Mercurial > hg > octave-lyh
annotate scripts/general/interp2.m @ 15466:d174210ce1ec stable
use ' instead of ` in error messages, warnings and most comments
* intro.txi, io.txi, munge-texi.cc, octave.texi, cmd-edit.cc,
data-conv.cc, file-ops.cc, glob-match.h, kpse.cc, oct-env.cc,
oct-locbuf.h, oct-md5.cc, oct-rand.cc, general/interp2.m, doc.m,
get_first_help_sentence.m, help.m, print_usage.m,
__additional_help_message__.m, type.m, unimplemented.m, which.m,
cast.m, dir.m, license.m, mkoctfile.m, recycle.m, tempdir.m,
optimset.m, pkg/pkg.m, closereq.m, colstyle.m, __fltk_print__.m,
__gnuplot_print__.m, __go_draw_figure__.m, __pie__.m, __pltopt__.m,
__print_parse_opts__.m, uigetdir.m, uigetfile.m, uiputfile.m, stft.m,
mean.m, anova.m, cor_test.m, t_test_regression.m, __magick_read__.cc,
dlmread.cc, schur.cc, data.cc, debug.cc, defun-dld.h, defun.cc,
defun.h, dynamic-ld.cc, error.cc, error.h, gl-render.cc, graphics.cc,
gripes.cc, input.cc, lex.ll, load-path.cc, load-save.cc, ls-hdf5.cc,
ls-mat-ascii.cc, ls-mat4.cc, ls-mat5.cc, ls-oct-ascii.cc,
ls-oct-binary.cc, oct-hist.cc, oct-parse.yy, oct-stream.cc,
oct-stream.h, octave.cc, ov-base-diag.cc, ov-base.cc, ov-class.cc,
ov-colon.h, ov-struct.cc, ov-typeinfo.cc, ov.cc, pager.cc,
pr-output.cc, pt-binop.cc, pt-eval.cc, pt-id.cc, pt-idx.cc,
pt-misc.cc, pt-unop.cc, symtab.cc, symtab.h, toplev.cc, txt-eng-ft.cc,
utils.cc, variables.cc, test_eval-catch.m, test_try.m:
Use ' instead of ` in error messages, warnings, and most comments.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 01 Oct 2012 17:18:49 -0400 |
| parents | 72c96de7a403 |
| children | 049e8bbff782 |
| rev | line source |
|---|---|
|
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1 ## Copyright (C) 2000-2012 Kai Habel |
| 8920 | 2 ## Copyright (C) 2009 Jaroslav Hajek |
| 5837 | 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. | |
| 5837 | 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/>. | |
| 5837 | 19 |
| 20 ## -*- texinfo -*- | |
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21 ## @deftypefn {Function File} {@var{zi} =} interp2 (@var{x}, @var{y}, @var{z}, @var{xi}, @var{yi}) |
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22 ## @deftypefnx {Function File} {@var{zi} =} interp2 (@var{Z}, @var{xi}, @var{yi}) |
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23 ## @deftypefnx {Function File} {@var{zi} =} interp2 (@var{Z}, @var{n}) |
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24 ## @deftypefnx {Function File} {@var{zi} =} interp2 (@dots{}, @var{method}) |
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25 ## @deftypefnx {Function File} {@var{zi} =} interp2 (@dots{}, @var{method}, @var{extrapval}) |
| 5837 | 26 ## |
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27 ## Two-dimensional interpolation. @var{x}, @var{y} and @var{z} describe a |
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28 ## surface function. If @var{x} and @var{y} are vectors their length |
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29 ## must correspondent to the size of @var{z}. @var{x} and @var{y} must be |
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30 ## monotonic. If they are matrices they must have the @code{meshgrid} |
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31 ## format. |
| 5837 | 32 ## |
| 33 ## @table @code | |
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34 ## @item interp2 (@var{x}, @var{y}, @var{Z}, @var{xi}, @var{yi}, @dots{}) |
| 5837 | 35 ## Returns a matrix corresponding to the points described by the |
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36 ## matrices @var{xi}, @var{yi}. |
| 5837 | 37 ## |
| 38 ## If the last argument is a string, the interpolation method can | |
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39 ## be specified. The method can be 'linear', 'nearest' or 'cubic'. |
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40 ## If it is omitted 'linear' interpolation is assumed. |
| 5837 | 41 ## |
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42 ## @item interp2 (@var{z}, @var{xi}, @var{yi}) |
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43 ## Assumes @code{@var{x} = 1:rows (@var{z})} and @code{@var{y} = |
| 5837 | 44 ## 1:columns (@var{z})} |
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45 ## |
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46 ## @item interp2 (@var{z}, @var{n}) |
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47 ## Interleaves the matrix @var{z} n-times. If @var{n} is omitted a value |
| 5837 | 48 ## of @code{@var{n} = 1} is assumed. |
| 49 ## @end table | |
| 50 ## | |
| 51 ## The variable @var{method} defines the method to use for the | |
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52 ## interpolation. It can take one of the following values |
| 5837 | 53 ## |
| 54 ## @table @asis | |
| 55 ## @item 'nearest' | |
| 6218 | 56 ## Return the nearest neighbor. |
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57 ## |
| 5837 | 58 ## @item 'linear' |
| 6218 | 59 ## Linear interpolation from nearest neighbors. |
