Mercurial > jwe > octave
annotate scripts/general/interpn.m @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 02 Jan 2012 14:25:41 -0500 |
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1 ## Copyright (C) 2007-2012 David Bateman |
6702 | 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 | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
6702 | 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 | |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
6702 | 18 |
19 ## -*- texinfo -*- | |
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20 ## @deftypefn {Function File} {@var{vi} =} interpn (@var{x1}, @var{x2}, @dots{}, @var{v}, @var{y1}, @var{y2}, @dots{}) |
6702 | 21 ## @deftypefnx {Function File} {@var{vi} =} interpn (@var{v}, @var{y1}, @var{y2}, @dots{}) |
22 ## @deftypefnx {Function File} {@var{vi} =} interpn (@var{v}, @var{m}) | |
23 ## @deftypefnx {Function File} {@var{vi} =} interpn (@var{v}) | |
24 ## @deftypefnx {Function File} {@var{vi} =} interpn (@dots{}, @var{method}) | |
25 ## @deftypefnx {Function File} {@var{vi} =} interpn (@dots{}, @var{method}, @var{extrapval}) | |
26 ## | |
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27 ## Perform @var{n}-dimensional interpolation, where @var{n} is at least two. |
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28 ## Each element of the @var{n}-dimensional array @var{v} represents a value |
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29 ## at a location given by the parameters @var{x1}, @var{x2}, @dots{}, @var{xn}. |
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30 ## The parameters @var{x1}, @var{x2}, @dots{}, @var{xn} are either |
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31 ## @var{n}-dimensional arrays of the same size as the array @var{v} in |
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32 ## the 'ndgrid' format or vectors. The parameters @var{y1}, etc. respect a |
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33 ## similar format to @var{x1}, etc., and they represent the points at which |
6702 | 34 ## the array @var{vi} is interpolated. |
35 ## | |
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36 ## If @var{x1}, @dots{}, @var{xn} are omitted, they are assumed to be |
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37 ## @code{x1 = 1 : size (@var{v}, 1)}, etc. If @var{m} is specified, then |
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38 ## the interpolation adds a point half way between each of the interpolation |
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39 ## points. This process is performed @var{m} times. If only @var{v} is |
6702 | 40 ## specified, then @var{m} is assumed to be @code{1}. |
41 ## | |
42 ## Method is one of: | |
43 ## | |
44 ## @table @asis | |
45 ## @item 'nearest' | |
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46 ## Return the nearest neighbor. |
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47 ## |
6702 | 48 ## @item 'linear' |
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49 ## Linear interpolation from nearest neighbors. |
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50 ## |
6702 | 51 ## @item 'cubic' |
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52 ## Cubic interpolation from four nearest neighbors (not implemented yet). |
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53 ## |
6702 | 54 ## @item 'spline' |
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55 ## Cubic spline interpolation---smooth first and second derivatives |
6702 | 56 ## throughout the curve. |
57 ## @end table | |
58 ## | |
59 ## The default method is 'linear'. | |
60 ## | |
8116 | 61 ## If @var{extrapval} is the scalar value, use it to replace the values |
