Mercurial > jwe > octave
annotate scripts/general/interpn.m @ 27923:b442ec6dda5c
use centralized file for copyright info for individual contributors
* COPYRIGHT.md: New file.
* In most other files, use "Copyright (C) YYYY-YYYY The Octave Project
Developers" instead of tracking individual names in separate source
files. The motivation is to reduce the effort required to update the
notices each year.
Until now, the Octave source files contained copyright notices that
list individual contributors. I adopted these file-scope copyright
notices because that is what everyone was doing 30 years ago in the
days before distributed version control systems. But now, with many
contributors and modern version control systems, having these
file-scope copyright notices causes trouble when we update copyright
years or refactor code.
Over time, the file-scope copyright notices may become outdated as new
contributions are made or code is moved from one file to
another. Sometimes people contribute significant patches but do not
add a line claiming copyright. Other times, people add a copyright
notice for their contribution but then a later refactoring moves part
or all of their contribution to another file and the notice is not
moved with the code. As a practical matter, moving such notices is
difficult -- determining what parts are due to a particular
contributor requires a time-consuming search through the project
history. Even managing the yearly update of copyright years is
problematic. We have some contributors who are no longer
living. Should we update the copyright dates for their contributions
when we release new versions? Probably not, but we do still want to
claim copyright for the project as a whole.
To minimize the difficulty of maintaining the copyright notices, I
would like to change Octave's sources to use what is described here:
https://softwarefreedom.org/resources/2012/ManagingCopyrightInformation.html
in the section "Maintaining centralized copyright notices":
The centralized notice approach consolidates all copyright
notices in a single location, usually a top-level file.
This file should contain all of the copyright notices
provided project contributors, unless the contribution was
clearly insignificant. It may also credit -- without a copyright
notice -- anyone who helped with the project but did not
contribute code or other copyrighted material.
This approach captures less information about contributions
within individual files, recognizing that the DVCS is better
equipped to record those details. As we mentioned before, it
does have one disadvantage as compared to the file-scope
approach: if a single file is separated from the distribution,
the recipient won't see the contributors' copyright notices.
But this can be easily remedied by including a single
copyright notice in each file's header, pointing to the
top-level file:
Copyright YYYY-YYYY The Octave Project Developers
See the COPYRIGHT file at the top-level directory
of this distribution or at https://octave.org/COPYRIGHT.html.
followed by the usual GPL copyright statement.
For more background, see the discussion here:
https://lists.gnu.org/archive/html/octave-maintainers/2020-01/msg00009.html
Most files in the following directories have been skipped intentinally
in this changeset:
doc
libgui/qterminal
liboctave/external
m4
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 15:38:17 -0500 |
parents | 3621f0bb50bb |
children | 1891570abac8 |
rev | line source |
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1 ## Copyright (C) 2007-2019 The Octave Project Developers |
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2 ## |
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution |
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4 ## or <https://octave.org/COPYRIGHT.html/>. |
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5 ## |
6702 | 6 ## |
7 ## This file is part of Octave. | |
8 ## | |
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9 ## Octave is free software: you can redistribute it and/or modify it |
6702 | 10 ## under the terms of the GNU General Public License as published by |
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11 ## the Free Software Foundation, either version 3 of the License, or |
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12 ## (at your option) any later version. |
6702 | 13 ## |
14 ## Octave is distributed in the hope that it will be useful, but | |
15 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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17 ## GNU General Public License for more details. |
6702 | 18 ## |
19 ## You should have received a copy of the GNU General Public License | |
7016 | 20 ## along with Octave; see the file COPYING. If not, see |
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21 ## <https://www.gnu.org/licenses/>. |
6702 | 22 |
23 ## -*- texinfo -*- | |
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24 ## @deftypefn {} {@var{vi} =} interpn (@var{x1}, @var{x2}, @dots{}, @var{v}, @var{y1}, @var{y2}, @dots{}) |
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25 ## @deftypefnx {} {@var{vi} =} interpn (@var{v}, @var{y1}, @var{y2}, @dots{}) |
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26 ## @deftypefnx {} {@var{vi} =} interpn (@var{v}, @var{m}) |