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60 ## |
| 5837 | 61 ## @item 'pchip' |
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62 ## Piecewise cubic Hermite interpolating polynomial. |
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63 ## |
| 5837 | 64 ## @item 'cubic' |
| 6218 | 65 ## Cubic interpolation from four nearest neighbors. |
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66 ## |
| 5837 | 67 ## @item 'spline' |
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68 ## Cubic spline interpolation---smooth first and second derivatives |
| 6702 | 69 ## throughout the curve. |
| 5837 | 70 ## @end table |
| 71 ## | |
| 72 ## If a scalar value @var{extrapval} is defined as the final value, then | |
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73 ## values outside the mesh as set to this value. Note that in this case |
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74 ## @var{method} must be defined as well. If @var{extrapval} is not |
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75 ## defined then NA is assumed. |
| 5837 | 76 ## |
| 77 ## @seealso{interp1} | |
| 78 ## @end deftypefn | |
| 79 | |
| 10549 | 80 ## Author: Kai Habel <kai.habel@gmx.de> |
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81 ## 2005-03-02 Thomas Weber <weber@num.uni-sb.de> |
| 5837 | 82 ## * Add test cases |
| 83 ## 2005-03-02 Paul Kienzle <pkienzle@users.sf.net> | |
| 84 ## * Simplify | |
| 85 ## 2005-04-23 Dmitri A. Sergatskov <dasergatskov@gmail.com> | |
| 86 ## * Modified demo and test for new gnuplot interface | |
| 87 ## 2005-09-07 Hoxide <hoxide_dirac@yahoo.com.cn> | |
| 88 ## * Add bicubic interpolation method | |
| 5838 | 89 ## * Fix the eat line bug when the last element of XI or YI is |
| 90 ## negative or zero. | |
| 5837 | 91 ## 2005-11-26 Pierre Baldensperger <balden@libertysurf.fr> |
| 92 ## * Rather big modification (XI,YI no longer need to be | |
| 93 ## "meshgridded") to be consistent with the help message | |
| 94 ## above and for compatibility. | |
| 95 | |
| 96 function ZI = interp2 (varargin) | |
| 5838 | 97 Z = X = Y = XI = YI = n = []; |
| 5837 | 98 method = "linear"; |
| 6742 | 99 extrapval = NA; |
| 5837 | 100 |
| 5838 | 101 switch (nargin) |
| 102 case 1 | |
| 103 Z = varargin{1}; | |
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104 n = 1; |
| 5838 | 105 case 2 |
| 106 if (ischar (varargin{2})) | |
| 10549 | 107 [Z, method] = deal (varargin{:}); |
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108 n = 1; |
| 5838 | 109 else |
| 10549 | 110 [Z, n] = deal (varargin{:}); |
| 5838 | 111 endif |
| 112 case 3 | |
| 113 if (ischar (varargin{3})) | |
| 10549 | 114 [Z, n, method] = deal (varargin{:}); |
| 5838 | 115 else |
| 10549 | 116 [Z, XI, YI] = deal (varargin{:}); |
| 5838 | 117 endif |
| 118 case 4 | |
| 119 if (ischar (varargin{4})) | |
| 10549 | 120 [Z, XI, YI, method] = deal (varargin{:}); |
| 5838 | 121 else |
| 10549 | 122 [Z, n, method, extrapval] = deal (varargin{:}); |
| 5838 | 123 endif |
| 124 case 5 | |
| 125 if (ischar (varargin{4})) | |
| 10549 | 126 [Z, XI, YI, method, extrapval] = deal (varargin{:}); |
| 5838 | 127 else |
| 10549 | 128 [X, Y, Z, XI, YI] = deal (varargin{:}); |
| 5838 | 129 endif |
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130 case 6 |
| 10549 | 131 [X, Y, Z, XI, YI, method] = deal (varargin{:}); |
| 5838 | 132 case 7 |
| 10549 | 133 [X, Y, Z, XI, YI, method, extrapval] = deal (varargin{:}); |
| 5838 | 134 otherwise |
| 135 print_usage (); | |
| 5837 | 136 endswitch |
| 137 | |
| 138 ## Type checking. | |
| 5838 | 139 if (!ismatrix (Z)) |
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140 error ("interp2: Z must be a matrix"); |
| 5837 | 141 endif |
| 5838 | 142 if (!isempty (n) && !isscalar (n)) |
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143 error ("interp2: N must be a scalar"); |
| 5837 | 144 endif |
| 5838 | 145 if (!ischar (method)) |
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146 error ("interp2: METHOD must be a string"); |
| 5837 | 147 endif |
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148 if (ischar (extrapval) || strcmp (extrapval, "extrap")) |
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149 extrapval = []; |
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150 elseif (!isscalar (extrapval)) |
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151 error ("interp2: EXTRAPVAL must be a scalar"); |
| 5837 | 152 endif |
| 153 | |
| 5838 | 154 ## Define X, Y, XI, YI if needed |
| 5837 | 155 [zr, zc] = size (Z); |
| 5838 | 156 if (isempty (X)) |
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157 X = 1:zc; |
| 5838 | 158 Y = 1:zr; |
| 5837 | 159 endif |
| 5838 | 160 if (! isnumeric (X) || ! isnumeric (Y)) |
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161 error ("interp2: X, Y must be numeric matrices"); |
| 5837 | 162 endif |
| 5838 | 163 if (! isempty (n)) |
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164 ## Calculate the interleaved input vectors. |
