Mercurial > octave
annotate scripts/general/del2.m @ 21546:f7f97d7e9294
doc: Wrap m-file docstrings to 79 characters + newline (80 total).
* isrecording.m, soundsc.m, delaunay3.m, cell2mat.m, cumtrapz.m, del2.m,
inputParser.m, interp1.m, interp3.m, narginchk.m, profile.m,
validateattributes.m, delaunayn.m, tsearchn.m, voronoin.m, brighten.m,
cmunique.m, colorcube.m, imfinfo.m, imshow.m, edit.m, orderfields.m, run.m,
warning_ids.m, ode23.m, ode45.m, odeget.m, integrate_adaptive.m, kahan.m,
ode_struct_value_check.m, runge_kutta_23.m, fminunc.m, fsolve.m, fzero.m,
pkg.m, build.m, specular.m, view.m, bar.m, barh.m, contour3.m, isosurface.m,
line.m, pie.m, pie3.m, quiver3.m, scatter.m, scatter3.m, stem3.m, stemleaf.m,
surfl.m, tetramesh.m, isfigure.m, mkpp.m, pchip.m, residue.m, splinefit.m,
rmpref.m, unique.m, eigs.m, ilu.m, factor.m, factorial.m, gallery.m, hankel.m,
histc.m, ols.m, finv.m, fpdf.m, kruskal_wallis_test.m, weekday.m:
Wrap m-file docstrings to 79 characters + newline (80 total).
author | Rik <rik@octave.org> |
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date | Sun, 27 Mar 2016 15:50:01 -0700 |
parents | 516bb87ea72e |
children | 6c2fd62db1f7 |
rev | line source |
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1 ## Copyright (C) 2000-2015 Kai Habel |
6788 | 2 ## Copyright (C) 2007 David Bateman |
3 ## | |
4 ## This file is part of Octave. | |
5 ## | |
6 ## Octave is free software; you can redistribute it and/or modify it | |
7 ## under the terms of the GNU General Public License as published by | |
7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
9 ## your option) any later version. | |
6788 | 10 ## |
11 ## Octave is distributed in the hope that it will be useful, but | |
12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 ## General Public License for more details. | |
15 ## | |
16 ## You should have received a copy of the GNU General Public License | |
7016 | 17 ## along with Octave; see the file COPYING. If not, see |
18 ## <http://www.gnu.org/licenses/>. | |
6788 | 19 |
20 ## -*- texinfo -*- | |
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21 ## @deftypefn {} {@var{d} =} del2 (@var{M}) |
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22 ## @deftypefnx {} {@var{d} =} del2 (@var{M}, @var{h}) |
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23 ## @deftypefnx {} {@var{d} =} del2 (@var{M}, @var{dx}, @var{dy}, @dots{}) |
6788 | 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 |
6788 | 34 ## @tex |
8499 | 35 ## $$d = {1 \over 4} \left( {d^2 \over dx^2} M(x,y) + {d^2 \over dy^2} M(x,y) \right)$$ |
6788 | 36 ## @end tex |
37 ## @ifnottex | |
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38 ## |
6788 | 39 ## @example |
40 ## @group | |
41 ## 1 / d^2 d^2 \ | |
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42 ## D = --- * | --- M(x,y) + --- M(x,y) | |
6788 | 43 ## 4 \ dx^2 dy^2 / |
44 ## @end group | |
45 ## @end example | |
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46 ## |
6788 | 47 ## @end ifnottex |
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48 ## For N-dimensional arrays the sum in parentheses is expanded to include |
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49 ## second derivatives over the additional higher dimensions. |
6788 | 50 ## |
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. |
6788 | 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. |
6788 | 61 ## |
62 ## @seealso{gradient, diff} | |
63 ## @end deftypefn | |
64 | |
65 ## Author: Kai Habel <kai.habel@gmx.de> | |
66 | |
67 function D = del2 (M, varargin) | |
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68 |
6788 | 69 if (nargin < 1) |
70 print_usage (); | |
71 endif | |
72 | |
73 nd = ndims (M); | |
74 sz = size (M); | |
75 dx = cell (1, nd); | |
76 if (nargin == 2 || nargin == 1) | |
77 if (nargin == 1) | |
78 h = 1; | |
79 else | |
7669 | 80 h = varargin{1}; |
6788 | 81 endif |
82 for i = 1 : nd | |
83 if (isscalar (h)) | |
10549 | 84 dx{i} = h * ones (sz (i), 1); |
6788 | 85 else |
10549 | 86 if (length (h) == sz (i)) |
87 dx{i} = diff (h)(:); | |
88 else | |
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89 error ("del2: dimensionality mismatch in %d-th spacing vector", i); |
10549 | 90 endif |
6788 | 91 endif |
92 endfor | |
93 elseif (nargin - 1 == nd) | |
94 ## Reverse dx{1} and dx{2} as the X-dim is the 2nd dim of the ND array | |
95 tmp = varargin{1}; | |
96 varargin{1} = varargin{2}; | |
97 varargin{2} = tmp; | |
98 | |
99 for i = 1 : nd | |
100 if (isscalar (varargin{i})) | |
10549 | 101 dx{i} = varargin{i} * ones (sz (i), 1); |
6788 | 102 else |
10549 | 103 if (length (varargin{i}) == sz (i)) |