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27 ## @deftypefnx {} {@var{vi} =} interpn (@var{v}) |
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28 ## @deftypefnx {} {@var{vi} =} interpn (@dots{}, @var{method}) |
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29 ## @deftypefnx {} {@var{vi} =} interpn (@dots{}, @var{method}, @var{extrapval}) |
6702 | 30 ## |
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31 ## Perform @var{n}-dimensional interpolation, where @var{n} is at least two. |
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32 ## |
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33 ## Each element of the @var{n}-dimensional array @var{v} represents a value |
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34 ## at a location given by the parameters @var{x1}, @var{x2}, @dots{}, @var{xn}. |
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35 ## The parameters @var{x1}, @var{x2}, @dots{}, @var{xn} are either |
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36 ## @var{n}-dimensional arrays of the same size as the array @var{v} in |
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37 ## the @qcode{"ndgrid"} format or vectors. The parameters @var{y1}, etc.@: |
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38 ## respect a similar format to @var{x1}, etc., and they represent the points |
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39 ## at which the array @var{vi} is interpolated. |
6702 | 40 ## |
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41 ## If @var{x1}, @dots{}, @var{xn} are omitted, they are assumed to be |
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42 ## @code{x1 = 1 : size (@var{v}, 1)}, etc. If @var{m} is specified, then |
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43 ## the interpolation adds a point half way between each of the interpolation |
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44 ## points. This process is performed @var{m} times. If only @var{v} is |
6702 | 45 ## specified, then @var{m} is assumed to be @code{1}. |
46 ## | |
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47 ## The interpolation @var{method} is one of: |
6702 | 48 ## |
49 ## @table @asis | |
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50 ## @item @qcode{"nearest"} |
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51 ## Return the nearest neighbor. |
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52 ## |
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53 ## @item @qcode{"linear"} (default) |
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54 ## Linear interpolation from nearest neighbors. |
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55 ## |
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56 ## @item @qcode{"pchip"} |
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57 ## Piecewise cubic Hermite interpolating polynomial---shape-preserving |
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58 ## interpolation with smooth first derivative (not implemented yet). |
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59 ## |
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60 ## @item @qcode{"cubic"} |
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61 ## Cubic interpolation (same as @qcode{"pchip"} [not implemented yet]). |
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62 ## |
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63 ## @item @qcode{"spline"} |
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64 ## Cubic spline interpolation---smooth first and second derivatives |
6702 | 65 ## throughout the curve. |
66 ## @end table | |
67 ## | |
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68 ## The default method is @qcode{"linear"}. |
6702 | 69 ## |
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70 ## @var{extrapval} is a scalar number. It replaces values beyond the endpoints |
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71 ## with @var{extrapval}. Note that if @var{extrapval} is used, @var{method} |
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72 ## must be specified as well. If @var{extrapval} is omitted and the |
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73 ## @var{method} is @qcode{"spline"}, then the extrapolated values of the |
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74 ## @qcode{"spline"} are used. Otherwise the default @var{extrapval} value for |
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75 ## any other @var{method} is @qcode{"NA"}. |
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76 ## @seealso{interp1, interp2, interp3, spline, ndgrid} |
6702 | 77 ## @end deftypefn |
78 | |
79 function vi = interpn (varargin) | |
80 | |
81 method = "linear"; | |
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82 extrapval = []; |
6702 | 83 nargs = nargin; |
84 | |
13151 | 85 if (nargin < 1 || ! isnumeric (varargin{1})) |
6702 | 86 print_usage (); |
87 endif | |
88 | |
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89 if (nargs > 1 && ischar (varargin{end-1})) |
7208 | 90 if (! isnumeric (varargin{end}) || ! isscalar (varargin{end})) |
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91 error ("interpn: EXTRAPVAL must be a numeric scalar"); |
6702 | 92 endif |
8116 | 93 extrapval = varargin{end}; |