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165 p = 2^n; |
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166 XI = (p:p*zc)/p; |
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167 YI = (p:p*zr)'/p; |
| 5837 | 168 endif |
| 5838 | 169 if (! isnumeric (XI) || ! isnumeric (YI)) |
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170 error ("interp2: XI, YI must be numeric"); |
| 5837 | 171 endif |
| 172 | |
| 6702 | 173 |
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174 if (strcmp (method, "linear") || strcmp (method, "nearest") ... |
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175 || strcmp (method, "pchip")) |
| 6702 | 176 |
| 177 ## If X and Y vectors produce a grid from them | |
| 178 if (isvector (X) && isvector (Y)) | |
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179 X = X(:); Y = Y(:); |
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180 elseif (size_equal (X, Y)) |
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181 X = X(1,:)'; Y = Y(:,1); |
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182 else |
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183 error ("interp2: X and Y must be matrices of same size"); |
| 6702 | 184 endif |
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185 if (columns (Z) != length (X) || rows (Z) != length (Y)) |
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186 error ("interp2: X and Y size must match the dimensions of Z"); |
| 6702 | 187 endif |
| 188 | |
| 189 ## If Xi and Yi are vectors of different orientation build a grid | |
| 190 if ((rows (XI) == 1 && columns (YI) == 1) | |
| 10549 | 191 || (columns (XI) == 1 && rows (YI) == 1)) |
| 6702 | 192 [XI, YI] = meshgrid (XI, YI); |
| 193 elseif (! size_equal (XI, YI)) | |
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194 error ("interp2: XI and YI must be matrices of equal size"); |
| 6702 | 195 endif |
| 5837 | 196 |
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197 ## if XI, YI are vectors, X and Y should share their orientation. |
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198 if (rows (XI) == 1) |
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199 if (rows (X) != 1) |
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200 X = X.'; |
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201 endif |
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202 if (rows (Y) != 1) |
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203 Y = Y.'; |
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204 endif |
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205 elseif (columns (XI) == 1) |
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206 if (columns (X) != 1) |
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207 X = X.'; |
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208 endif |
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209 if (columns (Y) != 1) |
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210 Y = Y.'; |
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211 endif |
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212 endif |
| 6702 | 213 |
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214 xidx = lookup (X, XI, "lr"); |
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215 yidx = lookup (Y, YI, "lr"); |
| 5837 | 216 |
| 6702 | 217 if (strcmp (method, "linear")) |
| 218 ## each quad satisfies the equation z(x,y)=a+b*x+c*y+d*xy | |
| 219 ## | |
| 220 ## a-b | |
| 221 ## | | | |
| 222 ## c-d | |
| 223 a = Z(1:(zr - 1), 1:(zc - 1)); | |
| 224 b = Z(1:(zr - 1), 2:zc) - a; | |
| 225 c = Z(2:zr, 1:(zc - 1)) - a; | |
| 226 d = Z(2:zr, 2:zc) - a - b - c; | |
| 5837 | 227 |
| 6702 | 228 ## scale XI, YI values to a 1-spaced grid |
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229 Xsc = (XI - X(xidx)) ./ (diff (X)(xidx)); |
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230 Ysc = (YI - Y(yidx)) ./ (diff (Y)(yidx)); |
| 6702 | 231 |
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232 ## Get 2D index. |
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233 idx = sub2ind (size (a), yidx, xidx); |
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234 ## We can dispose of the 1D indices at this point to save memory. |
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235 clear xidx yidx; |
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236 |
| 6702 | 237 ## apply plane equation |
| 238 ZI = a(idx) + b(idx).*Xsc + c(idx).*Ysc + d(idx).*Xsc.*Ysc; | |
| 5837 | 239 |
| 6702 | 240 elseif (strcmp (method, "nearest")) |
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241 ii = (XI - X(xidx) >= X(xidx + 1) - XI); |
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242 jj = (YI - Y(yidx) >= Y(yidx + 1) - YI); |
| 6702 | 243 idx = sub2ind (size (Z), yidx+jj, xidx+ii); |
| 244 ZI = Z(idx); | |
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245 |
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246 elseif (strcmp (method, "pchip")) |
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247 |