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62 ## beyond the endpoints with that number. If @var{extrapval} is missing, |
8116 | 63 ## assume NA. |
6702 | 64 ## @seealso{interp1, interp2, spline, ndgrid} |
65 ## @end deftypefn | |
66 | |
67 function vi = interpn (varargin) | |
68 | |
69 method = "linear"; | |
6742 | 70 extrapval = NA; |
6702 | 71 nargs = nargin; |
72 | |
13151 | 73 if (nargin < 1 || ! isnumeric (varargin{1})) |
6702 | 74 print_usage (); |
75 endif | |
76 | |
7208 | 77 if (ischar (varargin{end})) |
78 method = varargin{end}; | |
6702 | 79 nargs = nargs - 1; |
13151 | 80 elseif (nargs > 1 && ischar (varargin{end - 1})) |
7208 | 81 if (! isnumeric (varargin{end}) || ! isscalar (varargin{end})) |
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82 error ("interpn: extrapal is expected to be a numeric scalar"); |
6702 | 83 endif |
7208 | 84 method = varargin{end - 1}; |
8116 | 85 extrapval = varargin{end}; |
6702 | 86 nargs = nargs - 2; |
87 endif | |
88 | |
89 if (nargs < 3) | |
7208 | 90 v = varargin{1}; |
6702 | 91 m = 1; |
92 if (nargs == 2) | |
13151 | 93 if (ischar (varargin{2})) |
94 method = varargin{2}; | |
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95 elseif (isnumeric (m) && isscalar (m) && fix (m) == m) |
13151 | 96 m = varargin{2}; |
97 else | |
98 print_usage (); | |
6702 | 99 endif |
100 endif | |
101 sz = size (v); | |
102 nd = ndims (v); | |
103 x = cell (1, nd); | |
104 y = cell (1, nd); | |
105 for i = 1 : nd; | |
106 x{i} = 1 : sz(i); | |
107 y{i} = 1 : (1 / (2 ^ m)) : sz(i); | |
108 endfor | |
13151 | 109 y{1} = y{1}.'; |
110 [y{:}] = ndgrid (y{:}); | |
7208 | 111 elseif (! isvector (varargin{1}) && nargs == (ndims (varargin{1}) + 1)) |
112 v = varargin{1}; | |
6702 | 113 sz = size (v); |
114 nd = ndims (v); | |
115 x = cell (1, nd); | |
116 y = varargin (2 : nargs); | |
117 for i = 1 : nd; | |
118 x{i} = 1 : sz(i); | |
119 endfor | |
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120 elseif (rem (nargs, 2) == 1 && nargs == |
10549 | 121 (2 * ndims (varargin{ceil (nargs / 2)})) + 1) |
6702 | 122 nv = ceil (nargs / 2); |
7208 | 123 v = varargin{nv}; |
6702 | 124 sz = size (v); |
125 nd = ndims (v); | |
126 x = varargin (1 : (nv - 1)); | |
127 y = varargin ((nv + 1) : nargs); | |
128 else | |
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129 error ("interpn: wrong number or incorrectly formatted input arguments"); |
6702 | 130 endif |
131 | |
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132 if (any (! cellfun ("isvector", x))) |
6702 | 133 for i = 2 : nd |
134 if (! size_equal (x{1}, x{i}) || ! size_equal (x{i}, v)) | |
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135 error ("interpn: dimensional mismatch"); |
6702 | 136 endif |
137 idx (1 : nd) = {1}; | |
138 idx (i) = ":"; | |
6721 | 139 x{i} = x{i}(idx{:})(:); |
6702 | 140 endfor |
141 idx (1 : nd) = {1}; | |
142 idx (1) = ":"; | |
6721 | 143 x{1} = x{1}(idx{:})(:); |
6702 | 144 endif |
145 | |
7421 | 146 method = tolower (method); |
6702 | 147 |
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148 all_vectors = all (cellfun ("isvector", y)); |
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149 different_lengths = numel (unique (cellfun ("numel", y))) > 1; |
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150 if (all_vectors && different_lengths) |
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151 [foobar(1:numel(y)).y] = ndgrid (y{:}); |
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152 y = {foobar.y}; |
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153 endif |
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154 |
6702 | 155 if (strcmp (method, "linear")) |
156 vi = __lin_interpn__ (x{:}, v, y{:}); | |
6742 | 157 vi (isna (vi)) = extrapval; |