104 dx{i} = diff (varargin{i})(:); | |
105 else | |
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106 error ("del2: dimensionality mismatch in %d-th spacing vector", i); |
10549 | 107 endif |
6788 | 108 endif |
109 endfor | |
110 else | |
111 print_usage (); | |
112 endif | |
113 | |
114 idx = cell (1, nd); | |
115 for i = 1: nd | |
116 idx{i} = ":"; | |
117 endfor | |
118 | |
119 D = zeros (sz); | |
120 for i = 1: nd | |
121 if (sz(i) >= 3) | |
122 DD = zeros (sz); | |
123 idx1 = idx2 = idx3 = idx; | |
124 | |
125 ## interior points | |
126 idx1{i} = 1 : sz(i) - 2; | |
127 idx2{i} = 2 : sz(i) - 1; | |
128 idx3{i} = 3 : sz(i); | |
129 szi = sz; | |
130 szi (i) = 1; | |
131 | |
132 h1 = repmat (shiftdim (dx{i}(1 : sz(i) - 2), 1 - i), szi); | |
133 h2 = repmat (shiftdim (dx{i}(2 : sz(i) - 1), 1 - i), szi); | |
134 DD(idx2{:}) = ((M(idx1{:}) - M(idx2{:})) ./ h1 + ... | |
10549 | 135 (M(idx3{:}) - M(idx2{:})) ./ h2) ./ (h1 + h2); |
6788 | 136 |
137 ## left and right boundary | |
138 if (sz(i) == 3) | |
10549 | 139 DD(idx1{:}) = DD(idx3{:}) = DD(idx2{:}); |
6788 | 140 else |
10549 | 141 idx1{i} = 1; |
142 idx2{i} = 2; | |
143 idx3{i} = 3; | |
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144 DD(idx1{:}) = (dx{i}(1) + dx{i}(2)) / dx{i}(2) * DD(idx2{:}) - ... |
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145 dx{i}(1) / dx{i}(2) * DD(idx3{:}); |
6788 | 146 |
10549 | 147 idx1{i} = sz(i); |
148 idx2{i} = sz(i) - 1; | |
149 idx3{i} = sz(i) - 2; | |
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150 DD(idx1{:}) = (dx{i}(sz(i) - 1) + dx{i}(sz(i) - 2)) / ... |
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151 dx{i}(sz(i) - 2) * DD(idx2{:}) - ... |
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152 dx{i}(sz(i) - 1) / dx{i}(sz(i) - 2) * DD(idx3{:}); |
6788 | 153 endif |
154 | |
155 D += DD; | |
156 endif | |
157 endfor | |
158 | |
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159 D ./= nd; |
6788 | 160 endfunction |
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161 |
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162 |
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163 ## 3x3 constant test |
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164 %!test |
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165 %! a = ones (3,3); |
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166 %! b = del2 (a); |
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167 %! assert (b(:,1), [0.00;0.00;0.00]); |
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168 %! assert (b(:,2), [0.00;0.00;0.00]); |
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169 %! assert (b(:,3), [0.00;0.00;0.00]); |
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170 |
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171 ## 3x3 planar test |
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172 %!test |
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173 %! a = [1,2,3;2,3,4;3,4,5]; |
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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 corner test |
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180 %!test |
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181 %! a = zeros (3,3); |
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182 %! a(1,1) = 1.0; |
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183 %! b = 2*del2 (a); |
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184 %! assert (b(:,1), [1.00;0.50;0.50]); |
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185 %! assert (b(:,2), [0.50;0.00;0.00]); |
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186 %! assert (b(:,3), [0.50;0.00;0.00]); |
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187 %! assert (b, flipud (2*del2 (flipud (a)))); |
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188 %! assert (b, fliplr (2*del2 (fliplr (a)))); |
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189 %! assert (b, flipud (fliplr (2*del2 (fliplr (flipud (a)))))); |
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190 |
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191 ## 3x3 boundary test |
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192 %!test |
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193 %! a = zeros (3,3); |
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194 %! a(2,1)=1.0; |
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195 %! b = 2*del2 (a); |
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196 %! assert (b(:,1), [-1.00;-0.50;-1.00]); |
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197 %! assert (b(:,2), [0.00;0.50;0.00]); |