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248 if (length (X) < 2 || length (Y) < 2) |
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249 error ("interp2: pchip2 requires at least 2 points in each dimension"); |
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250 endif |
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251 |
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252 ## first order derivatives |
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253 DX = __pchip_deriv__ (X, Z, 2); |
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254 DY = __pchip_deriv__ (Y, Z, 1); |
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255 ## Compute mixed derivatives row-wise and column-wise, use the average. |
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256 DXY = (__pchip_deriv__ (X, DY, 2) + __pchip_deriv__ (Y, DX, 1))/2; |
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257 |
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258 ## do the bicubic interpolation |
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259 hx = diff (X); hx = hx(xidx); |
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260 hy = diff (Y); hy = hy(yidx); |
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261 |
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262 tx = (XI - X(xidx)) ./ hx; |
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263 ty = (YI - Y(yidx)) ./ hy; |
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264 |
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265 ## construct the cubic hermite base functions in x, y |
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266 |
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267 ## formulas: |
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268 ## b{1,1} = ( 2*t.^3 - 3*t.^2 + 1); |
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269 ## b{2,1} = h.*( t.^3 - 2*t.^2 + t ); |
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270 ## b{1,2} = (-2*t.^3 + 3*t.^2 ); |
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271 ## b{2,2} = h.*( t.^3 - t.^2 ); |
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272 |
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273 ## optimized equivalents of the above: |
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274 t1 = tx.^2; |
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275 t2 = tx.*t1 - t1; |
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276 xb{2,2} = hx.*t2; |
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277 t1 = t2 - t1; |
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278 xb{2,1} = hx.*(t1 + tx); |
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279 t2 += t1; |
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280 xb{1,2} = -t2; |
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281 xb{1,1} = t2 + 1; |
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282 |
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283 t1 = ty.^2; |
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284 t2 = ty.*t1 - t1; |
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285 yb{2,2} = hy.*t2; |
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286 t1 = t2 - t1; |
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287 yb{2,1} = hy.*(t1 + ty); |
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288 t2 += t1; |
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289 yb{1,2} = -t2; |
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290 yb{1,1} = t2 + 1; |
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291 |
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292 ZI = zeros (size (XI)); |
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293 for i = 1:2 |
| 10549 | 294 for j = 1:2 |
| 295 zidx = sub2ind (size (Z), yidx+(j-1), xidx+(i-1)); | |
| 296 ZI += xb{1,i} .* yb{1,j} .* Z(zidx); | |
| 297 ZI += xb{2,i} .* yb{1,j} .* DX(zidx); | |
| 298 ZI += xb{1,i} .* yb{2,j} .* DY(zidx); | |
| 299 ZI += xb{2,i} .* yb{2,j} .* DXY(zidx); | |
| 300 endfor | |
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301 endfor |
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302 |
| 6702 | 303 endif |
| 5837 | 304 |
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305 if (! isempty (extrapval)) |
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306 ## set points outside the table to 'extrapval' |
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307 if (X (1) < X (end)) |
| 10549 | 308 if (Y (1) < Y (end)) |
| 309 ZI (XI < X(1,1) | XI > X(end) | YI < Y(1,1) | YI > Y(end)) = ... | |
| 310 extrapval; | |
| 311 else | |
| 312 ZI (XI < X(1) | XI > X(end) | YI < Y(end) | YI > Y(1)) = ... | |
| 313 extrapval; | |
| 314 endif | |
| 6979 | 315 else |
| 10549 | 316 if (Y (1) < Y (end)) |
| 317 ZI (XI < X(end) | XI > X(1) | YI < Y(1) | YI > Y(end)) = ... | |
| 318 extrapval; | |
| 319 else | |
| 320 ZI (XI < X(1,end) | XI > X(1) | YI < Y(end) | YI > Y(1)) = ... | |
| 321 extrapval; | |
| 322 endif | |
| 6979 | 323 endif |
| 324 endif | |
| 325 | |