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94 method = varargin{end-1}; |
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95 nargs -= 2; |
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96 elseif (ischar (varargin{end})) |
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97 method = varargin{end}; |
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98 nargs -= 1; |
6702 | 99 endif |
100 | |
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101 if (method(1) == "*") |
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102 warning ("interpn: ignoring unsupported '*' flag to METHOD"); |
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103 method(1) = []; |
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104 endif |
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105 method = validatestring (method, ... |
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106 {"nearest", "linear", "pchip", "cubic", "spline"}); |
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107 |
6702 | 108 if (nargs < 3) |
7208 | 109 v = varargin{1}; |
6702 | 110 m = 1; |
111 if (nargs == 2) | |
13151 | 112 if (ischar (varargin{2})) |
113 method = varargin{2}; | |
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114 elseif (isnumeric (m) && isscalar (m) && fix (m) == m) |
13151 | 115 m = varargin{2}; |
116 else | |
117 print_usage (); | |
6702 | 118 endif |
119 endif | |
120 sz = size (v); | |
121 nd = ndims (v); | |
122 x = cell (1, nd); | |
123 y = cell (1, nd); | |
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124 for i = 1 : nd |
6702 | 125 x{i} = 1 : sz(i); |
126 y{i} = 1 : (1 / (2 ^ m)) : sz(i); | |
127 endfor | |
13151 | 128 y{1} = y{1}.'; |
129 [y{:}] = ndgrid (y{:}); | |
7208 | 130 elseif (! isvector (varargin{1}) && nargs == (ndims (varargin{1}) + 1)) |
131 v = varargin{1}; | |
6702 | 132 sz = size (v); |
133 nd = ndims (v); | |
134 x = cell (1, nd); | |
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135 y = varargin(2 : nargs); |
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136 for i = 1 : nd |
6702 | 137 x{i} = 1 : sz(i); |
138 endfor | |
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139 elseif (rem (nargs, 2) == 1 |
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140 && nargs == (2 * ndims (varargin{ceil (nargs / 2)})) + 1) |
6702 | 141 nv = ceil (nargs / 2); |
7208 | 142 v = varargin{nv}; |
6702 | 143 sz = size (v); |
144 nd = ndims (v); | |
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145 x = varargin(1 : (nv - 1)); |
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146 y = varargin((nv + 1) : nargs); |
6702 | 147 else |
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148 error ("interpn: wrong number or incorrectly formatted input arguments"); |
6702 | 149 endif |
150 | |
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151 if (any (! cellfun ("isvector", x))) |
6702 | 152 for i = 2 : nd |
153 if (! size_equal (x{1}, x{i}) || ! size_equal (x{i}, v)) | |
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154 error ("interpn: dimensional mismatch"); |
6702 | 155 endif |
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156 idx(1 : nd) = {1}; |
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157 idx(i) = ":"; |
6721 | 158 x{i} = x{i}(idx{:})(:); |
6702 | 159 endfor |
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160 idx(1 : nd) = {1}; |
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161 idx(1) = ":"; |
6721 | 162 x{1} = x{1}(idx{:})(:); |
6702 | 163 endif |
164 | |
7421 | 165 method = tolower (method); |
6702 | 166 |
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167 all_vectors = all (cellfun ("isvector", y)); |
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168 different_lengths = numel (unique (cellfun ("numel", y))) > 1; |
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169 if (all_vectors && different_lengths) |
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170 [foobar(1:numel(y)).y] = ndgrid (y{:}); |
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171 y = {foobar.y}; |
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172 endif |
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173 |
6702 | 174 if (strcmp (method, "linear")) |
175 vi = __lin_interpn__ (x{:}, v, y{:}); | |
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176 if (isempty (extrapval)) |
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177 extrapval = NA; |
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178 endif |
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179 vi(isna (vi)) = extrapval; |
6702 | 180 elseif (strcmp (method, "nearest")) |
181 yshape = size (y{1}); | |
182 yidx = cell (1, nd); | |
183 for i = 1 : nd | |
184 y{i} = y{i}(:); | |
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185 yidx{i} = lookup (x{i}, y{i}, "lr"); |
6702 | 186 endfor |
187 idx = cell (1,nd); | |
188 for i = 1 : nd | |
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189 idx{i} = yidx{i} ... |
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190 + (y{i} - x{i}(yidx{i})(:) >= x{i}(yidx{i} + 1)(:) - y{i}); |
6702 | 191 endfor |
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192 vi = v(sub2ind (sz, idx{:})); |
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193 idx = zeros (prod (yshape), 1); |