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198 %! assert (b(:,3), [0.00;0.50;0.00]); |
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199 %! assert (b, flipud (2*del2 (flipud (a)))); |
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200 %! assert (b, fliplr (2*del2 (fliplr (a)))); |
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201 %! assert (b, flipud (fliplr (2*del2 (fliplr (flipud (a)))))); |
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202 |
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203 ## 3x3 center test |
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204 %!test |
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205 %! a = zeros (3,3); |
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206 %! a(2,2) = 1.0; |
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207 %! b = del2 (a); |
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208 %! assert (b(:,1), [0.00;-0.50;0.00]); |
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209 %! assert (b(:,2), [-0.50;-1.00;-0.50]); |
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210 %! assert (b(:,3), [0.00;-0.50;0.00]); |
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211 |
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212 ## 4x4 constant test |
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213 %!test |
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214 %! a = ones (4,4); |
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215 %! b = del2 (a); |
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216 %! assert (b(:,1), [0.00;0.00;0.00;0.00]); |
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217 %! assert (b(:,2), [0.00;0.00;0.00;0.00]); |
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218 %! assert (b(:,3), [0.00;0.00;0.00;0.00]); |
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219 %! assert (b(:,4), [0.00;0.00;0.00;0.00]); |
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220 |
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221 ## 4x4 planar test |
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222 %!test |
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223 %! a = [1,2,3,4;2,3,4,5;3,4,5,6;4,5,6,7]; |
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224 %! b = del2 (a); |
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225 %! assert (b(:,1), [0.00;0.00;0.00;0.00]); |
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226 %! assert (b(:,2), [0.00;0.00;0.00;0.00]); |
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227 %! assert (b(:,3), [0.00;0.00;0.00;0.00]); |
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228 %! assert (b(:,4), [0.00;0.00;0.00;0.00]); |
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229 |
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230 ## 4x4 corner test |
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231 %!test |
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232 %! a = zeros (4,4); |
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233 %! a(1,1) = 1.0; |
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234 %! b = 2*del2 (a); |
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235 %! assert (b(:,1), [2.00;0.50;0.00;-0.50]); |
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236 %! assert (b(:,2), [0.50;0.00;0.00;0.00]); |
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237 %! assert (b(:,3), [0.00;0.00;0.00;0.00]); |
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238 %! assert (b(:,4), [-0.50;0.00;0.00;0.00]); |
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239 %! assert (b, flipud (2*del2 (flipud (a)))); |
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240 %! assert (b, fliplr (2*del2 (fliplr (a)))); |
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241 %! assert (b, flipud (fliplr (2*del2 (fliplr (flipud (a)))))); |
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242 |
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243 ## 9x9 center test |
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244 %!test |
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245 %! a = zeros (9,9); |
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246 %! a(5,5) = 1.0; |
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247 %! b = 2*del2 (a); |
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248 %! 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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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); |
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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 |