| 6702 | 326 else |
| 5837 | 327 |
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328 ## Check dimensions of X and Y |
| 6702 | 329 if (isvector (X) && isvector (Y)) |
| 330 X = X(:).'; | |
| 331 Y = Y(:); | |
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332 if (!isequal ([length(Y), length(X)], size(Z))) |
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333 error ("interp2: X and Y size must match the dimensions of Z"); |
| 6702 | 334 endif |
| 335 elseif (!size_equal (X, Y)) | |
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336 error ("interp2: X and Y must be matrices of equal size"); |
| 6702 | 337 if (! size_equal (X, Z)) |
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338 error ("interp2: X and Y size must match the dimensions of Z"); |
| 6702 | 339 endif |
| 340 endif | |
| 5837 | 341 |
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342 ## Check dimensions of XI and YI |
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343 if (isvector (XI) && isvector (YI) && ! size_equal (XI, YI)) |
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344 XI = XI(:).'; |
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345 YI = YI(:); |
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346 [XI, YI] = meshgrid (XI, YI); |
| 6702 | 347 elseif (! size_equal (XI, YI)) |
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348 error ("interp2: XI and YI must be matrices of equal size"); |
| 6702 | 349 endif |
| 5837 | 350 |
| 6702 | 351 if (strcmp (method, "cubic")) |
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352 if (isgriddata (XI) && isgriddata (YI')) |
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353 ZI = bicubic (X, Y, Z, XI (1, :), YI (:, 1), extrapval); |
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354 elseif (isgriddata (X) && isgriddata (Y')) |
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355 ## Allocate output |
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356 ZI = zeros (size (X)); |
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357 |
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358 ## Find inliers |
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359 inside = !(XI < X (1) | XI > X (end) | YI < Y (1) | YI > Y (end)); |
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360 |
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361 ## Scale XI and YI to match indices of Z |
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362 XI = (columns (Z) - 1) * (XI - X (1)) / (X (end) - X (1)) + 1; |
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363 YI = (rows (Z) - 1) * (YI - Y (1)) / (Y (end) - Y (1)) + 1; |
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364 |
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365 ## Start the real work |
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366 K = floor (XI); |
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367 L = floor (YI); |
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368 |
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369 ## Coefficients |
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370 AY1 = bc ((YI - L + 1)); |
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371 AX1 = bc ((XI - K + 1)); |
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372 AY0 = bc ((YI - L + 0)); |
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373 AX0 = bc ((XI - K + 0)); |
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374 AY_1 = bc ((YI - L - 1)); |
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375 AX_1 = bc ((XI - K - 1)); |
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376 AY_2 = bc ((YI - L - 2)); |
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377 AX_2 = bc ((XI - K - 2)); |
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378 |
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379 ## Perform interpolation |
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380 sz = size(Z); |
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381 ZI = AY_2 .* AX_2 .* Z (sym_sub2ind (sz, L+2, K+2)) ... |
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382 + AY_2 .* AX_1 .* Z (sym_sub2ind (sz, L+2, K+1)) ... |
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383 + AY_2 .* AX0 .* Z (sym_sub2ind (sz, L+2, K)) ... |
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384 + AY_2 .* AX1 .* Z (sym_sub2ind (sz, L+2, K-1)) ... |
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385 + AY_1 .* AX_2 .* Z (sym_sub2ind (sz, L+1, K+2)) ... |
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386 + AY_1 .* AX_1 .* Z (sym_sub2ind (sz, L+1, K+1)) ... |
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387 + AY_1 .* AX0 .* Z (sym_sub2ind (sz, L+1, K)) ... |
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388 + AY_1 .* AX1 .* Z (sym_sub2ind (sz, L+1, K-1)) ... |
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389 + AY0 .* AX_2 .* Z (sym_sub2ind (sz, L, K+2)) ... |
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390 + AY0 .* AX_1 .* Z (sym_sub2ind (sz, L, K+1)) ... |