6702 | 158 elseif (strcmp (method, "nearest")) |
159 yshape = size (y{1}); | |
160 yidx = cell (1, nd); | |
161 for i = 1 : nd | |
162 y{i} = y{i}(:); | |
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163 yidx{i} = lookup (x{i}, y{i}, "lr"); |
6702 | 164 endfor |
165 idx = cell (1,nd); | |
166 for i = 1 : nd | |
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167 idx{i} = yidx{i} + (y{i} - x{i}(yidx{i})(:) >= x{i}(yidx{i} + 1)(:) - y{i}); |
6702 | 168 endfor |
169 vi = v (sub2ind (sz, idx{:})); | |
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170 idx = zeros (prod (yshape), 1); |
6702 | 171 for i = 1 : nd |
172 idx |= y{i} < min (x{i}(:)) | y{i} > max (x{i}(:)); | |
173 endfor | |
174 vi(idx) = extrapval; | |
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175 vi = reshape (vi, yshape); |
6721 | 176 elseif (strcmp (method, "spline")) |
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177 if (any (! cellfun ("isvector", y))) |
7423 | 178 for i = 2 : nd |
10549 | 179 if (! size_equal (y{1}, y{i})) |
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180 error ("interpn: dimensional mismatch"); |
10549 | 181 endif |
182 idx (1 : nd) = {1}; | |
183 idx (i) = ":"; | |
184 y{i} = y{i}(idx{:}); | |
7423 | 185 endfor |
186 idx (1 : nd) = {1}; | |
187 idx (1) = ":"; | |
188 y{1} = y{1}(idx{:}); | |
189 endif | |
7421 | 190 |
6702 | 191 vi = __splinen__ (x, v, y, extrapval, "interpn"); |
7421 | 192 |
7423 | 193 if (size_equal (y{:})) |
194 ly = length (y{1}); | |
195 idx = cell (1, ly); | |
196 q = cell (1, nd); | |
197 for i = 1 : ly | |
10549 | 198 q(:) = i; |
199 idx {i} = q; | |
7423 | 200 endfor |
201 vi = vi (cellfun (@(x) sub2ind (size(vi), x{:}), idx)); | |
7424 | 202 vi = reshape (vi, size(y{1})); |
7423 | 203 endif |
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204 elseif (strcmp (method, "cubic")) |
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205 error ("interpn: cubic interpolation not yet implemented"); |
6702 | 206 else |
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207 error ("interpn: unrecognized interpolation METHOD"); |
6702 | 208 endif |
209 | |
210 endfunction | |
211 | |
212 %!demo | |
213 %! A=[13,-1,12;5,4,3;1,6,2]; | |
214 %! x=[0,1,4]; y=[10,11,12]; | |
215 %! xi=linspace(min(x),max(x),17); | |
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216 %! yi=linspace(min(y),max(y),26)'; |
6702 | 217 %! mesh(xi,yi,interpn(x,y,A.',xi,yi,"linear").'); |
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218 %! [x,y] = meshgrid(x,y); |
6702 | 219 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
220 | |
221 %!demo | |
222 %! A=[13,-1,12;5,4,3;1,6,2]; | |
223 %! x=[0,1,4]; y=[10,11,12]; | |
224 %! xi=linspace(min(x),max(x),17); | |
225 %! yi=linspace(min(y),max(y),26)'; | |
226 %! mesh(xi,yi,interpn(x,y,A.',xi,yi,"nearest").'); | |
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227 %! [x,y] = meshgrid(x,y); |
6702 | 228 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
229 | |
230 %!#demo | |
231 %! A=[13,-1,12;5,4,3;1,6,2]; | |
232 %! x=[0,1,2]; y=[10,11,12]; | |
233 %! xi=linspace(min(x),max(x),17); | |
234 %! yi=linspace(min(y),max(y),26)'; | |
235 %! mesh(xi,yi,interpn(x,y,A.',xi,yi,"cubic").'); | |
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236 %! [x,y] = meshgrid(x,y); |
6702 | 237 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
238 | |
239 %!demo | |
240 %! A=[13,-1,12;5,4,3;1,6,2]; | |
241 %! x=[0,1,2]; y=[10,11,12]; | |
242 %! xi=linspace(min(x),max(x),17); | |
243 %! yi=linspace(min(y),max(y),26)'; | |
244 %! mesh(xi,yi,interpn(x,y,A.',xi,yi,"spline").'); | |
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245 %! [x,y] = meshgrid(x,y); |
6702 | 246 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
