Mercurial > hg > octave-nkf
annotate scripts/general/interp3.m @ 19794:db92e7e28e1f
strip trailing whitespace from most source files
* NEWS, doc/interpreter/contributors.in, doc/interpreter/func.txi,
doc/interpreter/genpropdoc.m, doc/interpreter/octave_logo.eps,
doc/interpreter/plot.txi, doc/interpreter/stmt.txi,
examples/data/Makefile.am, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/error.cc,
libinterp/corefcn/file-io.cc, libinterp/corefcn/gl-render.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/graphics.in.h,
libinterp/corefcn/load-path.cc, libinterp/corefcn/pr-output.cc,
libinterp/corefcn/pt-jit.cc, libinterp/corefcn/strfind.cc,
libinterp/corefcn/toplev.cc, libinterp/corefcn/toplev.h,
libinterp/corefcn/urlwrite.cc, libinterp/corefcn/variables.cc,
libinterp/octave-value/ov-classdef.cc,
libinterp/octave-value/ov-classdef.h, libinterp/octave.cc,
libinterp/parse-tree/lex.h, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-classdef.h, liboctave/system/file-ops.cc,
liboctave/system/oct-env.cc, m4/acinclude.m4,
scripts/deprecated/finite.m, scripts/deprecated/fmod.m,
scripts/deprecated/fnmatch.m, scripts/deprecated/luinc.m,
scripts/deprecated/octave_tmp_file_name.m, scripts/deprecated/syl.m,
scripts/deprecated/usage.m, scripts/general/inputParser.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/isequal.m,
scripts/general/private/__isequal__.m, scripts/geometry/voronoi.m,
scripts/image/image.m, scripts/image/imshow.m,
scripts/image/ind2rgb.m, scripts/linear-algebra/bandwidth.m,
scripts/linear-algebra/isbanded.m, scripts/miscellaneous/bzip2.m,
scripts/miscellaneous/cast.m, scripts/miscellaneous/copyfile.m,
scripts/miscellaneous/delete.m, scripts/miscellaneous/fullfile.m,
scripts/miscellaneous/getappdata.m, scripts/miscellaneous/gunzip.m,
scripts/miscellaneous/isappdata.m, scripts/miscellaneous/ls.m,
scripts/miscellaneous/mex.m, scripts/miscellaneous/movefile.m,
scripts/miscellaneous/orderfields.m, scripts/miscellaneous/recycle.m,
scripts/miscellaneous/rmappdata.m, scripts/miscellaneous/setfield.m,
scripts/miscellaneous/symvar.m, scripts/miscellaneous/tar.m,
scripts/miscellaneous/tmpnam.m, scripts/miscellaneous/unpack.m,
scripts/miscellaneous/ver.m, scripts/miscellaneous/what.m,
scripts/miscellaneous/xor.m, scripts/miscellaneous/zip.m,
scripts/optimization/fminbnd.m, scripts/optimization/sqp.m,
scripts/path/private/getsavepath.m, scripts/path/savepath.m,
scripts/pkg/pkg.m, scripts/pkg/private/installed_packages.m,
scripts/plot/draw/plotyy.m, scripts/plot/draw/polar.m,
scripts/plot/draw/private/__quiver__.m,
scripts/plot/draw/private/__scatter__.m,
scripts/plot/draw/private/__stem__.m, scripts/plot/draw/surface.m,
scripts/plot/draw/surfnorm.m, scripts/plot/util/copyobj.m,
scripts/plot/util/hgload.m, scripts/plot/util/hgsave.m,
scripts/plot/util/isprop.m, scripts/plot/util/linkprop.m,
scripts/plot/util/private/__go_draw_axes__.m, scripts/set/setdiff.m,
scripts/set/union.m, scripts/signal/periodogram.m,
scripts/sparse/eigs.m, scripts/sparse/ilu.m, scripts/sparse/qmr.m,
scripts/sparse/sprand.m, scripts/sparse/sprandn.m,
scripts/specfun/beta.m, scripts/specfun/ellipke.m,
scripts/specfun/isprime.m, scripts/statistics/base/lscov.m,
scripts/testfun/__run_test_suite__.m, scripts/testfun/test.m:
Strip trailing whitespace.