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391 + AY0 .* AX0 .* Z (sym_sub2ind (sz, L, K)) ... |
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392 + AY0 .* AX1 .* Z (sym_sub2ind (sz, L, K-1)) ... |
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393 + AY1 .* AX_2 .* Z (sym_sub2ind (sz, L-1, K+2)) ... |
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394 + AY1 .* AX_1 .* Z (sym_sub2ind (sz, L-1, K+1)) ... |
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395 + AY1 .* AX0 .* Z (sym_sub2ind (sz, L-1, K)) ... |
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396 + AY1 .* AX1 .* Z (sym_sub2ind (sz, L-1, K-1)); |
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397 ZI (!inside) = extrapval; |
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398 |
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399 else |
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400 error ("interp2: input data must have 'meshgrid' format"); |
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401 endif |
| 5837 | 402 |
| 6702 | 403 elseif (strcmp (method, "spline")) |
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404 if (isgriddata (XI) && isgriddata (YI')) |
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405 ZI = __splinen__ ({Y(:,1).', X(1,:)}, Z, {YI(:,1), XI(1,:)}, extrapval, |
| 10549 | 406 "spline"); |
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407 else |
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408 error ("interp2: input data must have 'meshgrid' format"); |
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409 endif |
| 6702 | 410 else |
|
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411 error ("interp2: interpolation METHOD not recognized"); |
| 6702 | 412 endif |
| 5837 | 413 |
| 6702 | 414 endif |
| 5837 | 415 endfunction |
| 416 | |
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417 function b = isgriddata (X) |
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418 d1 = diff (X, 1, 1); |
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419 b = all (d1 (:) == 0); |
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420 endfunction |
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421 |
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422 ## Compute the bicubic interpolation coefficients |
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423 function o = bc(x) |
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424 x = abs(x); |
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425 o = zeros(size(x)); |
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426 idx1 = (x < 1); |
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427 idx2 = !idx1 & (x < 2); |
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428 o(idx1) = 1 - 2.*x(idx1).^2 + x(idx1).^3; |
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429 o(idx2) = 4 - 8.*x(idx2) + 5.*x(idx2).^2 - x(idx2).^3; |
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430 endfunction |
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431 |
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432 ## This version of sub2ind behaves as if the data was symmetrically padded |
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433 function ind = sym_sub2ind(sz, Y, X) |
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434 Y (Y < 1) = 1 - Y (Y < 1); |
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435 while (any (Y (:) > 2 * sz (1))) |
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436 Y (Y > 2 * sz (1)) = round (Y (Y > 2 * sz (1)) / 2); |
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437 endwhile |
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438 Y (Y > sz (1)) = 1 + 2 * sz (1) - Y (Y > sz (1)); |
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439 X (X < 1) = 1 - X (X < 1); |
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440 while (any (X (:) > 2 * sz (2))) |
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441 X (X > 2 * sz (2)) = round (X (X > 2 * sz (2)) / 2); |
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442 endwhile |
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443 X (X > sz (2)) = 1 + 2 * sz (2) - X (X > sz (2)); |
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444 ind = sub2ind(sz, Y, X); |
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445 endfunction |
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446 |
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447 |
| 5837 | 448 %!demo |
| 449 %! A=[13,-1,12;5,4,3;1,6,2]; | |
| 450 %! x=[0,1,4]; y=[10,11,12]; | |
| 451 %! xi=linspace(min(x),max(x),17); | |
| 452 %! yi=linspace(min(y),max(y),26)'; | |
| 453 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'linear')); | |
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454 %! [x,y] = meshgrid(x,y); |
| 5837 | 455 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
| 456 | |
| 457 %!demo | |
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458 %! [x,y,A] = peaks(10); |