247 | |
6721 | 248 |
249 %!demo | |
250 %! x = y = z = -1:1; | |
251 %! f = @(x,y,z) x.^2 - y - z.^2; | |
252 %! [xx, yy, zz] = meshgrid (x, y, z); | |
253 %! v = f (xx,yy,zz); | |
254 %! xi = yi = zi = -1:0.1:1; | |
255 %! [xxi, yyi, zzi] = ndgrid (xi, yi, zi); | |
256 %! vi = interpn(x, y, z, v, xxi, yyi, zzi, 'spline'); | |
257 %! mesh (yi, zi, squeeze (vi(1,:,:))); | |
258 | |
7421 | 259 |
260 %!test | |
261 %! [x,y,z] = ndgrid(0:2); | |
262 %! f = x+y+z; | |
263 %! assert (interpn(x,y,z,f,[.5 1.5],[.5 1.5],[.5 1.5]), [1.5, 4.5]) | |
264 %! assert (interpn(x,y,z,f,[.51 1.51],[.51 1.51],[.51 1.51],'nearest'), [3, 6]) | |
265 %! assert (interpn(x,y,z,f,[.5 1.5],[.5 1.5],[.5 1.5],'spline'), [1.5, 4.5]) | |
266 %! assert (interpn(x,y,z,f,x,y,z), f) | |
267 %! assert (interpn(x,y,z,f,x,y,z,'nearest'), f) | |
268 %! assert (interpn(x,y,z,f,x,y,z,'spline'), f) | |
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270 %!test |
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271 %! [x, y, z] = ndgrid (0:2, 1:4, 2:6); |
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272 %! f = x + y + z; |
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273 %! xi = [0.5 1.0 1.5]; |
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274 %! yi = [1.5 2.0 2.5 3.5]; |
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275 %! zi = [2.5 3.5 4.0 5.0 5.5]; |
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276 %! fi = interpn (x, y, z, f, xi, yi, zi); |
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277 %! [xi, yi, zi] = ndgrid (xi, yi, zi); |
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278 %! assert (fi, xi + yi + zi) |
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279 |
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280 %!test |
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281 %! xi = 0:2; |
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282 %! yi = 1:4; |
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283 %! zi = 2:6; |
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284 %! [x, y, z] = ndgrid (xi, yi, zi); |
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285 %! f = x + y + z; |
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286 %! fi = interpn (x, y, z, f, xi, yi, zi, "nearest"); |
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287 %! assert (fi, x + y + z) |
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288 |
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289 %!test |
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290 %! [x,y,z] = ndgrid(0:2); |
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291 %! f = x.^2+y.^2+z.^2; |
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292 %! assert (interpn(x,y,-z,f,1.5,1.5,-1.5), 7.5) |
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293 |
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294 %!test % for Matlab-compatible rounding for 'nearest' |
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295 %! X = meshgrid (1:4); |
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296 %! assert (interpn (X, 2.5, 2.5, 'nearest'), 3); |
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297 |
13151 | 298 %!shared z, zout, tol |
299 %! z = zeros (3, 3, 3); | |
300 %! zout = zeros (5, 5, 5); | |
301 %! z(:,:,1) = [1 3 5; 3 5 7; 5 7 9]; | |
302 %! z(:,:,2) = z(:,:,1) + 2; | |
303 %! z(:,:,3) = z(:,:,2) + 2; | |
304 %! for n = 1:5 | |
305 %! zout(:,:,n) = [1 2 3 4 5; | |
306 %! 2 3 4 5 6; | |
307 %! 3 4 5 6 7; | |
308 %! 4 5 6 7 8; | |
309 %! 5 6 7 8 9] + (n-1); | |
310 %! end | |
311 %! tol = 10 * eps; | |
312 %!assert (interpn (z), zout, tol) | |
313 %!assert (interpn (z, "linear"), zout, tol) | |
314 %!assert (interpn (z, "spline"), zout, tol) |