Mercurial > octave-nkf
annotate scripts/general/interp3.m @ 14138:72c96de7a403 stable
maint: update copyright notices for 2012
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 02 Jan 2012 14:25:41 -0500 |
| parents | 25effffba9b0 |
| children | 7277fe922e99 |
| rev | line source |
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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} =} 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}) |
| 22 ## @deftypefnx {Function File} {@var{vi} =} interp3 (@var{v}, @var{m}) | |
| 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 ## Perform 3-dimensional interpolation. Each element of the 3-dimensional |
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28 ## array @var{v} represents a value at a location given by the parameters |
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29 ## @var{x}, @var{y}, and @var{z}. The parameters @var{x}, @var{x}, and |
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30 ## @var{z} are either 3-dimensional arrays of the same size as the array |
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31 ## @var{v} in the 'meshgrid' format or vectors. The parameters @var{xi}, etc. |
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32 ## respect a similar format to @var{x}, etc., and they represent the points |
| 6702 | 33 ## at which the array @var{vi} is interpolated. |
| 34 ## | |
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35 ## If @var{x}, @var{y}, @var{z} are omitted, they are assumed to be |
| 6702 | 36 ## @code{x = 1 : size (@var{v}, 2)}, @code{y = 1 : size (@var{v}, 1)} and |
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37 ## @code{z = 1 : size (@var{v}, 3)}. 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 ## | |
| 61 ## If @var{extrap} is the string 'extrap', then extrapolate values beyond | |
| 62 ## the endpoints. If @var{extrap} is a number, replace values beyond the | |
| 6742 | 63 ## endpoints with that number. If @var{extrap} is missing, assume NA. |
| 6702 | 64 ## @seealso{interp1, interp2, spline, meshgrid} |
| 65 ## @end deftypefn | |
| 66 | |
| 67 function vi = interp3 (varargin) | |
| 68 method = "linear"; | |
| 6742 | 69 extrapval = NA; |
| 6702 | 70 nargs = nargin; |
| 71 | |
| 13151 | 72 if (nargin < 1 || ! isnumeric (varargin{1})) |
| 6702 | 73 print_usage (); |
| 74 endif | |
| 75 | |
| 7174 | 76 if (ischar (varargin{end})) |
| 77 method = varargin{end}; | |
| 6702 | 78 nargs = nargs - 1; |
| 13151 | 79 elseif (nargs > 1 && ischar (varargin{end - 1})) |
| 7174 | 80 if (! isnumeric (varargin{end}) || ! isscalar (varargin{end})) |
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81 error ("interp3: extrapal is expected to be a numeric scalar"); |
| 6702 | 82 endif |
| 7174 | 83 extrapval = varargin{end}; |
| 84 method = varargin{end-1}; | |
| 6702 | 85 nargs = nargs - 2; |
| 86 endif | |
| 87 | |
| 7174 | 88 if (nargs < 3 || (nargs == 4 && ! isvector (varargin{1}) |
| 10549 | 89 && nargs == (ndims (varargin{1}) + 1))) |
| 7174 | 90 v = varargin{1}; |
| 6702 | 91 if (ndims (v) != 3) |
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92 error ("interp3: expect 3-dimensional array of values"); |
| 6702 | 93 endif |
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94 x = varargin (2:end); |
| 6722 | 95 if (any (! cellfun (@isvector, x))) |
| 96 for i = 2 : 3 | |
| 10549 | 97 if (! size_equal (x{1}, x{i})) |
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98 error ("interp3: dimensional mismatch"); |
| 10549 | 99 endif |
| 100 x{i} = permute (x{i}, [2, 1, 3]); | |
| 6722 | 101 endfor |
| 102 x{1} = permute (x{1}, [2, 1, 3]); | |
| 103 endif | |
| 104 v = permute (v, [2, 1, 3]); | |
| 105 vi = ipermute (interpn (v, x{:}, method, extrapval), [2, 1, 3]); | |
| 7174 | 106 elseif (nargs == 7 && nargs == (2 * ndims (varargin{ceil (nargs / 2)})) + 1) |
| 107 v = varargin{4}; | |
| 6702 | 108 if (ndims (v) != 3) |
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109 error ("interp3: expect 3-dimensional array of values"); |
| 6702 | 110 endif |
| 6722 | 111 x = varargin (1:3); |
| 112 if (any (! cellfun (@isvector, x))) | |
| 113 for i = 2 : 3 | |
| 10549 | 114 if (! size_equal (x{1}, x{i}) || ! size_equal (x{i}, v)) |
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115 error ("interp3: dimensional mismatch"); |
| 10549 | 116 endif |
| 117 x{i} = permute (x{i}, [2, 1, 3]); | |
| 6722 | 118 endfor |
| 119 x{1} = permute (x{1}, [2, 1, 3]); | |
| 120 endif | |
| 121 y = varargin (5:7); | |
| 122 if (any (! cellfun (@isvector, y))) | |
| 123 for i = 2 : 3 | |
| 10549 | 124 if (! size_equal (y{1}, y{i})) |
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125 error ("interp3: dimensional mismatch"); |
| 10549 | 126 endif |
| 127 y{i} = permute (y{i}, [2, 1, 3]); | |
| 6722 | 128 endfor |
| 129 y{1} = permute (y{1}, [2, 1, 3]); | |
| 130 endif | |
| 131 v = permute (v, [2, 1, 3]); | |
| 7174 | 132 vi = ipermute (interpn (x{:}, v, y{:}, method, extrapval), [2, 1, 3]); |
| 6702 | 133 else |
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134 error ("interp3: wrong number or incorrectly formatted input arguments"); |
| 6702 | 135 endif |
| 136 endfunction | |
| 137 | |
| 138 %!test | |
| 139 %! x = y = z = -1:1; | |
| 140 %! f = @(x,y,z) x.^2 - y - z.^2; | |
| 141 %! [xx, yy, zz] = meshgrid (x, y, z); | |
| 142 %! v = f (xx,yy,zz); | |
| 143 %! xi = yi = zi = -1:0.5:1; | |
| 144 %! [xxi, yyi, zzi] = meshgrid (xi, yi, zi); | |
| 145 %! vi = interp3(x, y, z, v, xxi, yyi, zzi); | |
| 146 %! [xxi, yyi, zzi] = ndgrid (xi, yi, zi); | |
| 147 %! vi2 = interpn(x, y, z, v, xxi, yyi, zzi); | |
| 148 %! assert (vi, vi2); | |
| 13151 | 149 |
| 150 %!shared z, zout, tol | |
| 151 %! z = zeros (3, 3, 3); | |
| 152 %! zout = zeros (5, 5, 5); | |
| 153 %! z(:,:,1) = [1 3 5; 3 5 7; 5 7 9]; | |
| 154 %! z(:,:,2) = z(:,:,1) + 2; | |
| 155 %! z(:,:,3) = z(:,:,2) + 2; | |
| 156 %! for n = 1:5 | |
| 157 %! zout(:,:,n) = [1 2 3 4 5; | |
| 158 %! 2 3 4 5 6; | |
| 159 %! 3 4 5 6 7; | |
| 160 %! 4 5 6 7 8; | |
| 161 %! 5 6 7 8 9] + (n-1); | |
| 162 %! end | |
| 163 %! tol = 10 * eps; | |
| 164 %!assert (interp3 (z), zout, tol) | |
| 165 %!assert (interp3 (z, "linear"), zout, tol) | |
| 166 %!assert (interp3 (z, "spline"), zout, tol) |