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459 %! x = x(1,:)'; y = y(:,1); |
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460 %! xi=linspace(min(x),max(x),41); |
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461 %! yi=linspace(min(y),max(y),41)'; |
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462 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'linear')); |
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463 %! [x,y] = meshgrid(x,y); |
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464 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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465 |
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466 %!demo |
| 5837 | 467 %! A=[13,-1,12;5,4,3;1,6,2]; |
| 468 %! x=[0,1,4]; y=[10,11,12]; | |
| 469 %! xi=linspace(min(x),max(x),17); | |
| 470 %! yi=linspace(min(y),max(y),26)'; | |
| 471 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'nearest')); | |
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472 %! [x,y] = meshgrid(x,y); |
| 5837 | 473 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
| 474 | |
| 6702 | 475 %!demo |
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476 %! [x,y,A] = peaks(10); |
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477 %! x = x(1,:)'; y = y(:,1); |
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478 %! xi=linspace(min(x),max(x),41); |
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479 %! yi=linspace(min(y),max(y),41)'; |
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480 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'nearest')); |
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481 %! [x,y] = meshgrid(x,y); |
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482 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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483 |
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484 %!demo |
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485 %! A=[13,-1,12;5,4,3;1,6,2]; |
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486 %! x=[0,1,2]; y=[10,11,12]; |
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487 %! xi=linspace(min(x),max(x),17); |
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488 %! yi=linspace(min(y),max(y),26)'; |
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489 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'pchip')); |
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490 %! [x,y] = meshgrid(x,y); |
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491 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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492 |
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493 %!demo |
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494 %! [x,y,A] = peaks(10); |
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495 %! x = x(1,:)'; y = y(:,1); |
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496 %! xi=linspace(min(x),max(x),41); |
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497 %! yi=linspace(min(y),max(y),41)'; |
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498 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'pchip')); |
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499 %! [x,y] = meshgrid(x,y); |
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500 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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501 |
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502 %!demo |
| 5837 | 503 %! A=[13,-1,12;5,4,3;1,6,2]; |
| 504 %! x=[0,1,2]; y=[10,11,12]; | |
| 505 %! xi=linspace(min(x),max(x),17); | |
| 6702 | 506 %! yi=linspace(min(y),max(y),26)'; |
| 5837 | 507 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'cubic')); |
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508 %! [x,y] = meshgrid(x,y); |
| 5837 | 509 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
| 510 | |
| 6702 | 511 %!demo |
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512 %! [x,y,A] = peaks(10); |
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513 %! x = x(1,:)'; y = y(:,1); |
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514 %! xi=linspace(min(x),max(x),41); |
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515 %! yi=linspace(min(y),max(y),41)'; |
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516 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'cubic')); |
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517 %! [x,y] = meshgrid(x,y); |
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518 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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519 |
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520 %!demo |
| 6702 | 521 %! A=[13,-1,12;5,4,3;1,6,2]; |
| 522 %! x=[0,1,2]; y=[10,11,12]; | |
| 523 %! xi=linspace(min(x),max(x),17); | |
| 524 %! yi=linspace(min(y),max(y),26)'; | |
| 525 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'spline')); | |
