %! assert (b, flipud (2*del2 (flipud (a)))); |
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208 %! assert (b, fliplr (2*del2 (fliplr (a)))); |
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209 %! assert (b, flipud (fliplr (2*del2 (fliplr (flipud (a)))))); |
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210 |
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211 ## 3x3 center test |
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212 %!test |
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213 %! a = zeros (3,3); |
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214 %! a(2,2) = 1.0; |
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215 %! b = del2 (a); |
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216 %! assert (b(:,1), [0.00;-0.50;0.00]); |
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217 %! assert (b(:,2), [-0.50;-1.00;-0.50]); |
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218 %! assert (b(:,3), [0.00;-0.50;0.00]); |
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219 |
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220 ## 4x4 constant test |
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221 %!test |
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222 %! a = ones (4,4); |
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223 %! b = del2 (a); |
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224 %! assert (b(:,1), [0.00;0.00;0.00;0.00]); |
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225 %! assert (b(:,2), [0.00;0.00;0.00;0.00]); |
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226 %! assert (b(:,3), [0.00;0.00;0.00;0.00]); |
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227 %! assert (b(:,4), [0.00;0.00;0.00;0.00]); |
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228 |
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229 ## 4x4 planar test |
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230 %!test |
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231 %! a = [1,2,3,4;2,3,4,5;3,4,5,6;4,5,6,7]; |
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232 %! b = del2 (a); |
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233 %! assert (b(:,1), [0.00;0.00;0.00;0.00]); |
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234 %! assert (b(:,2), [0.00;0.00;0.00;0.00]); |
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235 %! assert (b(:,3), [0.00;0.00;0.00;0.00]); |
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236 %! assert (b(:,4), [0.00;0.00;0.00;0.00]); |
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237 |
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238 ## 4x4 corner test |
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239 %!test |
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240 %! a = zeros (4,4); |
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241 %! a(1,1) = 1.0; |
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242 %! b = 2*del2 (a); |
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243 %! assert (b(:,1), [2.00;0.50;0.00;-0.50]); |
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244 %! assert (b(:,2), [0.50;0.00;0.00;0.00]); |
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245 %! assert (b(:,3), [0.00;0.00;0.00;0.00]); |
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246 %! assert (b(:,4), [-0.50;0.00;0.00;0.00]); |
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247 %! assert (b, flipud (2*del2 (flipud (a)))); |
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248 %! assert (b, fliplr (2*del2 (fliplr (a)))); |
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249 %! assert (b, flipud (fliplr (2*del2 (fliplr (flipud (a)))))); |
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250 |
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251 ## 9x9 center test |
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252 %!test |
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253 %! a = zeros (9,9); |
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254 %! a(5,5) = 1.0; |
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255 %! b = 2*del2 (a); |
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256 %! assert (b(:,1), [0.00;0.00;0.00;0.00;0.00;0.00;0.00;0.00;0.00]); |
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257 %! 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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258 %! 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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259 %! 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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260 %! 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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261 %! assert (b(:,6), b(:,4)); |
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262 %! assert (b(:,7), b(:,3)); |
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263 %! assert (b(:,8), b(:,2)); |
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264 %! assert (b(:,9), b(:,1)); |
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265 |
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266 ## 9x9 boundary test |
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267 %!test |
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268 %! a = zeros (9,9); |
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269 %! a(1,5) = 1.0; |
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270 %! b = 2*del2 (a); |
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271 %! 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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272 %! 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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273 %! assert (b(3:9,:), zeros (7,9)); |
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274 %! a(1,5) = 0.0; |
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275 %! a(5,1) = 1.0; |
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276 %! b = 2*del2 (a); |
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277 %! 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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278 %! 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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279 %! assert (b(:,3:9), zeros (9,7)); |
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280 |
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281 ## 9x9 dh center test |
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282 %!test |
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283 %! a = zeros (9,9); |
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284 %! a(5,5) = 1.0; |
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285 %! b = 8*del2 (a,2); |
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286 %! assert (b(:,1:3), zeros (9,3)); |
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287 %! 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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288 %! 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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289 %! assert (b(:,6), b(:,4)); |
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290 %! assert (b(:,7:9), zeros (9,3)); |
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291 |
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292 ## 9x9 dx test |
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293 %!test |
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294 %! a = zeros (9,9); |
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295 %! a(5,5) = 1.0; |
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296 %! b = 4*del2 (a,2,1); |
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297 %! assert (b(1:3,:), zeros (3,9)); |
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298 %! 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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299 %! 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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300 %! assert (b(6,:), b(4,:)); |
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301 %! assert (b(7:9,:), zeros (3,9)); |
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302 |
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303 ## 9x9 dy test |
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304 %!test |
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305 %! a = zeros (9,9); |
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306 %! a(5,5) = 1.0; |
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307 %! b = 4*del2 (a,1,2); |
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308 %! assert (b(:,1:3), zeros (9,3)); |
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309 %! 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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310 %! 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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311 %! assert (b(:,6), b(:,4)); |
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312 %! assert (b(:,7:9), zeros (9,3)); |
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313 |
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314 ## 3-D test |
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315 %!test |
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316 %! a = zeros (9,9,9); |
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317 %! a(5,5,5) = 1.0; |
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318 %! b = 8*3*del2 (a,2); |
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319 %! assert (b(:,:,1:3), zeros (9,9,3)); |
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320 %! assert (b(:,1:3,:), zeros (9,3,9)); |
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321 %! assert (b(1:3,:,:), zeros (3,9,9)); |
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322 %! assert (b(4:5,4,4), [0.0,0.0]'); |
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323 %! assert (b(5,5,4), 1.00); |
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324 %! assert (b(4,4,5), 0.00); |
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325 %! assert (b(5,4,5), 1.00); |
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326 %! assert (b(5,5,5),-6.00); |
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327 %! assert (b, flip (b,1)); |
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328 %! assert (b, flip (b,2)); |
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329 %! assert (b, flip (b,3)); |
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330 |
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331 %!test <*51728> |
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332 %! x = linspace (-2*pi, 2*pi); |
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333 %! U = cos (x); |
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334 %! L = 4*del2 (U, x); |
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335 |
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336 ## Test input validation |
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337 %!error <Invalid call> del2 () |
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338 %!error <Invalid call> del2 (1, 1, 2, 3) |
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339 %!error <in spacing vector 1> del2 (1, 2, [1 1]) |
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340 %!error <in spacing vector 2> del2 (1, [1 1], 2) |
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341 %!error <must be a scalar or vector> del2 (1, ones (2,2), 2) |
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342 |