6702 | 194 for i = 1 : nd |
195 idx |= y{i} < min (x{i}(:)) | y{i} > max (x{i}(:)); | |
196 endfor | |
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197 if (isempty (extrapval)) |
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198 extrapval = NA; |
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199 endif |
6702 | 200 vi(idx) = extrapval; |
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201 vi = reshape (vi, yshape); |
6721 | 202 elseif (strcmp (method, "spline")) |
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203 if (any (! cellfun ("isvector", y))) |
7423 | 204 for i = 2 : nd |
10549 | 205 if (! size_equal (y{1}, y{i})) |
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206 error ("interpn: dimensional mismatch"); |
10549 | 207 endif |
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208 idx(1 : nd) = {1}; |
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209 idx(i) = ":"; |
10549 | 210 y{i} = y{i}(idx{:}); |
7423 | 211 endfor |
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212 idx(1 : nd) = {1}; |
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213 idx(1) = ":"; |
7423 | 214 y{1} = y{1}(idx{:}); |
215 endif | |
7421 | 216 |
6702 | 217 vi = __splinen__ (x, v, y, extrapval, "interpn"); |
7421 | 218 |
7423 | 219 if (size_equal (y{:})) |
220 ly = length (y{1}); | |
221 idx = cell (1, ly); | |
222 q = cell (1, nd); | |
223 for i = 1 : ly | |
10549 | 224 q(:) = i; |
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225 idx{i} = q; |
7423 | 226 endfor |
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227 vi = vi(cellfun (@(x) sub2ind (size (vi), x{:}), idx)); |
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228 vi = reshape (vi, size (y{1})); |
7423 | 229 endif |
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230 elseif (strcmp (method, "cubic")) |
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231 error ("interpn: cubic interpolation not yet implemented"); |
6702 | 232 else |
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233 error ("interpn: unrecognized interpolation METHOD"); |
6702 | 234 endif |
235 | |
236 endfunction | |
237 | |
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238 |
6702 | 239 %!demo |
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240 %! clf; |
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241 %! colormap ("default"); |
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242 %! A = [13,-1,12;5,4,3;1,6,2]; |
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243 %! x = [0,1,4]; y = [10,11,12]; |
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244 %! xi = linspace (min (x), max (x), 17); |
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245 %! yi = linspace (min (y), max (y), 26)'; |
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246 %! mesh (xi, yi, interpn (x,y,A.',xi,yi, "linear").'); |
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247 %! [x,y] = meshgrid (x,y); |
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248 %! hold on; plot3 (x(:),y(:),A(:),"b*"); hold off; |
6702 | 249 |
250 %!demo | |
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251 %! clf; |
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252 %! colormap ("default"); |
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253 %! A = [13,-1,12;5,4,3;1,6,2]; |
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254 %! x = [0,1,4]; y = [10,11,12]; |
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255 %! xi = linspace (min (x), max (x), 17); |
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256 %! yi = linspace (min (y), max (y), 26)'; |
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257 %! mesh (xi, yi, interpn (x,y,A.',xi,yi, "nearest").'); |
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258 %! [x,y] = meshgrid (x,y); |
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259 %! hold on; plot3 (x(:),y(:),A(:),"b*"); hold off; |
6702 | 260 |
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261 %!#demo # FIXME: Uncomment when support for "cubic" has been added |
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262 %! clf; |
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263 %! colormap ("default"); |
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264 %! A = [13,-1,12;5,4,3;1,6,2]; |
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265 %! x = [0,1,2]; y = [10,11,12]; |
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266 %! xi = linspace (min (x), max (x), 17); |
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267 %! yi = linspace (min (y), max (y), 26)'; |
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268 %! mesh (xi, yi, interpn (x,y,A.',xi,yi, "cubic").'); |
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269 %! [x,y] = meshgrid (x,y); |
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270 %! hold on; plot3 (x(:),y(:),A(:),"b*"); hold off; |
6702 | 271 |
272 %!demo | |
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273 %! clf; |
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274 %! colormap ("default"); |
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275 %! A = [13,-1,12;5,4,3;1,6,2]; |
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276 %! x = [0,1,2]; y = [10,11,12]; |