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526 %! [x,y] = meshgrid(x,y); |
| 6702 | 527 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
| 528 | |
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529 %!demo |
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530 %! [x,y,A] = peaks(10); |
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531 %! x = x(1,:)'; y = y(:,1); |
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532 %! xi=linspace(min(x),max(x),41); |
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533 %! yi=linspace(min(y),max(y),41)'; |
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534 %! mesh(xi,yi,interp2(x,y,A,xi,yi,'spline')); |
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535 %! [x,y] = meshgrid(x,y); |
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536 %! hold on; plot3(x(:),y(:),A(:),"b*"); hold off; |
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537 |
| 5837 | 538 %!test % simple test |
| 539 %! x = [1,2,3]; | |
| 540 %! y = [4,5,6,7]; | |
| 541 %! [X, Y] = meshgrid(x,y); | |
| 542 %! Orig = X.^2 + Y.^3; | |
| 543 %! xi = [1.2,2, 1.5]; | |
| 544 %! yi = [6.2, 4.0, 5.0]'; | |
| 545 %! | |
| 546 %! Expected = ... | |
| 547 %! [243, 245.4, 243.9; | |
| 548 %! 65.6, 68, 66.5; | |
| 549 %! 126.6, 129, 127.5]; | |
| 550 %! Result = interp2(x,y,Orig, xi, yi); | |
| 551 %! | |
| 552 %! assert(Result, Expected, 1000*eps); | |
| 553 | |
| 554 %!test % 2^n form | |
| 555 %! x = [1,2,3]; | |
| 556 %! y = [4,5,6,7]; | |
| 557 %! [X, Y] = meshgrid(x,y); | |
| 558 %! Orig = X.^2 + Y.^3; | |
| 559 %! xi = [1:0.25:3]; yi = [4:0.25:7]'; | |
| 560 %! Expected = interp2(x,y,Orig, xi, yi); | |
| 561 %! Result = interp2(Orig,2); | |
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562 %! |
| 5837 | 563 %! assert(Result, Expected, 10*eps); |
| 564 | |
| 565 %!test % matrix slice | |
| 566 %! A = eye(4); | |
| 567 %! assert(interp2(A,[1:4],[1:4]),[1,1,1,1]); | |
| 568 | |
| 569 %!test % non-gridded XI,YI | |
| 570 %! A = eye(4); | |
| 571 %! assert(interp2(A,[1,2;3,4],[1,3;2,4]),[1,0;0,1]); | |
| 572 | |
| 573 %!test % for values outside of boundaries | |
| 574 %! x = [1,2,3]; | |
| 575 %! y = [4,5,6,7]; | |
| 576 %! [X, Y] = meshgrid(x,y); | |
| 577 %! Orig = X.^2 + Y.^3; | |
| 578 %! xi = [0,4]; | |
| 579 %! yi = [3,8]'; | |
| 6742 | 580 %! assert(interp2(x,y,Orig, xi, yi),[NA,NA;NA,NA]); |
| 5837 | 581 %! assert(interp2(x,y,Orig, xi, yi,'linear', 0),[0,0;0,0]); |
| 582 | |
| 583 %!test % for values at boundaries | |
| 584 %! A=[1,2;3,4]; | |
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585 %! x=[0,1]; |
| 5837 | 586 %! y=[2,3]'; |
| 587 %! assert(interp2(x,y,A,x,y,'linear'), A); | |
| 588 %! assert(interp2(x,y,A,x,y,'nearest'), A); | |
| 589 | |
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590 %!test % for Matlab-compatible rounding for 'nearest' |
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591 %! X = meshgrid (1:4); |
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592 %! assert (interp2 (X, 2.5, 2.5, 'nearest'), 3); |
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593 |
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594 %!shared z, zout, tol |
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595 %! z = [1 3 5; 3 5 7; 5 7 9]; |
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596 %! zout = [1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8; 5 6 7 8 9]; |
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597 %! tol = 2 * eps; |
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598 %!assert (interp2 (z), zout, tol); |
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599 %!assert (interp2 (z, "linear"), zout, tol); |
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600 %!assert (interp2 (z, "pchip"), zout, tol); |
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601 %!assert (interp2 (z, "cubic"), zout, 10 * tol); |
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602 %!assert (interp2 (z, "spline"), zout, tol); |
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603 %!assert (interp2 (z, [2 3 1], [2 2 2]', "linear"), repmat ([5, 7, 3], [3, 1]), tol) |
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604 %!assert (interp2 (z, [2 3 1], [2 2 2]', "pchip"), repmat ([5, 7, 3], [3, 1]), tol) |
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605 %!assert (interp2 (z, [2 3 1], [2 2 2]', "cubic"), repmat ([5, 7, 3], [3, 1]), 10 * tol) |
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606 %!assert (interp2 (z, [2 3 1], [2 2 2]', "spline"), repmat ([5, 7, 3], [3, 1]), tol) |
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607 %!assert (interp2 (z, [2 3 1], [2 2 2], "linear"), [5 7 3], tol); |
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608 %!assert (interp2 (z, [2 3 1], [2 2 2], "pchip"), [5 7 3], tol); |
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609 %!assert (interp2 (z, [2 3 1], [2 2 2], "cubic"), [5 7 3], 10 * tol); |
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610 %!assert (interp2 (z, [2 3 1], [2 2 2], "spline"), [5 7 3], tol); |