author | John W. Eaton <jwe@octave.org> |
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date | Tue, 20 Jan 2015 10:29:54 -0500 |
parents | 0e1f5a750d00 |
children | 5a59c0e1203d |
rev | line source |
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1 ## Copyright (C) 2007-2013 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} =} interp3 (@var{x}, @var{y}, @var{z}, @var{v}, @var{xi}, @var{yi}, @var{zi}) |
6702 | 21 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}, @var{xi}, @var{yi}, @var{zi}) |
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22 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}, @var{n}) |
6702 | 23 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}) |
24 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@dots{}, @var{method}) | |
25 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@dots{}, @var{method}, @var{extrapval}) | |
26 ## | |
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27 ## Three-dimensional interpolation. |
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28 ## |
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29 ## Interpolate reference data @var{x}, @var{y}, @var{z}, @var{v} to determine |
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30 ## @var{vi} at the coordinates @var{xi}, @var{yi}, @var{zi}. The reference |
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31 ## data @var{x}, @var{y}, @var{z} can be matrices, as returned by |
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32 ## @code{meshgrid}, in which case the sizes of |
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33 ## @var{x}, @var{y}, @var{z}, and @var{v} must be equal. If @var{x}, @var{y}, |
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34 ## @var{z} are vectors describing a cubic grid then |
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35 ## @code{length (@var{x}) == columns (@var{v})}, |
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36 ## @code{length (@var{y}) == rows (@var{v})}, |
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37 ## and @code{length (@var{z}) == size (@var{v}, 3)}. In either case the input |
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38 ## data must be strictly monotonic. |
6702 | 39 ## |
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40 ## If called without @var{x}, @var{y}, @var{z}, and just a single reference |
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41 ## data matrix @var{v}, the 3-D region |
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42 ## @code{@var{x} = 1:columns (@var{v}), @var{y} = 1:rows (@var{v}), |
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43 ## @var{z} = 1:size (@var{v}, 3)} is assumed. |
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44 ## This saves memory if the grid is regular and the distance between points is |
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45 ## not important. |
6702 | 46 ## |
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47 ## If called with a single reference data matrix @var{v} and a refinement |
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48 ## value @var{n}, then perform interpolation over a 3-D grid where each original |
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49 ## interval has been recursively subdivided @var{n} times. This results in |
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50 ## @code{2^@var{n}-1} additional points for every interval in the original |
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51 ## grid. If @var{n} is omitted a value of 1 is used. As an example, the |
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52 ## interval [0,1] with @code{@var{n}==2} results in a refined interval with |
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53 ## points at [0, 1/4, 1/2, 3/4, 1]. |
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54 ## |
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55 ## The interpolation @var{method} is one of: |
6702 | 56 ## |
57 ## @table @asis | |
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58 ## @item @qcode{"nearest"} |
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59 ## Return the nearest neighbor. |
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60 ## |
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61 ## @item @qcode{"linear"} (default) |
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62 ## Linear interpolation from nearest neighbors. |
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63 ## |
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64 ## @item @qcode{"pchip"} |
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65 ## Piecewise cubic Hermite interpolating polynomial---shape-preserving |
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66 ## interpolation with smooth first derivative (not implemented yet). |
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67 ## |
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68 ## @item @qcode{"cubic"} |
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69 ## Cubic interpolation (same as @qcode{"pchip"} [not implemented yet]). |
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70 ## |
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71 ## @item @qcode{"spline"} |
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72 ## Cubic spline interpolation---smooth first and second derivatives |
6702 | 73 ## throughout the curve. |
74 ## @end table | |
75 ## | |
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76 ## If @var{extrapval} is a number, then replace values beyond the endpoints |
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77 ## with that number. When unspecified, @var{extrapval} defaults to @code{NA}. |
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78 ## Note that if @var{extrapval} is used, @var{method} must be specified as well. |
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79 ## @seealso{interp1, interp2, interpn, meshgrid} |
6702 | 80 ## @end deftypefn |
81 | |
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82 ## FIXME: Need to validate N argument (maybe change interpn). |
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83 ## FIXME: Need to add support for 'pchip' method (maybe change interpn). |
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84 ## FIXME: Need to add support for "extrap" string value (maybe change interpn). |
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85 |
6702 | 86 function vi = interp3 (varargin) |
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87 |