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277 %! xi = linspace (min (x), max (x), 17); |
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278 %! yi = linspace (min (y), max (y), 26)'; |
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279 %! mesh (xi, yi, interpn (x,y,A.',xi,yi, "spline").'); |
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280 %! [x,y] = meshgrid (x,y); |
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281 %! hold on; plot3 (x(:),y(:),A(:),"b*"); hold off; |
6721 | 282 |
283 %!demo | |
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284 %! clf; |
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285 %! colormap ("default"); |
6721 | 286 %! x = y = z = -1:1; |
287 %! f = @(x,y,z) x.^2 - y - z.^2; | |
288 %! [xx, yy, zz] = meshgrid (x, y, z); | |
289 %! v = f (xx,yy,zz); | |
290 %! xi = yi = zi = -1:0.1:1; | |
291 %! [xxi, yyi, zzi] = ndgrid (xi, yi, zi); | |
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292 %! vi = interpn (x, y, z, v, xxi, yyi, zzi, "spline"); |
6721 | 293 %! mesh (yi, zi, squeeze (vi(1,:,:))); |
294 | |
7421 | 295 %!test |
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296 %! [x,y,z] = ndgrid (0:2); |
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297 %! f = x + y + z; |
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298 %! assert (interpn (x,y,z,f,[.5 1.5],[.5 1.5],[.5 1.5]), [1.5, 4.5]); |
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299 %! assert (interpn (x,y,z,f,[.51 1.51],[.51 1.51],[.51 1.51],"nearest"), [3, 6]); |
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300 %! assert (interpn (x,y,z,f,[.5 1.5],[.5 1.5],[.5 1.5],"spline"), [1.5, 4.5]); |
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301 %! assert (interpn (x,y,z,f,x,y,z), f); |
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302 %! assert (interpn (x,y,z,f,x,y,z,"nearest"), f); |
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303 %! assert (interpn (x,y,z,f,x,y,z,"spline"), f); |
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304 |
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305 %!test |
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306 %! [x, y, z] = ndgrid (0:2, 1:4, 2:6); |
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307 %! f = x + y + z; |
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308 %! xi = [0.5 1.0 1.5]; yi = [1.5 2.0 2.5 3.5]; zi = [2.5 3.5 4.0 5.0 5.5]; |
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309 %! fi = interpn (x, y, z, f, xi, yi, zi); |
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310 %! [xi, yi, zi] = ndgrid (xi, yi, zi); |
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311 %! assert (fi, xi + yi + zi); |
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312 |
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313 %!test |
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314 %! xi = 0:2; yi = 1:4; zi = 2:6; |
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315 %! [x, y, z] = ndgrid (xi, yi, zi); |
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316 %! f = x + y + z; |
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317 %! fi = interpn (x, y, z, f, xi, yi, zi, "nearest"); |
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318 %! assert (fi, x + y + z); |
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319 |
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320 %!test |
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321 %! [x,y,z] = ndgrid (0:2); |
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322 %! f = x.^2 + y.^2 + z.^2; |
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323 %! assert (interpn (x,y,-z,f,1.5,1.5,-1.5), 7.5); |
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324 |
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325 %!test # for Matlab-compatible rounding for "nearest" |
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326 %! x = meshgrid (1:4); |
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327 %! assert (interpn (x, 2.5, 2.5, "nearest"), 3); |
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328 |
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329 %!test |
13151 | 330 %! z = zeros (3, 3, 3); |
331 %! zout = zeros (5, 5, 5); | |
332 %! z(:,:,1) = [1 3 5; 3 5 7; 5 7 9]; | |
333 %! z(:,:,2) = z(:,:,1) + 2; | |
334 %! z(:,:,3) = z(:,:,2) + 2; | |
335 %! for n = 1:5 | |
336 %! zout(:,:,n) = [1 2 3 4 5; | |
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337 %! 2 3 4 5 6; |
13151 | 338 %! 3 4 5 6 7; |
339 %! 4 5 6 7 8; | |
340 %! 5 6 7 8 9] + (n-1); | |
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341 %! endfor |
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342 %! tol = 10*eps; |
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343 %! assert (interpn (z), zout, tol); |
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344 %! assert (interpn (z, "linear"), zout, tol); |
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345 %! assert (interpn (z, "spline"), zout, tol); |
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346 |
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347 ## Test input validation |
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348 %!warning <ignoring unsupported '\*' flag> interpn (rand (3,3), 1, "*linear"); |