6702 | 88 method = "linear"; |
6742 | 89 extrapval = NA; |
6702 | 90 nargs = nargin; |
91 | |
13151 | 92 if (nargin < 1 || ! isnumeric (varargin{1})) |
6702 | 93 print_usage (); |
94 endif | |
95 | |
7174 | 96 if (ischar (varargin{end})) |
97 method = varargin{end}; | |
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98 nargs--; |
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99 elseif (nargs > 1 && ischar (varargin{end-1})) |
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100 ## FIXME: No support for "extrap" string |
7174 | 101 if (! isnumeric (varargin{end}) || ! isscalar (varargin{end})) |
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102 error ("interp3: EXTRAPVAL must be a numeric scalar"); |
6702 | 103 endif |
7174 | 104 extrapval = varargin{end}; |
105 method = varargin{end-1}; | |
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106 nargs -= 2; |
6702 | 107 endif |
108 | |
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109 if (method(1) == "*") |
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110 warning ("interp3: ignoring unsupported '*' flag to METHOD"); |
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111 method(1) = []; |
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112 endif |
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113 |
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114 if (nargs < 3) |
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115 ## Calling form interp3 (v) OR interp3 (v, n) |
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118 error ("interp3: V must be a 3-D array of values"); |
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120 n = varargin(2:nargs); |
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121 v = permute (v, [2, 1, 3]); |
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122 vi = ipermute (interpn (v, n{:}, method, extrapval), [2, 1, 3]); |
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123 |
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124 elseif (nargs == 4 && ! isvector (varargin{1})) |
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125 ## Calling form interp3 (v, xi, yi, zi) |
7174 | 126 v = varargin{1}; |
6702 | 127 if (ndims (v) != 3) |
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128 error ("interp3: V must be a 3-D array of values"); |
6702 | 129 endif |
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130 xi = varargin(2:4); |
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131 if (any (! cellfun (@isvector, xi))) |
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132 ## Meshgridded values rather than vectors |
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133 if (! size_equal (xi{:})) |
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134 error ("interp3: XI, YI, and ZI dimensions must be equal"); |
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135 endif |
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136 for i = 1 : 3 |
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137 xi{i} = permute (xi{i}, [2, 1, 3]); |
6722 | 138 endfor |
139 endif | |
140 v = permute (v, [2, 1, 3]); | |
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141 vi = ipermute (interpn (v, xi{:}, method, extrapval), [2, 1, 3]); |
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142 |
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143 elseif (nargs == 7) |
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144 ## Calling form interp3 (x, y, z, v, xi, yi, zi) |
7174 | 145 v = varargin{4}; |
6702 | 146 if (ndims (v) != 3) |
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147 error ("interp3: V must be a 3-D array of values"); |
6702 | 148 endif |
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149 x = varargin(1:3); |
6722 | 150 if (any (! cellfun (@isvector, x))) |
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151 ## Meshgridded values rather than vectors |
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152 if (! size_equal (x{:}, v)) |
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153 error ("interp3: X, Y, Z, and V dimensions must be equal"); |
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154 endif |
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155 for i = 1 : 3 |
10549 | 156 x{i} = permute (x{i}, [2, 1, 3]); |
6722 | 157 endfor |
158 endif | |
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159 xi = varargin(5:7); |
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160 if (any (! cellfun (@isvector, xi))) |
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161 ## Meshgridded values rather than vectors |
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162 if (! size_equal (xi{:})) |
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163 error ("interp3: XI, YI, and ZI dimensions must be equal"); |
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164 endif |
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165 for i = 1 : 3 |
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166 xi{i} = permute (xi{i}, [2, 1, 3]); |
6722 | 167 endfor |
168 endif | |
169 v = permute (v, [2, 1, 3]); | |
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170 vi = ipermute (interpn (x{:}, v, xi{:}, method, extrapval), [2, 1, 3]); |
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171 |
6702 | 172 else |
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173 error ("interp3: wrong number or incorrectly formatted input arguments"); |
6702 | 174 endif |
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175 |
6702 | 176 endfunction |
177 | |
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178 |
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179 %% FIXME: Need some demo blocks here to show off the function like interp2.m. |
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180 |
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181 %!test # basic test |
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182 %! x = y = z = -1:1; y = y + 2; |
6702 | 183 %! f = @(x,y,z) x.^2 - y - z.^2; |
184 %! [xx, yy, zz] = meshgrid (x, y, z); | |
185 %! v = f (xx,yy,zz); | |
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186 %! xi = yi = zi = -1:0.5:1; yi = yi + 2.1; |
6702 | 187 %! [xxi, yyi, zzi] = meshgrid (xi, yi, zi); |
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188 %! vi = interp3 (x, y, z, v, xxi, yyi, zzi); |
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189 %! [xxi, yyi, zzi] = ndgrid (yi, xi, zi); |
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190 %! vi2 = interpn (y, x, z, v, xxi, yyi, zzi); |
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191 %! assert (vi, vi2, 10*eps); |
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192 |
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193 %!test # meshgridded xi, yi, zi |
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194 %! x = z = 1:2; y = 1:3; |
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195 %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; |
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196 %! xi = zi = .6:1.6; yi = 1; |
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197 %! [xxi3, yyi3, zzi3] = meshgrid (xi, yi, zi); |
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198 %! [xxi, yyi, zzi] = ndgrid (yi, xi, zi); |
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199 %! vi = interp3 (x, y, z, v, xxi3, yyi3, zzi3, "nearest"); |
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200 %! vi2 = interpn (y, x, z, v, xxi, yyi, zzi, "nearest"); |
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201 %! assert (vi, vi2); |
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202 |
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203 %!test # vector xi, yi, zi |
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204 %! x = z = 1:2; y = 1:3; |
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205 %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; |
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206 %! xi = zi = .6:1.6; yi = 1; |
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207 %! vi = interp3 (x, y, z, v, xi, yi, zi, "nearest"); |
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208 %! vi2 = interpn (y, x, z, v, yi, xi, zi,"nearest"); |
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209 %! assert (vi, vi2); |
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210 |
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211 %!test # vector xi+1 with extrap value |
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212 %! x = z = 1:2; y = 1:3; |
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213 %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; |
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214 %! xi = zi = .6:1.6; yi = 1; |
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215 %! vi = interp3 (x, y, z, v, xi+1, yi, zi, "nearest", 3); |
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216 %! vi2 = interpn (y, x, z, v, yi, xi+1, zi, "nearest", 3); |
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217 %! assert (vi, vi2); |
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218 |
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219 %!test # input value matrix--no x,y,z |
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220 %! x = z = 1:2; y = 1:3; |
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221 %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; |
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222 %! xi = zi = .6:1.6; yi = 1; |
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223 %! vi = interp3 (v, xi, yi, zi, "nearest"); |
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224 %! vi2 = interpn (v, yi, xi, zi,"nearest"); |
6702 | 225 %! assert (vi, vi2); |
13151 | 226 |
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227 %!test # input value matrix--no x,y,z, with extrap value |
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228 %! x = z = 1:2; y = 1:3; |
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229 %! v = ones ([3,2,2]); v(:,2,1) = [7;5;4]; v(:,1,2) = [2;3;5]; |
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230 %! xi = zi = .6:1.6; yi = 1; |
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231 %! vi = interp3 (v, xi, yi, zi, "nearest", 3); |
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232 %! vi2 = interpn (v, yi, xi, zi, "nearest", 3); |
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233 %! assert (vi, vi2); |
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234 |
13151 | 235 %!shared z, zout, tol |
236 %! z = zeros (3, 3, 3); | |
237 %! zout = zeros (5, 5, 5); | |
238 %! z(:,:,1) = [1 3 5; 3 5 7; 5 7 9]; | |
239 %! z(:,:,2) = z(:,:,1) + 2; | |
240 %! z(:,:,3) = z(:,:,2) + 2; | |
241 %! for n = 1:5 | |
242 %! zout(:,:,n) = [1 2 3 4 5; | |
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243 %! 2 3 4 5 6; |
13151 | 244 %! 3 4 5 6 7; |
245 %! 4 5 6 7 8; | |
246 %! 5 6 7 8 9] + (n-1); | |
247 %! end | |
248 %! tol = 10 * eps; | |
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249 %! |
13151 | 250 %!assert (interp3 (z), zout, tol) |
251 %!assert (interp3 (z, "linear"), zout, tol) | |
252 %!assert (interp3 (z, "spline"), zout, tol) | |
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253 |
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254 %% Test input validation |
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255 %!error interp3 () |
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256 %!error interp3 ({1}) |
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257 %!error <EXTRAPVAL must be a numeric scalar> interp3 (1,2,3,4,1,2,3,"linear", {1}) |
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258 %!error <EXTRAPVAL must be a numeric scalar> interp3 (1,2,3,4,1,2,3,"linear", ones (2,2)) |
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259 %!warning <ignoring unsupported '\*' flag> interp3 (rand (3,3,3), 1, "*linear"); |
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260 %!error <V must be a 3-D array> interp3 (rand (2,2)) |
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261 %!error <V must be a 3-D array> interp3 (rand (2,2), 1,1,1) |
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262 %!error <XI, YI, and ZI dimensions must be equal> interp3 (rand (2,2,2), 1,1, ones (2,2)) |
0ede4dbb37f1
Overhaul interp1, interp2, interp3 functions.
Rik <rik@octave.org>
parents:
18722
diff
changeset
|
263 %!error <V must be a 3-D array> interp3 (1:2, 1:2, 1:2, rand (2,2), 1,1,1) |
0ede4dbb37f1
Overhaul interp1, interp2, interp3 functions.
Rik <rik@octave.org>
parents:
18722
diff
changeset
|
264 %!error <X, Y, Z, and V dimensions must be equal> interp3 (ones(1,2,2), ones(2,2,2), ones(2,2,2), rand (2,2,2), 1,1,1) |
0ede4dbb37f1
Overhaul interp1, interp2, interp3 functions.
Rik <rik@octave.org>
parents:
18722
diff
changeset
|
265 %!error <XI, YI, and ZI dimensions must be equal> interp3 (1:2, 1:2, 1:2, rand (2,2,2), 1,1, ones (2,2)) |
0ede4dbb37f1
Overhaul interp1, interp2, interp3 functions.
Rik <rik@octave.org>
parents:
18722
diff
changeset
|
266 |